Documents published in 2020 : Scipedia

Combined molecular/continuum modeling reveals the role of friction during fast unfolding of coiled-coil proteins
A. Torres-Sánchez, J. Vanegas, P. Purohit, M. Arroyo

Soft Matter (2019). Vol. 15, pp. 4961-4975 (Preprint)

Abstract
Coiled-coils are filamentous proteins that form the basic building block of important force-bearing cellular elements, such as intermediate filaments and myosin motors. In addition to their biological importance, coiled-coil proteins are increasingly used in new biomaterials including fibers, nanotubes, or hydrogels. Coiled-coils undergo a structural transition from an a-helical coil to an unfolded state upon extension, which allows them to sustain large strains and is critical for their biological function. By performing equilibrium and out-of-equilibrium all-atom molecular dynamics (MD) simulations of coiledcoils in explicit solvent, we show that two-state models based on Kramers’ or Bell’s theories fail to predict the rate of unfolding at high pulling rates. We further show that an atomistically informed continuum rod model accounting for phase transformations and for the hydrodynamic interactions with the solvent can reconcile two-state models with our MD results. Our results show that frictional forces, usually neglected in theories of fibrous protein unfolding, reduce the thermodynamic force acting on the interface, and thus control the dynamics of unfolding at different pulling rates. Our results may help interpret MD simulations at high pulling rates, and could be pertinent to cytoskeletal networks or protein-based artificial materials subjected to shocks or blasts.
Abstract
Coiled-coils are filamentous proteins that form the basic building block of important force-bearing cellular elements, such as intermediate filaments and myosin motors. In [...]
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Swimming Euglena respond to confinement with a behavioural change enabling effective crawling
G. Noselli, A. Beran, M. Arroyo, A. DeSimone

Nature physics (2019). Vol. 15, pp. 496-502 (Preprint)

Abstract
Some euglenids, a family of aquatic unicellular organisms, can develop highly concerted, large-amplitude peristaltic body deformations. This remarkable behaviour has been known for centuries. Yet, its function remains controversial, and is even viewed as a functionless ancestral vestige. Here, by examining swimming Euglena¿gracilis in environments of controlled crowding and geometry, we show that this behaviour is triggered by confinement. Under these conditions, it allows cells to switch from unviable flagellar swimming to a new and highly robust mode of fast crawling, which can deal with extreme geometric confinement and turn both frictional and hydraulic resistance into propulsive forces. To understand how a single cell can control such an adaptable and robust mode of locomotion, we developed a computational model of the motile apparatus of Euglena cells consisting of an active striated cell envelope. Our modelling shows that gait adaptability does not require specific mechanosensitive feedback but instead can be explained by the mechanical self-regulation of an elastic and extended motor system. Our study thus identifies a locomotory function and the operating principles of the adaptable peristaltic body deformation of Euglena cells.
Abstract
Some euglenids, a family of aquatic unicellular organisms, can develop highly concerted, large-amplitude peristaltic body deformations. This remarkable behaviour has been [...]
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Smart helical structures inspired by the pellicle of euglenids
G. Noselli, M. Arroyo, A. DeSimone

Journal of the Mechanics and Physics of Solids (2019). Vol. 123, pp. 234-246 (Preprint)

Abstract
This paper deals with a concept for a reconfigurable structure bio-inspired by the cell wall architecture of euglenids, a family of unicellular protists, and based on the relative sliding of adjacent strips. Uniform sliding turns a cylinder resulting from the assembly of straight and parallel strips into a cylinder of smaller height and larger radius, in which the strips are deformed into a family of parallel helices. We examine the mechanics of this cylindrical assembly, in which the interlocking strips are allowed to slide freely at their junctions, and compute the external forces (axial force and axial torque at the two ends, or pressure on the lateral surface) necessary to drive and control the shape changes of the composite structure. Despite the simplicity of the structure, we find a remarkably complex mechanical behaviour that can be tuned by the spontaneous curvature or twist of the strips.
Abstract
This paper deals with a concept for a reconfigurable structure bio-inspired by the cell wall architecture of euglenids, a family of unicellular protists, and based on the [...]
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Active superelasticity in three-dimensional epithelia of controlled shape
E. Latorre, S. Kale, L. Casares, M. Gómez-González, M. Uroz, L. Valon, R. Nair, E. Garreta, N. Monstserrat, A. Campo, B. Ladoux, M. Arroyo, X. Trepat

Nature (2018). Vol. 563 (7730), pp. 203-208 (Preprint)

Abstract
Fundamental biological processes are carried out by curved epithelial sheets that enclose a pressurized lumen. How these sheets develop and withstand three-dimensional deformations has remained unclear. Here we combine measurements of epithelial tension and shape with theoretical modelling to show that epithelial sheets are active superelastic materials. We produce arrays of epithelial domes with controlled geometry. Quantification of luminal pressure and epithelial tension reveals a tensional plateau over several-fold areal strains. These extreme strains in the tissue are accommodated by highly heterogeneous strains at a cellular level, in seeming contradiction to the measured tensional uniformity. This phenomenon is reminiscent of superelasticity, a behaviour that is generally attributed to microscopic material instabilities in metal alloys. We show that in epithelial cells this instability is triggered by a stretch-induced dilution of the actin cortex, and is rescued by the intermediate filament network. Our study reveals a type of mechanical behaviour—which we term active superelasticity—that enables epithelial sheets to sustain extreme stretching under constant tension.
Abstract
Fundamental biological processes are carried out by curved epithelial sheets that enclose a pressurized lumen. How these sheets develop and withstand three-dimensional deformations [...]
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A variational model of fracture for tearing brittle thin sheets
B. Li, D. Millán, A. Torres-Sánchez, B. Roman, M. Arroyo

Journal of the Mechanics and Physics of Solids (2018). Vol. 119, pp. 334-348 (Preprint)

Abstract
Tearing of brittle thin elastic sheets, possibly adhered to a substrate, involves a rich interplay between nonlinear elasticity, geometry, adhesion, and fracture mechanics. In addition to its intrinsic and practical interest, tearing of thin sheets has helped elucidate fundamental aspects of fracture mechanics including the mechanism of crack path selection. A wealth of experimental observations in different experimental setups is available, which has been often rationalized with insightful yet simplified theoretical models based on energetic considerations. In contrast, no computational method has addressed tearing in brittle thin elastic sheets. Here, motivated by the variational nature of simplified models that successfully explain crack paths in tearing sheets, we present a variational phase-field model of fracture coupled to a nonlinear Koiter thin shell model including stretching and bending. We show that this general yet straightforward approach is able to reproduce the observed phenomenology, including spiral or power-law crack paths in free standing films, or converging/diverging cracks in thin films adhered to negatively/positively curved surfaces, a scenario not amenable to simple models. Turning to more quantitative experiments on thin sheets adhered to planar surfaces, our simulations allow us to examine the boundaries of existing theories and suggest that homogeneous damage induced by moving folds is responsible for a systematic discrepancy between theory and experiments. Thus, our computational approach to tearing provides a new tool to understand these complex processes involving fracture, geometric nonlinearity and delamination, complementing experiments and simplified theories.
Abstract
Tearing of brittle thin elastic sheets, possibly adhered to a substrate, involves a rich interplay between nonlinear elasticity, geometry, adhesion, and fracture mechanics. [...]
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Coexistence of wrinkles and blisters in supported graphene
K. Zang, M. Arroyo

Extreme Mechanics Letters (2017). Vol. 14, pp. 23-30 (Preprint)

Abstract
Blisters induced by gas trapped in the interstitial space between supported graphene and the substrate are commonly observed. These blisters are often quasi-spherical with a circular rim, but polygonal blisters are also common and coexist with wrinkles emanating from their vertices. Here, we show that these different blister morphologies can be understood mechanically in terms of free energy minimization of the supported graphene sheet for a given mass of trapped gas and for a given lateral strain. Using a nonlinear continuum model for supported graphene closely reproducing experimental images of blisters, we build a morphological diagram as a function of strain and trapped mass. We show that the transition from quasi-spherical to polygonal of blisters as compressive strain is increased is a process of stretching energy relaxation and focusing, as many other crumpling events in thin sheets. Furthermore, to characterize this transition, we theoretically examine the onset of nucleation of short wrinkles in the periphery of a quasi-spherical blister. Our results are experimentally testable and provide a framework to control complex out-of-plane motifs in supported graphene combining blisters and wrinkles for strain engineering of graphene.
Abstract
Blisters induced by gas trapped in the interstitial space between supported graphene and the substrate are commonly observed. These blisters are often quasi-spherical with [...]
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Hydraulic fracturing in cells and tissues: fracking meets cell biology
M. Arroyo, X. Trepat

Current opinion in cell biology (2017). Vol. 44, pp. 1-6 (Preprint)

Abstract
The animal body is largely made of water. A small fraction of body water is freely flowing in blood and lymph, but most of it is trapped in hydrogels such as the extracellular matrix (ECM), the cytoskeleton, and chromatin. Besides providing a medium for biological molecules to diffuse, water trapped in hydrogels plays a fundamental mechanical role. This role is well captured by the theory of poroelasticity, which explains how any deformation applied to a hydrogel causes pressure gradients and water flows, much like compressing a sponge squeezes water out of it. Here we review recent evidence that poroelastic pressures and flows can fracture essential biological barriers such as the nuclear envelope, the cellular cortex, and epithelial layers. This type of fracture is known in engineering literature as hydraulic fracturing or ‘fracking’.
Abstract
The animal body is largely made of water. A small fraction of body water is freely flowing in blood and lymph, but most of it is trapped in hydrogels such as the extracellular [...]
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Sticking and sliding of lipid bilayers on deformable substrates
L. Stubbington, M. Arroyo, M. Staykova

Soft Matter (2017). Vol. 13 (1), pp. 181-186

Abstract
We examine here the properties of lipid bilayers coupled to deformable substrates. We show that by changing the extent of the substrate hydrophilicity, we can control the membrane–substrate coupling and the response of the bilayer to strain deformation. Our results demonstrate that lipid bilayers coupled to flexible substrates can easily accommodate large strains, form stable protrusions and open reversibly pores. These properties, which differ significantly from those of free standing membranes, can extend the applications of the current lipid technologies. Moreover, such systems better capture the mechanical architecture of the cell interface and can provide insights into the capacity of cells to reshape and respond to mechanical perturbations.
Abstract
We examine here the properties of lipid bilayers coupled to deformable substrates. We show that by changing the extent of the substrate hydrophilicity, we can control the [...]
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Fourth order phase-field model for local max-ent approximants applied to crack propagation
F. Amiri, D. Millán, M. Arroyo, M. Silani, T. Rabczuk

Comput. Methods Appl. Mech. Engrg., (2016). Vol. 312, pp. 254-275 (Preprint)

Abstract
We apply a fourth order phase-field model for fracture based on local maximum entropy (LME) approximants. The higher order continuity of the meshfree LME approximants allows to directly solve the fourth order phase-field equations without splitting the fourth order differential equation into two second order differential equations. We will first show that the crack surface can be captured more accurately in the fourth order model. Furthermore, less nodes are needed for the fourth order model to resolve the crack path. Finally, we demonstrate the performance of the proposed meshfree fourth order phase-field formulation for 5 representative numerical examples. Computational results will be compared to analytical solutions within linear elastic fracture mechanics and experimental data for three-dimensional crack propagation.
Abstract
We apply a fourth order phase-field model for fracture based on local maximum entropy (LME) approximants. The higher order continuity of the meshfree LME approximants allows [...]
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Charting molecular free-energy landscapes with an atlas of collective variables
B. Hashemian, D. Millán, M. Arroyo

Journal of chemical physics (2016). Vol. 145 (17), pp. 1-33 (Preprint)

Abstract
Collective variables (CVs) are a fundamental tool to understand molecular flexibility, to compute free energy landscapes, and to enhance sampling in molecular dynamics simulations. However, identifying suitable CVs is challenging, and is increasingly addressed with systematic data-driven manifold learning techniques. Here, we provide a flexible framework to model molecular systems in terms of a collection of locally valid and partially overlapping CVs: an atlas of CVs. The specific motivation for such a framework is to enhance the applicability and robustness of CVs based on manifold learning methods, which fail in the presence of periodicities in the underlying conformational manifold. More generally, using an atlas of CVs rather than a single chart may help us better describe different regions of conformational space. We develop the statistical mechanics foundation for our multi-chart description and propose an algorithmic implementation. The resulting atlas of data-based CVs are then used to enhance sampling and compute free energy surfaces in two model systems, alanine dipeptide and ß-D-glucopyranose, whose conformational manifolds have toroidal and spherical topologies.
Abstract
Collective variables (CVs) are a fundamental tool to understand molecular flexibility, to compute free energy landscapes, and to enhance sampling in molecular dynamics simulations. [...]
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Geometric derivation of the microscopic stress: a covariant central force decomposition
A. Torres-Sánchez, J. Vanegas, M. Arroyo

Journal of the Mechanics and Physics of Solids (2016). Vol. 93, pp. 224-239 (preprint)

Abstract
We revisit the derivation of the microscopic stress, linking the statistical mechanics of particle systems and continuum mechanics. The starting point in our geometric derivation is the Doyle-Ericksen formula, which states that the Cauchy stress tensor is the derivative of the free-energy with respect to the ambient metric tensor and which follows from a covariance argument. Thus, our approach to define the microscopic stress tensor does not rely on the statement of balance of linear momentum as in the classical Irving-Kirkwood-Noll approach. Nevertheless, the resulting stress tensor satisfies balance of linear and angular momentum. Furthermore, our approach removes the ambiguity in the definition of the microscopic stress in the presence of multibody interactions by naturally suggesting a canonical and physically motivated force decomposition into pairwise terms, a key ingredient in this theory. As a result, our approach provides objective expressions to compute a microscopic stress for a system in equilibrium and for force-fields expanded into multibody interactions of arbitrarily high order. We illustrate the proposed methodology with molecular dynamics simulations of a fibrous protein using a force-field involving up to 5-body interactions.
Abstract
We revisit the derivation of the microscopic stress, linking the statistical mechanics of particle systems and continuum mechanics. The starting point in our geometric derivation [...]
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Shape transformations of lipid bilayers following rapid cholesterol uptake
M. Rahimi, D. Regan, M. Arroyo, A. Subramaniam, H. Stone, M. Staykova

Biophysical journal (2016). Vol. 111 (12), pp. 2651-2657 (Preprint)

Abstract
High cholesterol levels in the blood increase the risk of atherosclerosis. A common explanation is that the cholesterol increase in the plasma membrane perturbs the shape and functions of cells by disrupting the cell signaling pathways and the formation of membrane rafts. In this work, we show that after enhanced transient uptake of cholesterol, mono-component lipid bilayers change their shape similarly to cell membranes in vivo. The bilayers either expel lipid protrusions or spread laterally as a result of the ensuing changes in their lipid density, the mechanical constraints imposed on them, and the properties of cyclodextrin used as a cholesterol donor. In light of the increasingly recognized link between membrane tension and cell behavior, we propose that the physical adaptation of the plasma membrane to cholesterol uptake may play a substantial role in the biological response.
Abstract
High cholesterol levels in the blood increase the risk of atherosclerosis. A common explanation is that the cholesterol increase in the plasma membrane perturbs the shape [...]
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Hydraulic fracture and toughening of a brittle layer bonded to a hydrogel
A. Lucantonio, G. Noselli, X. Trepat, A. DeSimone, M. Arroyo

Physical review letters (2015). Vol. 115 (18), pp. 188105-1/188105-5

Abstract
Brittle materials propagate opening cracks under tension. When stress increases beyond a critical magnitude, then quasistatic crack propagation becomes unstable. In the presence of several precracks, a brittle material always propagates only the weakest crack, leading to catastrophic failure. Here, we show that all these features of brittle fracture are fundamentally modified when the material susceptible to cracking is bonded to a hydrogel, a common situation in biological tissues. In the presence of the hydrogel, the brittle material can fracture in compression and can hydraulically resist cracking in tension. Furthermore, the poroelastic coupling regularizes the crack dynamics and enhances material toughness by promoting multiple cracking.
Abstract
Brittle materials propagate opening cracks under tension. When stress increases beyond a critical magnitude, then quasistatic crack propagation becomes unstable. In the presence [...]
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Fracture toughening and toughness asymmetry induced by flexoelectricity
A. Abdollahi, C. Peco, M. Arroyo, G. Catalan, I. Arias

Physical review B: condensed matter and material physics (2015). Vol. 92 (9), pp. 1-7 (Preprint)

Abstract
Cracks generate the largest strain gradients that any material can withstand. Flexoelectricity (coupling between strain gradient and polarization) must therefore play an important role in fracture physics. Here we use a self-consistent continuum model to evidence two consequences of flexoelectricity in fracture: the resistance to fracture increases as structural size decreases, and it becomes asymmetric with respect to the sign of polarization. The latter phenomenon manifests itself in a range of intermediate sizes where piezo- and flexoelectricity compete. In BaTiO3 at room temperature, this range spans from 0.1 to 50 nm, a typical thickness range for epitaxial ferroelectric thin films.
Abstract
Cracks generate the largest strain gradients that any material can withstand. Flexoelectricity (coupling between strain gradient and polarization) must therefore play an important [...]
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A stabilized formulation with maximum entropy meshfree approximants for viscoplastic flow simulation in metal forming
F. Greco, L. Filice, C. Peco, M. Arroyo

Int. J. Numer. Meth. Engng. (2015). Vol. 8 (3), pp. 341-353 (preprint)

Abstract
The finite element method is the reference technique in the simulation of metal forming and provides excellent results with both Eulerian and Lagrangian implementations. The latter approach is more natural and direct but the large deformations involved in such processes require remeshing-rezoning algorithms that increase the computational times and reduce the quality of the results. Meshfree methods can better handle large deformations and have shown encouraging results. However, viscoplastic flows are nearly incompressible, which poses a challenge to meshfree methods. In this paper we propose a simple model of viscoplasticity, where both the pressure and velocity fields are discretized with maximum entropy approximants. The inf-sup condition is circumvented with a numerically consistent stabilized formulation that involves the gradient of the pressure. The performance of the method is studied in some benchmark problems including metal forming and orthogonal cutting.
Abstract
The finite element method is the reference technique in the simulation of metal forming and provides excellent results with both Eulerian and Lagrangian implementations. The [...]
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Examining the mechanical equilibrium of microscopic stresses in molecular simulations
A. Torres-Sánchez, J. Vanegas, M. Arroyo

Physical review letters (2015). Vol. 114 (25), pp. 258102-1/258102-5 (Preprint)

Abstract
The microscopic stress field provides a unique connection between atomistic simulations and mechanics at the nanoscale. However, its definition remains ambiguous. Rather than a mere theoretical preoccupation, we show that this fact acutely manifests itself in local stress calculations of defective graphene, lipid bilayers, and fibrous proteins. We find that popular definitions of the microscopic stress violate the continuum statements of mechanical equilibrium, and we propose an unambiguous and physically sound definition.
Abstract
The microscopic stress field provides a unique connection between atomistic simulations and mechanics at the nanoscale. However, its definition remains ambiguous. Rather than [...]
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D7.1 DELIVERY OF GEOMETRY AND COMPUTATIONAL MODEL
A. Michalski, D. Andersson, R. Rossi, C. Soriano

Open Access Repository of the ExaQUte project: Deliverables (2021). 7

Abstract
This document describes the industrial application, on which the developments of the project are implemented, and the CFD set-up. The developments are implemented over six analysis cases with increasing complexity starting from a 2D geometry with mean wind inflow to a 3D geometry with turbulent inflow and real-time shape optimization. The application represents the CAARC tall building model, which has served as a benchmark model for many studies since the 1970’s when it was first developed. Base moments (bending and torsional moments) of the building are extracted for validation by comparison of the results with the benchmark study. Page 3 of 19 Deliverable 7.1
Abstract
This document describes the industrial application, on which the developments of the project are implemented, and the CFD set-up. The developments are implemented over six [...]
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Physical principles of membrane remodelling during cell mechanoadaptation
A. Kosmalska, L. Casares, A. Elosegui-Artola, J. Thottacherry, R. Moreno-Vicente, V. González-Tarragó, M. Pozo, S. Mayor, M. Arroyo, D. Navajas, X. Trepat, N. Gauthier, P. Roca

Nature communications (2015). Vol. 6 (7292), pp. 1-11

Abstract
Biological processes in any physiological environment involve changes in cell shape, which must be accommodated by their physical envelope-the bilayer membrane. However, the fundamental biophysical principles by which the cell membrane allows for and responds to shape changes remain unclear. Here we show that the 3D remodelling of the membrane in response to a broad diversity of physiological perturbations can be explained by a purely mechanical process. This process is passive, local, almost instantaneous, before any active remodelling and generates different types of membrane invaginations that can repeatedly store and release large fractions of the cell membrane. We further demonstrate that the shape of those invaginations is determined by the minimum elastic and adhesive energy required to store both membrane area and liquid volume at the cell-substrate interface. Once formed, cells reabsorb the invaginations through an active process with duration of the order of minutes.
Abstract
Biological processes in any physiological environment involve changes in cell shape, which must be accommodated by their physical envelope-the bilayer membrane. However, the [...]
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Phase-field modeling and simulation of fracture in brittle materials with strongly anisotropic surface energy
B. Li, C. Peco, D. Millán, I. Arias, M. Arroyo

Int. J. Numer. Meth. Engng. (2015). Vol. 102 (3-4), pp. 711-727 (Preprint)

Abstract
Crack propagation in brittle materials with anisotropic surface energy is important in applications involving single crystals, extruded polymers, or geological and organic materials. Furthermore, when this anisotropy is strong, the phenomenology of crack propagation becomes very rich, with forbidden crack propagation directions or complex sawtooth crack patterns. This problem interrogates fundamental issues in fracture mechanics, including the principles behind the selection of crack direction. Here, we propose a variational phase-field model for strongly anisotropic fracture, which resorts to the extended Cahn-Hilliard framework proposed in the context of crystal growth. Previous phase-field models for anisotropic fracture were formulated in a framework only allowing for weak anisotropy. We implement numerically our higher-order phase-field model with smooth local maximum entropy approximants in a direct Galerkin method. The numerical results exhibit all the features of strongly anisotropic fracture and reproduce strikingly well recent experimental observations. rack propagation in brittle materials with anisotropic surface energy is important in applications involving single crystals, extruded polymers, or geological and organic materials. Furthermore, when this anisotropy is strong, the phenomenology of crack propagation becomes very rich, with forbidden crack propagation directions or complex sawtooth crack patterns. This problem interrogates fundamental issues in fracture mechanics, including the principles behind the selection of crack direction. Here, we propose a variational phase-field model for strongly anisotropic fracture, which resorts to the extended Cahn-Hilliard framework proposed in the context of crystal growth. Previous phase-field models for anisotropic fracture were formulated in a framework only allowing for weak anisotropy. We implement numerically our higher-order phase-field model with smooth local maximum entropy approximants in a direct Galerkin method. The numerical results exhibit all the features of strongly anisotropic fracture and reproduce strikingly well recent experimental observations.
Abstract
Crack propagation in brittle materials with anisotropic surface energy is important in applications involving single crystals, extruded polymers, or geological and organic [...]
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Efficient implementation of Galerkin meshfree methods for large-scale problems with an emphasis on maximum entropy approximants
C. Peco, D. Millán, A. Rosolen, M. Arroyo

Computers and Structures (2015). Vol. 150, pp. 52-62 (Preprint)

Abstract
In Galerkin meshfree methods, because of a denser and unstructured connectivity, the creation and assembly of sparse matrices is expensive. Additionally, the cost of computing basis functions can be significant in problems requiring repetitive evaluations. We show that it is possible to overcome these two bottlenecks resorting to simple and effective algorithms. First, we create and fill the matrix by coarse-graining the connectivity between quadrature points and nodes. Second, we store only partial information about the basis functions, striking a balance between storage and computation. We show the performance of these strategies in relevant problems.
Abstract
In Galerkin meshfree methods, because of a denser and unstructured connectivity, the creation and assembly of sparse matrices is expensive. Additionally, the cost of computing [...]
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Revisiting pyramid compression to quantify flexoelectricity: a three-dimensional simulation study
A. Abdollahi, D. Millán, C. Peco, M. Arroyo, I. Arias

Physical review B: condensed matter and material physics (2015). Vol. 91 (10), pp. 104103 (preprint)

Abstract
Flexoelectricity is a universal property of all dielectrics by which they generate a voltage in response to an inhomogeneous deformation. One of the controversial issues in this field concerns the magnitude of flexoelectric coefficients measured experimentally, which greatly exceed theoretical estimates. Furthermore, there is a broad scatter amongst experimental measurements. The truncated pyramid compression method is one of the common setups to quantify flexoelectricity, the interpretation of which relies on simplified analytical equations to estimate strain gradients. However, the deformation fields in three-dimensional pyramid configurations are highly complex, particularly around its edges. In the present work, using three-dimensional self-consistent simulations of flexoelectricity, we show that the simplified analytical estimations of strain gradients in compressed pyramids significantly overestimate flexoelectric coefficients, thus providing a possible explanation to reconcile different estimates. In fact, the interpretation of pyramid compression experiments is highly nontrivial. We systematically characterize the magnitude of this overestimation, of over one order of magnitude, as a function of the truncated pyramid configuration. These results are important to properly characterize flexoelectricity, and provide design guidelines for effective electromechanical transducers exploiting flexoelectricity.
Abstract
Flexoelectricity is a universal property of all dielectrics by which they generate a voltage in response to an inhomogeneous deformation. One of the controversial issues in [...]
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Hydraulic fracture during epithelial stretching
L. Casares, R. Vincent, D. Zalvidea, N. Campillo, D. Navajas, M. Arroyo, X. Trepat

Nature materials (2015). Vol. 14 (3), pp. 343-351

Abstract
The origin of fracture in epithelial cell sheets subject to stretch is commonly attributed to excess tension in the cells' cytoskeleton, in the plasma membrane, or in cell-cell contacts. Here, we demonstrate that for a variety of synthetic and physiological hydrogel substrates the formation of epithelial cracks is caused by tissue stretching independently of epithelial tension. We show that the origin of the cracks is hydraulic; they result from a transient pressure build-up in the substrate during stretch and compression manoeuvres. After pressure equilibration, cracks heal readily through actomyosin-dependent mechanisms. The observed phenomenology is captured by the theory of poroelasticity, which predicts the size and healing dynamics of epithelial cracks as a function of the stiffness, geometry and composition of the hydrogel substrate. Our findings demonstrate that epithelial integrity is determined in a tension-independent manner by the coupling between tissue stretching and matrix hydraulics.
Abstract
The origin of fracture in epithelial cell sheets subject to stretch is commonly attributed to excess tension in the cells' cytoskeleton, in the plasma membrane, or in [...]
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Computing the volume enclosed by a periodic surface and its variation to model a follower pressure
M. Rahimi, K. Zhang, M. Arroyo

Computational Mechanics (preprint) (2015). Vol. 55 (3), pp. 519-525

Abstract
In modeling and numerically implementing a follower pressure in a geometrically nonlinear setting, one needs to compute the volume enclosed by a surface and its variation. For closed surfaces, the volume can be expressed as a surface integral invoking the divergence theorem. For periodic systems, widely used in computational physics and materials science, the enclosed volume calculation and its variation is more delicate and has not been examined before. Here, we develop simple expressions involving integrals on the surface, on its boundary lines, and point contributions. We consider two specific situations, a periodic tubular surface and a doubly periodic surface enclosing a volume with a nearby planar substrate, which are useful to model systems such as pressurized carbon nanotubes, supported lipid bilayers or graphene. We provide a set of numerical examples, which show that the familiar surface integral term alone leads to an incorrect volume evaluation and spurious forces at the periodic boundaries.
Abstract
In modeling and numerically implementing a follower pressure in a geometrically nonlinear setting, one needs to compute the volume enclosed by a surface and its variation. [...]
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D6.2 Report on the calculation of stochastic sensitivities
S. Ganesh, Q. Ayoul-Guilmard, F. Nobile, C. Soriano, R. Rossi

Open Access Repository of the ExaQUte project: Deliverables (2021). 2

Abstract
In the following sections, the formulation of a possible stochastic optimisation problem relevant to the ExaQUte project is first presented.
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D5.2 Release of ExaQUte MLMC Python engine
R. Amela, Q. Ayoul-Guilmard, S. Ganesh, R. Tosi, R. Badia, F. Nobile, R. Rossi, C. Soriano

Open Access Repository of the ExaQUte project: Deliverables (2021). 3

Abstract
In this deliverable, the ExaQUte xmc library is introduced. This report is meant to serve as a supplement to the publicly release of the library. In the following sections, the ExaQUte xmc library is described along with its current and future capabilities. The structure of the library, along with its dynamic import mechanism, are described using samples of code. The algorithms behind the example files supplied with the public release are explained in detail as well.
Abstract
In this deliverable, the ExaQUte xmc library is introduced. This report is meant to serve as a supplement to the publicly release of the library. In the following sections, [...]
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D4.2 Profiling report of the partner’s tools, complete with performance suggestions
R. Amela, R. Badia, S. Böhm, R. Tosi, C. Soriano, R. Rossi

Open Access Repository of the ExaQUte project: Deliverables (2021). 4

Abstract
This deliverable focuses on the proling activities developed in the project with the partner's applications. To perform this proling activities, a couple of benchmarks were dened in collaboration with WP5. The rst benchmark is an embarrassingly parallel benchmark that performs a read and then multiple writes of the same object, with the objective of stressing the memory and storage systems and evaluate the overhead when these reads and writes are performed in parallel. A second benchmark is dened based on the Continuation Multi Level Monte Carlo (C-MLMC) algorithm. While this algorithm is normally executed using multiple levels, for the proling and performance analysis objectives, the execution of a single level was enough since the forthcoming levels have similar performance characteristics. Additionally, while the simulation tasks can be executed as parallel (multi-threaded tasks), in the benchmark, single threaded tasks were executed to increase the number of simulations to be scheduled and stress the scheduling engines. A set of experiments based on these two benchmarks have been executed in the MareNostrum 4 supercomputer and using PyCOMPSs as underlying programming model and dynamic scheduler of the tasks involved in the executions. While the rst benchmark was executed several times in a single iteration, the second benchmark was executed in an iterative manner, with cycles of 1) Execution and trace generation; 2) Performance analysis; 3) Improvements. This had enabled to perform several improvements in the benchmark and in the scheduler of PyCOMPSs. The initial iterations focused on the C-MLMC structure itself, performing re-factors of the code to remove ne grain and sequential tasks and merging them in larger granularity tasks. The next iterations focused on improving the PyCOMPSs scheduler, removing existent bottlenecks and increasing its performance by making the scheduler a multithreaded engine. While the results can still be improved, we are satised with the results since the granularity of the simulations run in this evaluation step are much ner than the one that will be used for the real scenarios. The deliverable nishes with some recommendations that should be followed along the project in order to obtain good performance in the execution of the project codes.
Abstract
This deliverable focuses on the proling activities developed in the project with the partner's applications. To perform this proling activities, a couple of benchmarks [...]
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D2.3. Adjoint-based error estimation routines
B. Keith, A. Apostolatos, A. Kodakkal, R. Rossi, R. Tosi, B. Wohlmuth, C. Soriano

Open Access Repository of the ExaQUte project: Deliverables (2021). 5

Abstract
This document presents a simple and ecient strategy for adaptive mesh renement (AMR) and a posteriori error estimation for the transient incompressible Navier{Stokes equations. This strategy is informed by the work of Prudhomme and Oden [22, 23] as well as modern goal-oriented methods such as [5]. The methods described in this document have been implemented in the Kratos Multiphysics software and uploaded to https://zenodo.org [27].1 This document includes: A review of the state-of-the-art in solution-oriented and goal-oriented AMR. The description of a 2D benchmark model problem of immediate relevance to the objectives of the ExaQUte project. The denition and a brief mathematical summary of the error estimator(s). The results obtained. A description of the API.
Abstract
This document presents a simple and ecient strategy for adaptive mesh renement (AMR) and a posteriori error estimation for the transient incompressible Navier{Stokes equations. [...]
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D3.1 Report on nonlinear domain decomposition preconditioners and release of the solvers
S. Badia, A. Martín, J. Principe, C. Soriano, R. Rossi

Open Access Repository of the ExaQUte project: Deliverables (2021). 6

Abstract
In this deliverable we provide the details related to the design, implementation, and scalability analysis of two nonlinear domain decomposition (DD) methods that have been released in the frame of the FEMPAR project [4]. First, we introduce the linear solvers being used in Sect. 2. Next, we will consider nonlinear domain decomposition solvers in Sect. 3. Two dierent nonlinear solvers are proposed. Sect. 4 is devoted to the numerical analysis of these algorithms. After a thorough analysis for the p-Laplacian problem, the method that provides better results will be used for the simulation of complex and highly nonlinear electromagnetics problems.
Abstract
In this deliverable we provide the details related to the design, implementation, and scalability analysis of two nonlinear domain decomposition (DD) methods that have been released [...]
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Cell-based maximum-entropy approximants
D. Millán, N. Sukumar, M. Arroyo

Comput. Methods Appl. Mech. Engrg., (2015). Vol. 284, pp. 712-731 (preprint)

Abstract
In this paper, we devise cell-based maximum-entropy (max-ent) basis functions that are used in a Galerkin method for the solution of partial differential equations. The motivation behind this work is the construction of smooth approximants with controllable support on unstructured meshes. In the variational scheme to obtain max-ent basis functions, the nodal prior weight function is constructed from an approximate distance function to a polygonal curve in R-2. More precisely, we take powers of the composition of R-functions via Boolean operations. The basis functions so constructed are nonnegative, smooth, linearly complete, and compactly-supported in a neighbor-ring of segments that enclose each node. The smoothness is controlled by two positive integer parameters: the normalization order of the approximation of the distance function and the power to which it is raised. The properties and mathematical foundations of the new compactly-supported approximants are described, and its use to solve two-dimensional elliptic boundary-value problems (Poisson equation and linear elasticity) is demonstrated. The sound accuracy and the optimal rates of convergence of the method in Sobolev norms are established.
Abstract
In this paper, we devise cell-based maximum-entropy (max-ent) basis functions that are used in a Galerkin method for the solution of partial differential equations. The motivation [...]
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D8.1 Data Management Plan
C. Soriano, R. Rossi, Q. Ayoul-Guilmard

Open Access Repository of the ExaQUte project: Deliverables (2021). 8

Abstract
The ExaQUte project participates in the Pilot on Open Research Data launched by the European Commission (EC) along with the H2020 program. This pilot is part of the Open Access to Scientific Publications and Research Data program in H2020. The goal of the program is to foster access to research data generated in H2020 projects. The use of a Data anagement Plan (DMP) is required for all projects participating in the Open Research Data Pilot, in which they will specify what data will be kept for the longer term. The underpinning idea is that Horizon 2020 beneficiaries have to make their research data findable, accessible, interoperable and re-usable (FAIR), to ensure it is soundly managed.
Abstract
The ExaQUte project participates in the Pilot on Open Research Data launched by the European Commission (EC) along with the H2020 program. This pilot is part of the Open Access [...]
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D6.1 Deterministic optimization software
A. Apostolatos, B. Keith, C. Soriano, R. Rossi

Open Access Repository of the ExaQUte project: Deliverables (2021). 9

Abstract
This deliverable focuses on the implementation of deterministic optimization algorithms and problem solvers within KRATOS open-source software. One of the main challenges of optimization algorithms in Finite-Element based optimization is how to get the gradient of response functions which are used as objective and constraints when this is not available in an explicit form. The idea is to use local sensitivity analysis to get the gradient of the response function(s)
Abstract
This deliverable focuses on the implementation of deterministic optimization algorithms and problem solvers within KRATOS open-source software. One of the main challenges [...]
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D5.1 ExaQUte API for MLMC
D. Drzisga, M. Parete, R. Wüchner, R. Rossi, C. Soriano

Open Access Repository of the ExaQUte project: Deliverables (2021). 1

Abstract
This deliverable focuses on the design of an interface between MLMC algorithms, the scheduling engine, and problem solvers. For this purpose an API denition is proposed together with a basic reference implementation in Python. This work serves as a rst step for the development of the ExaQUte MLMC Python engine. It includes: API denition Demonstrator code and description Example of usage
Abstract
This deliverable focuses on the design of an interface between MLMC algorithms, the scheduling engine, and problem solvers. For this purpose an API denition is proposed together [...]
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D4.1 Working Python API to schedule MLC routines
R. Amela, R. Badia, R. Rossi, S. Böhm, J. Beranek, C. Soriano

Open Access Repository of the ExaQUte project: Deliverables (2021). 10

Abstract
This deliverable focuses on the denition of a common API for the PyCOMPSs programming model and HyperLoom scheduler provided respectively by BSC and IT4I. The objective of the work is to hide the details of the actual task scheduling technology, so that the Multi Level Monte Carlo Python engine is agnostic of the backend being employed. It includes the description of: Common API for calls Examples of usage Basic Documentation The document also contains an initial description on how MPI-distributed data shall be treated from the scheduling point of view.
Abstract
This deliverable focuses on the denition of a common API for the PyCOMPSs programming model and HyperLoom scheduler provided respectively by BSC and IT4I. The objective [...]
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Topological obstructions in the way of data-driven collective variables
B. Hashemian, M. Arroyo

Journal of chemical physics (2015). Vol. 142 (4), pp. 044102-1/044102-6 (preprint)

Abstract
Nonlinear dimensionality reduction (NLDR) techniques are increasingly used to visualize molecular trajectories and to create data-driven collective variables for enhanced sampling simulations. The success of these methods relies on their ability to identify the essential degrees of freedom characterizing conformational changes. Here, we show that NLDR methods face serious obstacles when the underlying collective variables present periodicities, e.g., arising from proper dihedral angles. As a result, NLDR methods collapse very distant configurations, thus leading to misinterpretations and inefficiencies in enhanced sampling. Here, we identify this largely overlooked problem and discuss possible approaches to overcome it. We also characterize the geometry and topology of conformational changes of alanine dipeptide, a benchmark system for testing new methods to identify collective variables. Nonlinear dimensionality reduction (NLDR) techniques are increasingly used to visualize molecular trajectories and to create data-driven collective variables for enhanced sampling simulations. The success of these methods relies on their ability to identify the essential degrees of freedom characterizing conformational changes. Here, we show that NLDR methods face serious obstacles when the underlying collective variables present periodicities, e.g., arising from proper dihedral angles. As a result, NLDR methods collapse very distant configurations, thus leading to misinterpretations and inefficiencies in enhanced sampling. Here, we identify this largely overlooked problem and discuss possible approaches to overcome it. We also characterize the geometry and topology of conformational changes of alanine dipeptide, a benchmark system for testing new methods to identify collective variables.
Abstract
Nonlinear dimensionality reduction (NLDR) techniques are increasingly used to visualize molecular trajectories and to create data-driven collective variables for enhanced [...]
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D2.1 Meshing ”stub” implementation of the capabilities to be delivered
A. Froehly, V. Mataix Ferrándiz, C. Roig, C. Soriano, R. Rossi

Open Access Repository of the ExaQUte project: Deliverables (2021). 11

Abstract
This document presents a description of the MMG interface adapted to Kratos as well as its parallel counterpart with ParMMG which will be implemented in task 2.1. In the description are included the following items: • Description of the requirements of the interfaces; • Description of the data structures used both in Kratos and MMG; • Proposal of an initial interface for ParMMG. • The input needed for the model; • The denition of the model system matrices; • The solver and time marching schemes; • The results obtained, and the link to the 3D detailed model
Abstract
This document presents a description of the MMG interface adapted to Kratos as well as its parallel counterpart with ParMMG which will be implemented in task 2.1. In the description [...]
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Force transduction and lipid binding in MscL: a continuum-molecular approach
J. Vanegas, M. Arroyo

PLoS one (2014). Vol. 9 (12), pp. e113947 (preprint)

Abstract
The bacterial mechanosensitive channel MscL, a small protein mainly activated by membrane tension, is a central model system to study the transduction of mechanical stimuli into chemical signals. Mutagenic studies suggest that MscL gating strongly depends on both intra-protein and interfacial lipid-protein interactions. However, there is a gap between this detailed chemical information and current mechanical models of MscL gating. Here, we investigate the MscL bilayer-protein interface through molecular dynamics simulations, and take a combined continuum-molecular approach to connect chemistry and mechanics. We quantify the effect of membrane tension on the forces acting on the surface of the channel, and identify interactions that may be critical in the force transduction between the membrane and MscL. We find that the local stress distribution on the protein surface is largely asymmetric, particularly under tension, with the cytoplasmic side showing significantly larger and more localized forces, which pull the protein radially outward. The molecular interactions that mediate this behavior arise from hydrogen bonds between the electronegative oxygens in the lipid headgroup and a cluster of positively charged lysine residues on the amphipathic S1 domain and the C-terminal end of the second trans-membrane helix. We take advantage of this strong interaction (estimated to be 10-13 kT per lipid) to actuate the channel (by applying forces on protein-bound lipids) and explore its sensitivity to the pulling magnitude and direction. We conclude by highlighting the simple motif that confers MscL with strong anchoring to the bilayer, and its presence in various integral membrane proteins including the human mechanosensitive channel K2P1 and bovine rhodopsin.
Abstract
The bacterial mechanosensitive channel MscL, a small protein mainly activated by membrane tension, is a central model system to study the transduction of mechanical stimuli [...]
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Understanding and strain-engineering wrinkle networks in supported graphene through simulations
K. Zhang, M. Arroyo

Journal of the Mechanics and Physics of Solids (2014). Vol. 72, pp. 61-74 (Preprint)

Abstract
Wrinkle networks are ubiquitous buckle-induced delaminations in supported graphene, which locally modify the electronic structure and degrade device performance. Although the strong property-deformation coupling of graphene can be potentially harnessed by strain engineering, it has not been possible to precisely control the geometry of wrinkle networks. Through numerical simulations based on an atomistically informed continuum theory, we understand how strain anisotropy, adhesion and friction govern spontaneous wrinkling. We then propose a strategy to control the location of wrinkles through patterns of weaker adhesion. This strategy is deceptively simple, and can in fact fail in several ways, particularly under biaxial compression. However, within bounds set by the physics of wrinkling, it is possible to robustly create by strain a variety of wrinkle network geometries and junction configurations. Graphene is nearly unstrained in the planar regions bounded by wrinkles, highly curved along wrinkles, and highly stretched and curved at junctions, which can either locally attenuate or amplify the applied strain depending on their configuration. These mechanically self-assembled networks are stable under the pressure produced by an enclosed fluid and form continuous channels, opening the door to nano-fluidic applications.
Abstract
Wrinkle networks are ubiquitous buckle-induced delaminations in supported graphene, which locally modify the electronic structure and degrade device performance. Although [...]
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Computational evaluation of the flexoelectric effect in dielectric solids
A. Abdollahi, C. Peco, D. Millán, I. Arias, M. Arroyo

Journal of applied physics (2014). Vol. 116 (9), pp. 093502-1/093502-10 (Preprint)

Abstract
Flexoelectricity is a size-dependent electromechanical mechanism coupling polarization and strain gradient. It exists in a wide variety of materials, and is most noticeable for nanoscale objects, where strain gradients are higher. Simulations are important to understand flexoelectricity because experiments at very small scales are difficult, and analytical solutions are scarce. Here, we computationally evaluate the role of flexoelectricity in the electromechanical response of linear dielectric solids in two-dimensions. We deal with the higher-order coupled partial differential equations using smooth meshfree basis functions in a Galerkin method, which allows us to consider general geometries and boundary conditions. We focus on the most common setups to quantify the flexoelectric response, namely, bending of cantilever beams and compression of truncated pyramids, which are generally interpreted through approximate solutions. While these approximations capture the size-dependent flexoelectric electromechanical coupling, we show that they only provide order-of-magnitude estimates as compared with a solution fully accounting for the multidimensional nature of the problem. We discuss the flexoelectric mechanism behind the enhanced size-dependent elasticity in beam configurations. We show that this mechanism is also responsible for the actuation of beams under purely electrical loading, supporting the idea that a mechanical flexoelectric sensor also behaves as an actuator. The predicted actuation-induced curvature is in a good agreement with experimental results. The truncated pyramid configuration highlights the critical role of geometry and boundary conditions on the effective electromechanical response. Our results suggest that computer simulations can help understanding and quantifying the physical properties of flexoelectric devices.
Abstract
Flexoelectricity is a size-dependent electromechanical mechanism coupling polarization and strain gradient. It exists in a wide variety of materials, and is [...]
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Interplay of packing and flip-flop in local bilayer deformation. How phosphatidylglycerol could rescue mitochondrial function in a cardiolipin-deficient yeast mutant
N. Khalifat, M. Rahimi, A. Bitbol, M. Seigneuret, J. Fournier, N. Puff, M. Arroyo, M. Angelova

Biophysical journal (2014). Vol. 107 (4), pp. 879-890 (preprint)

Abstract
In a previous work, we have shown that a spatially localized transmembrane pH gradient, produced by acid micro-injection near the external side of cardiolipin-containing giant unilamellar vesicles, leads to the formation of tubules that retract after the dissipation of this gradient. These tubules have morphologies similar to mitochondrial cristae. The tubulation effect is attributable to direct phospholipid packing modification in the outer leaflet, that is promoted by protonation of cardiolipin head-groups. In this study, we compare the case of cardiolipin-containing giant unilamellar vesicles with that of giant unilamellar vesicles that contain phosphatidylglycerol (PG). Local acidification also promotes formation of tubules in the latter. However, compared with cardiolipin-containing giant unilamellar vesicles the tubules are longer, exhibit a visible pearling, and have a much longer lifetime after acid micro-injection is stopped. We attribute these differences to an additional mechanism that increases monolayer surface imbalance, namely inward PG flip-flop promoted by the local transmembrane pH gradient. Simulations using a fully nonlinear membrane model as well as geometrical calculations are in agreement with this hypothesis. Interestingly, among yeast mutants deficient in cardiolipin biosynthesis, only the crd1-null mutant, which accumulates phosphatidylglycerol, displays significant mitochondria! activity. Our work provides a possible explanation of such a property and further emphasizes the salient role of specific lipids in mitochondria! function. n a previous work, we have shown that a spatially localized transmembrane pH gradient, produced by acid micro-injection near the external side of cardiolipin-containing giant unilamellar vesicles, leads to the formation of tubules that retract after the dissipation of this gradient. These tubules have morphologies similar to mitochondrial cristae. The tubulation effect is attributable to direct phospholipid packing modification in the outer leaflet, that is promoted by protonation of cardiolipin headgroups. In this study, we compare the case of cardiolipin-containing giant unilamellar vesicles with that of giant unilamellar vesicles that contain phosphatidylglycerol (PG). Local acidification also promotes formation of tubules in the latter. However, compared with cardiolipin-containing giant unilamellar vesicles the tubules are longer, exhibit a visible pearling, and have a much longer lifetime after acid micro-injection is stopped. We attribute these differences to an additional mechanism that increases monolayer surface imbalance, namely inward PG flip-flop promoted by the local transmembrane pH gradient. Simulations using a fully nonlinear membrane model as well as geometrical calculations are in agreement with this hypothesis. Interestingly, among yeast mutants deficient in cardiolipin biosynthesis, only the crd1-null mutant, which accumulates phosphatidylglycerol, displays significant mitochondrial activity. Our work provides a possible explanation of such a property and further emphasizes the salient role of specific lipids in mitochondrial function.
Abstract
In a previous work, we have shown that a spatially localized transmembrane pH gradient, produced by acid micro-injection near the external side of cardiolipin-containing giant [...]
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Importance of force decomposition for local stress calculations in biomembrane molecular simulations
J. Vanegas, A. Torres-Sánchez, M. Arroyo

Journal of chemical theory and computation (2014). Vol. 10 (2), pp. 691-702 (preprint)

Abstract
Local stress fields are routinely computed from molecular dynamics trajectories to understand the structure and mechanical properties of lipid bilayers. These calculations can be systematically understood with the Irving-Kirkwood-Noll theory. In identifying the stress tensor, a crucial step is the decomposition of the forces on the particles into pairwise contributions. However, such a decomposition is not unique in general, leading to an ambiguity in the definition of the stress tensor, particularly for multibody potentials. Furthermore, a theoretical treatment of constraints in local stress calculations has been lacking. Here, we present a new implementation of local stress calculations that systematically treats constraints and considers a privileged decomposition, the central force decomposition, that leads to a symmetric stress tensor by construction. We focus on biomembranes, although the methodology presented here is widely applicable. Our results show that some unphysical behavior obtained with previous implementations (e.g. nonconstant normal stress profiles along an isotropic bilayer in equilibrium) is a consequence of an improper treatment of constraints. Furthermore, other valid force decompositions produce significantly different stress profiles, particularly in the presence of dihedral potentials. Our methodology reveals the striking effect of unsaturations on the bilayer mechanics, missed by previous stress calculation implementations.
Abstract
Local stress fields are routinely computed from molecular dynamics trajectories to understand the structure and mechanical properties of lipid bilayers. These calculations [...]
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Phase-field modeling of fracture in linear thin shells
F. Amiri, D. Millán, Y. Shen, T. Rabzuk, M. Arroyo

Theoretical and applied fracture mechanics (2014). Vol. 69, pp. 102-109 (preprint)

Abstract
We present a phase-field model for fracture in Kirchoff-Love thin shells using the local maximum-entropy (LME) meshfree method. Since the crack is a natural outcome of the analysis it does not require an explicit representation and tracking, which is advantage over techniques as the extended finite element method that requires tracking of the crack paths. The geometric description of the shell is based on statistical learning techniques that allow dealing with general point set surfaces avoiding a global parametrization, which can be applied to tackle surfaces of complex geometry and topology. We show the flexibility and robustness of the present methodology for two examples: plate in tension and a set of open connected pipes.
Abstract
We present a phase-field model for fracture in Kirchoff-Love thin shells using the local maximum-entropy (LME) meshfree method. Since the crack is a natural outcome of the [...]
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XLME interpolants, a seamless bridge between XFEM and enriched meshless methods
F. Amiri, C. Anitescu, M. Arroyo, S. Bordas, T. Rabezuk

Computational Mechanics (2014). Vol. 53 (1), pp. 45-57 (Preprint)

Abstract
In this paper, we develop a method based on local maximum entropy shape functions together with enrichment functions used in partition of unity methods to discretize problems in linear elastic fracture mechanics. We obtain improved accuracy relative to the standard extended finite element method at a comparable computational cost. In addition, we keep the advantages of the LME shape functions, such as smoothness and non-negativity. We show numerically that optimal convergence (same as in FEM) for energy norm and stress intensity factors can be obtained through the use of geometric (fixed area) enrichment with no special treatment of the nodes near the crack such as blending or shifting.
Abstract
In this paper, we develop a method based on local maximum entropy shape functions together with enrichment functions used in partition of unity methods to discretize problems [...]
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Shape control of active surfaces inspired by the movement of euglenids
M. Arroyo, A. DeSimone

Journal of the Mechanics and Physics of Solids (2014). Vol. 62, pp. 99-112 (Preprint)

Abstract
We examine a novel mechanism for active surface morphing inspired by the cell body deformations of euglenids. Actuation is accomplished through in-plane simple shear along prescribed slip lines decorating the surface. Under general non-uniform actuation, such local deformation produces Gaussian curvature, and therefore leads to shape changes. Geometrically, a deformation that realizes the prescribed local shear is an isometric embedding. We explore the possibilities and limitations of this bio- inspired shape morphing mechanism, by first characterizing isometric embeddings un- der axisymmetry, understanding the limits of embeddability, and studying in detail the accessibility of surfaces of zero and constant curvature. Modeling mechanically the active surface as a non-Euclidean plate (NEP), we further examine the mechanism beyond the geometric singularities arising from embeddability, where mechanics and buckling play a decisive role. We also propose a non-axisymmetric actuation strategy to accomplish large amplitude bending and twisting motions of elongated cylindrical surfaces. Besides helping understand how euglenids delicately control their shape, our results may provide the background to engineer soft machines
Abstract
We examine a novel mechanism for active surface morphing inspired by the cell body deformations of euglenids. Actuation is accomplished through in-plane simple shear along [...]
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Nonsingular isogeometric boundary element method for stokes flows in 3D
L. Heltai, M. Arroyo, A. DeSimone

Comput. Methods Appl. Mech. Engrg., (2014). Vol. 268, pp. 514-539 (preprint)

Abstract
Isogeometric analysis (IGA) is emerging as a technology bridging computer aided geometric design (CAGD), most commonly based on Non-Uniform Rational B-Splines (NURBS) surfaces, and engineering analysis. In finite element and boundary element isogeometric methods (FE-IGA and IGA-BEM), the NURBS basis functions that describe the geometry define also the approximation spaces. In the FE-IGA approach, the surfaces generated by the CAGD tools need to be extended to volumetric descriptions, a major open problem in 3D. This additional passage can be avoided in principle when the partial differential equations to be solved admit a formulation in terms of boundary integral equations, leading to boundary element isogeometric analysis (IGA-BEM). The main advantages of such an approach are given by the dimensionality reduction of the problem (from volumetric-based to surface-based), by the fact that the interface with CAGD tools is direct, and by the possibility to treat exterior problems, where the computational domain is infinite. By contrast, these methods produce system matrices which are full, and require the integration of singular kernels. In this paper we address the second point and propose a nonsingular formulation of IGA-BEM for 3D Stokes flows, whose convergence is carefully tested numerically. Standard Gaussian quadrature rules suffice to integrate the boundary integral equations, and carefully chosen known exact solutions of the interior Stokes problem are used to correct the resulting matrices, extending the work by Klaseboer et al. (2012) [27] to IGA-BEM.
Abstract
Isogeometric analysis (IGA) is emerging as a technology bridging computer aided geometric design (CAGD), most commonly based on Non-Uniform Rational B-Splines (NURBS) surfaces, [...]
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An adaptive meshfree method for phase-field models of biomembranes. Part II: A Lagrangian approach for membranes in viscous fluids
C. Peco, A. Rosolen, M. Arroyo

Journal of Computational Physics (2013). Vol. 249 (5), pp. 320-336 (Preprint)

Abstract
We present a Lagrangian phase-field method to study the low Reynolds number dynamics of vesicles embedded in a viscous fluid. In contrast to previous approaches, where the field variables are the phase-field and the fluid velocity, here we exploit the fact that the phasefield tracks a material interface to reformulate the problem in terms of the Lagrangian motion of a background medium, containing both the biomembrane and the fluid. We discretize the equations in space with maximum-entropy approximants, carefully shown to perform well in phase-field models of biomembranes in a companion paper. The proposed formulation is variational, lending itself to implicit time-stepping algorithms based on minimization of a time-incremental energy, which are automatically nonlinearly stable. The proposed method deals with two of the major challenges in the numerical treatment of coupled fluid/phase-field models of biomembranes, namely the adaptivity of the grid to resolve the sharp features of the phase-field, and the stiffness of the equations, leading to very small time-steps. In our method, local refinement follows the features of the phasefield as both are advected by the Lagrangian motion, and large time-steps can be robustly chosen in the variational time-stepping algorithm, which also lends itself to time adaptivity. The method is presented in the axisymmetric setting, but it can be directly extended to 3D. We present a Lagrangian phase-field method to study the low Reynolds number dynamics of vesicles embedded in a viscous fluid. In contrast to previous approaches, where the field variables are the phase-field and the fluid velocity, here we exploit the fact that the phase-field tracks a material interface to reformulate the problem in terms of the Lagrangian motion of a background medium, containing both the biomembrane and the fluid. We discretize the equations in space with maximum-entropy approximants, carefully shown to perform well in phase-field models of biomembranes in a companion paper. The proposed formulation is variational, lending itself to implicit time-stepping algorithms based on minimization of a time-incremental energy, which are automatically nonlinearly stable. The proposed method deals with two of the major challenges in the numerical treatment of coupled fluid/phase-field models of biomembranes, namely the adaptivity of the grid to resolve the sharp features of the phase-field, and the stiffness of the equations, leading to very small time-steps. In our method, local refinement follows the features of the phase-field as both are advected by the Lagrangian motion, and large time-steps can be robustly chosen in the variational time-stepping algorithm, which also lends itself to time adaptivity. The method is presented in the axisymmetric setting, but it can be directly extended to 3D.
Abstract
We present a Lagrangian phase-field method to study the low Reynolds number dynamics of vesicles embedded in a viscous fluid. In contrast to previous approaches, where the [...]
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Blending isogeometric analysis and local maximum entropy meshfree approximants
A. Rosolen, M. Arroyo

Comput. Methods Appl. Mech. Engrg., (2013). Vol. 264, pp. 95-107 (preprint)

Abstract
We present a method to blend local maximum entropy (LME) meshfree approximants and isogeometric analysis. The coupling strategy exploits the optimization program behind LME approximation, treats isogeometric and LME basis functions on an equal footing in the reproducibility constraints, but views the former as data in the constrained minimization. The resulting scheme exploits the best features and overcomes the main drawbacks of each of these approximants. Indeed, it preserves the high fidelity boundary representation (exact CAD geometry) of isogeometric analysis, out of reach for bare meshfree methods, and easily handles volume discretization and unstructured grids with possibly local refinement, while maintaining the smoothness and non-negativity of the basis functions. We implement the method with B-Splines in two dimensions, but the procedure carries over to higher spatial dimensions or to other non-negative approximants such as NURBS or subdivision schemes. The performance of the method is illustrated with the heat equation, and linear and nonlinear elasticity. The ability of the proposed method to impose directly essential boundary conditions in non-convex domains, and to deal with unstructured grids and local refinement in domains of complex geometry and topology is highlighted by the numerical examples.
Abstract
We present a method to blend local maximum entropy (LME) meshfree approximants and isogeometric analysis. The coupling strategy exploits the optimization program behind LME [...]
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An adaptive meshfree method for phase-field models of biomembranes. Part I: Approximation with maximum-entropy basis functions
A. Rosolen, C. Peco, M. Arroyo

Journal of Computational Physics (2013). Vol. 249 (15), pp. 303-319 (Preprint)

Abstract
We present an adaptive meshfree method to approximate phase-field models of biomembranes. In such models, the Helfrich curvature elastic energy, the surface area, and the enclosed volume of a vesicle are written as functionals of a continuous phase-field, which describes the interface in a smeared manner. Such functionals involve up to second-order spatial derivatives of the phase-field, leading to fourth-order Euler–Lagrange partial differential equations (PDE). The solutions develop sharp internal layers in the vicinity of the putative interface, and are nearly constant elsewhere. Thanks to the smoothness of the local maximum-entropy (max-ent) meshfree basis functions, we approximate numerically this high-order phase-field model with a direct Ritz–Galerkin method. The flexibility of the meshfree method allows us to easily adapt the grid to resolve the sharp features of the solutions. Thus, the proposed approach is more efficient than common tensor product methods (e.g. finite differences or spectral methods), and simpler than unstructured Cº finite element methods, applicable by reformulating the model as a system of second-order PDE. The proposed method, implemented here under the assumption of axisymmetry, allows us to show numerical evidence of convergence of the phase-field solutions to the sharp interface limit as the regularization parameter approaches zero. In a companion paper, we present a Lagrangian method based on the approximants analyzed here to study the dynamics of vesicles embedded in a viscous fluid. We present an adaptive meshfree method to approximate phase-field models of biomembranes. In such models, the Helfrich curvature elastic energy, the surface area, and the enclosed volume of a vesicle are written as functionals of a continuous phase-field, which describes the interface in a smeared manner. Such functionals involve up to second-order spatial derivatives of the phase-field, leading to fourth-order Euler–Lagrange partial differential equations (PDE). The solutions develop sharp internal layers in the vicinity of the putative interface, and are nearly constant elsewhere. Thanks to the smoothness of the local maximum-entropy (max-ent) meshfree basis functions, we approximate numerically this high-order phase-field model with a direct Ritz–Galerkin method. The flexibility of the meshfree method allows us to easily adapt the grid to resolve the sharp features of the solutions. Thus, the proposed approach is more efficient than common tensor product methods (e.g. finite differences or spectral methods), and simpler than unstructured C0C0 finite element methods, applicable by reformulating the model as a system of second-order PDE. The proposed method, implemented here under the assumption of axisymmetry, allows us to show numerical evidence of convergence of the phase-field solutions to the sharp interface limit as the regularization parameter approaches zero. In a companion paper, we present a Lagrangian method based on the approximants analyzed here to study the dynamics of vesicles embedded in a viscous fluid.
Abstract
We present an adaptive meshfree method to approximate phase-field models of biomembranes. In such models, the Helfrich curvature elastic energy, the surface area, and the [...]
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Curved fluid membranes behave laterally as an effective viscoelastic medium
M. Rahimi, A. DeSimone, M. Arroyo

Soft Matter (2013). Vol. 9, pp. 11033-11045 (Preprint)

Abstract
The lateral mobility of membrane inclusions is essential in biological processes involving membrane-bound macromolecules, which often take place in highly curved geometries such as membrane tubes or small organelles. Probe mobility is assisted by the lateral fluidity, which is thought to be purely viscous for lipid bilayers and synthetic systems such as polymersomes. In previous theoretical studies, the hydrodynamical mobility is estimated assuming a fixed membrane geometry. However, fluid membranes are very flexible out-of-plane. By accounting for the deformability of the membrane and in the presence of curvature, we show that the lateral motion of an inclusion produces a normal force, which results in a nonuniform membrane deformation. Such a deformation mobilizes the bending elasticity, produces extra lateral viscous and elastic forces, and results in an effective lateral viscoelastic behavior. The coupling between lateral and out-of-plane mechanics is mediated by the interfacial hydrodynamics and curvature. We analyze the frequency and curvature dependent rheology of flexible fluid membranes, and interpret it with a simple four-element model, which provides a background for microrheological experiments. Two key technical aspects of the present work are a new formulation for the interfacial hydrodynamics, and the linearization of the governing equations around a cylindrical geometry.
Abstract
The lateral mobility of membrane inclusions is essential in biological processes involving membrane-bound macromolecules, which often take place in highly curved geometries [...]
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Adhesion and friction control localized folding in supported graphene
K. Zhang, M. Arroyo

Journal of Applied Physics (2013). Vol. 113 (19), pp. 193501-1/193501-8 (Preprint)

Abstract
Graphene deposited on planar surfaces often exhibits sharp and localized folds delimiting seemingly planar regions, as a result of compressive stresses transmitted by the substrate. Such folds alter the electronic and chemical properties of graphene, and therefore, it is important to understand their emergence, to either suppress them or control their morphology. Here, we study the emergence of out-of-plane deformations in supported and laterally strained graphene with high-fidelity simulations and a simpler theoretical model. We characterize the onset of buckling and the nonlinear behavior after the instability in terms of the adhesion and frictional material parameters of the graphene-substrate interface. We find that localized folds evolve from a distributed wrinkling linear instability due to the nonlinearity in the van der Waals graphene-substrate interactions. We identify friction as a selection mechanism for the separation between folds, as the formation of far apart folds is penalized by the work of friction. Our systematic analysis is a first step towards strain engineering of supported graphene, and is applicable to other compressed thin elastic films weakly coupled to a substrate.
Abstract
Graphene deposited on planar surfaces often exhibits sharp and localized folds delimiting seemingly planar regions, as a result of compressive stresses transmitted by the [...]
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Second order convex maximum entropy approximants with applications to high order PDE
A. Rosolen, D. Millán, M. Arroyo

Int. J. Numer. Meth. Engng. (2013). Vol. 94 (2), pp. 150-182 (Preprint)

Abstract
We present a new approach for second order maximum entropy (max-ent) meshfree approximants that produces positive and smooth basis functions of uniform aspect ratio even for non-uniform node sets, and prescribes robustly feasible constraints for the entropy maximization program defining the approximants. We examine the performance of the proposed approximation scheme in the numerical solution by a direct Galerkin method of a number of partial differential equations (PDEs), including structural vibrations, elliptic second order PDEs, and fourth order PDEs for Kirchhoff-Love thin shells and for a phase field model describing the mechanics of biomembranes. The examples highlight the ability of the method to deal with non-uniform node distributions, and the high accuracy of the solutions. Surprisingly, the first order meshfree max-ent approximants with large supports are competitive when compared to the proposed second order approach in all the tested examples, even in the higher order PDEs.
Abstract
We present a new approach for second order maximum entropy (max-ent) meshfree approximants that produces positive and smooth basis functions of uniform aspect ratio even for [...]
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Nonlinear manifold learning for meshfree finite deformation thin shell analysis
D. Millán, M. Arroyo, A. Rosolen

Int. J. Numer. Meth. Engng. (2013). Vol. 93 (7), pp. 685-713 (Preprint)

Abstract
Calculations on general point-set surfaces are attractive because of their flexibility and simplicity in the preprocessing but present important challenges. The absence of a mesh makes it nontrivial to decide if two neighboring points in the three-dimensional embedding are nearby or rather far apart on the manifold. Furthermore, the topology of surfaces is generally not that of an open two-dimensional set, ruling out global parametrizations. We propose a general and simple numerical method analogous to the mathematical theory of manifolds, in which the point-set surface is described by a set of overlapping charts forming a complete atlas. We proceed in four steps: (1) partitioning of the node set into subregions of trivial topology; (2) automatic detection of the geometric structure of the surface patches by nonlinear dimensionality reduction methods; (3) parametrization of the surface using smooth meshfree (here maximum-entropy ) approximants; and (4) gluing together the patch representations by means of a partition of unity. Each patch may be viewed as a meshfree macro-element. We exemplify the generality, flexibility, and accuracy of the proposed approach by numerically approximating the geometrically nonlinear Kirchhoff–Love theory of thin-shells. We analyze standard benchmark tests as well as point-set surfaces of complex geometry and topology.
Abstract
Calculations on general point-set surfaces are attractive because of their flexibility and simplicity in the preprocessing but present important challenges. The absence of [...]
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Confined bilayers passively regulate shape and stress
M. Staykova, M. Arroyo, M. Rahimi, H. Stone

Physical review letters (2013). Vol. 110 (2), pp. 1-5 (Preprint)

Abstract
Lipid membranes are commonly confined to adjacent subcellular structures or to artificial substrates and particles. We develop an experimental and theoretical framework to investigate the mechanics of confined membranes, including the influence of adhesion, strain, and osmotic pressure. We find that supported lipid bilayers respond to stress by nucleating and evolving spherical and tubular protrusions. In cells, such transformations are generally attributed to proteins. Our results offer insights into the mechanics of cell membranes and can further extend the applications of supported bilayers.
Abstract
Lipid membranes are commonly confined to adjacent subcellular structures or to artificial substrates and particles. We develop an experimental and theoretical framework to [...]
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An atomistic-based foliation model for multilayer graphene materials and nanotubes
M. Arroyo

Journal of the Mechanics and Physics of Solids (2013). Vol. 61 (1), pp. 235-253 (preprint)

Abstract
We present a three-dimensional continuum model for layered crystalline materials made out of weakly interacting two-dimensional crystalline sheets. We specialize the model to multilayer graphene materials, including multi-walled carbon nanotubes (MWCNTs). We view the material as a foliation, partitioning of space into a continuous stack of leaves, thus loosing track of the location of the individual graphene layers. The constitutive model for the bulk is derived from the atomistic interactions by appropriate kinematic assumptions, adapted to the foliation structure and mechanics. In particular, the elastic energy along the leaves of the foliation results from the bonded interactions, while the interaction energy between the walls, resulting from van der Waals forces, is parametrized with a stretch transversal to the foliation. The resulting theory is distinct from conventional anisotropic models, and can be readily discretized with finite elements. The discretization is not tied to the individual walls and allows us to coarse-grain the system in all directions. Furthermore, the evaluation of the non-bonded interactions becomes local. We test the accuracy of the foliation model against a previously proposed atomistic-based continuum model that explicitly describes each and every wall. We find that the new model is very efficient and accurate. Furthermore, it allows us to rationalize the rippling deformation modes characteristic of thick MWCNTs, highlighting the role of the van der Waals forces and the sliding between the walls. By exercising the model with very large systems of hollow MWCNTs and suspended multilayer graphene, containing up to 109 atoms, we find new complex post-buckling deformation patterns.
Abstract
We present a three-dimensional continuum model for layered crystalline materials made out of weakly interacting two-dimensional crystalline sheets. We specialize the model [...]
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Modeling and enhanced sampling of molecular systems with smooth and nonlinear data-driven collective variables
B. Hashemian, D. Millán, M. Arroyo

Journal of chemical physics (2013). Vol. 139, pp. 214101/214101-12

Abstract
Collective variables (CVs) are low-dimensional representations of the state of a complex system, which help us rationalize molecular conformations and sample free energy landscapes with molecular dynamics simulations. Given their importance, there is need for systematic methods that effectively identify CVs for complex systems. In recent years, nonlinear manifold learning has shown its ability to automatically characterize molecular collective behavior. Unfortunately, these methods fail to provide a differentiable function mapping high-dimensional configurations to their low-dimensional representation, as required in enhanced sampling methods. We introduce a methodology that, starting from an ensemble representative of molecular flexibility, builds smooth and nonlinear data-driven collective variables (SandCV) from the output of nonlinear manifold learning algorithms. We demonstrate the method with a standard benchmark molecule, alanine dipeptide, and show how it can be non-intrusively combined with off-the-shelf enhanced sampling methods, here the adaptive biasing force method. We illustrate how enhanced sampling simulations with SandCV can explore regions that were poorly sampled in the original molecular ensemble. We further explore the transferability of SandCV from a simpler system, alanine dipeptide in vacuum, to a more complex system, alanine dipeptide in explicit water.
Abstract
Collective variables (CVs) are low-dimensional representations of the state of a complex system, which help us rationalize molecular conformations and sample free energy landscapes [...]
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Nonlinear manifold learning for model reduction in finite elastodynamics
D. Zurita, M. Arroyo

Comput. Methods Appl. Mech. Engrg., (2013). Vol. 261-262, pp. 118-131 (preprint)

Abstract
Model reduction in computational mechanics is generally addressed with linear dimensionality reduction methods such as Principal Components Analysis (PCA). Hypothesizing that in many applications of interest the essential dynamics evolve on a nonlinear manifold, we explore here reduced order modeling based on nonlinear dimen- sionality reduction methods. Such methods are gaining popularity in diverse fields of science and technology, such as machine perception or molecular simulation. We consider finite deformation elastodynamics as a model problem, and identify the manifold where the dynamics essentially take place –the slow manifold– by nonlinear dimensionality reduction methods applied to a database of snapshots. Contrary to linear dimensionality reduction, the smooth parametrization of the slow manifold needs special techniques, and we use local maximum entropy approximants. We then formulate the Lagrangian mechanics on these data-based generalized coordinates, and de- velop variational time-integrators. Our proof-of-concept example shows that a few nonlinear collective variables provide similar accuracy to tens of PCA modes, suggesting that the proposed method may be very attractive in control or optimization applications. Furthermore, the reduced number of variables brings insight into the me- chanics of the system under scrutiny. Our simulations also highlight the need of modeling the net e ¿ ect of the disregarded degrees of freedom on the reduced dynamics at long times.
Abstract
Model reduction in computational mechanics is generally addressed with linear dimensionality reduction methods such as Principal Components Analysis (PCA). Hypothesizing that [...]
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Reverse engineering the euglenoid movement
M. Arroyo, L. Heltai, D. Millán, A. DeSimone

Proceedings of the National Academy of Sciences of the United States of America (2012). Vol. 109 (44), pp. 17874-17879

Abstract
Euglenids exhibit an unconventional motility strategy amongst unicellular eukaryotes, consisting of large-amplitude highly concerted deformations of the entire body (euglenoid movement or metaboly). A plastic cell envelope called pellicle mediates these deformations. Unlike ciliary or flagellar motility, the biophysics of this mode is not well understood, including its efficiency and molecular machinery. We quantitatively examine video recordings of four euglenids executing such motions with statistical learning methods. This analysis reveals strokes of high uniformity in shape and pace. We then interpret the observations in the light of a theory for the pellicle kinematics, providing a precise understanding of the link between local actuation by pellicle shear and shape control. We systematically understand common observations, such as the helical conformations of the pellicle, and identify previously unnoticed features of metaboly. While two of our euglenids execute their stroke at constant body volume, the other two exhibit deviations of about 20% from their average volume, challenging current models of low Reynolds number locomotion. We find that the active pellicle shear deformations causing shape changes can reach 340%, and estimate the velocity of the molecular motors. Moreover, we find that metaboly accomplishes locomotion at hydrodynamic efficiencies comparable to those of ciliates and flagellates. Our results suggest new quantitative experiments, provide insight into the evolutionary history of euglenids, and suggest that the pellicle may serve as a model for engineered active surfaces with applications in microfluidics.
Abstract
Euglenids exhibit an unconventional motility strategy amongst unicellular eukaryotes, consisting of large-amplitude highly concerted deformations of the entire body (euglenoid [...]
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Shape dynamics, lipid hydrodynamics, and the complex viscoelasticity of bilayer membranes
M. Rahimi, M. Arroyo

Physical review E: statistical, nonlinear and soft matter physics (2012). Vol. 86 (1), pp. 1-15

Abstract
Biological membranes are continuously brought out of equilibrium, as they shape organelles, package and transport cargo, or respond to external actions. Even the dynamics of plain lipid membranes in experimental model systems are very complex due to the tight interplay between the bilayer architecture, the shape dynamics, and the rearrangement of the lipid molecules. We formulate and numerically implement a continuum model of the shape dynamics and lipid hydrodynamics, which describes the bilayer by its midsurface and by a lipid density field for each monolayer. The viscoelastic response of bilayers is determined by the stretching and curvature elasticity, and by the inter-monolayer friction and the membrane interfacial shear viscosity. While the bilayer equilibria are well understood theoretically, dynamical calculations have relied on simplified continuum approaches of uncertain transferability, or on molecular simulations reaching very limited length and time scales. Our approach incorporates the main physics, is fully nonlinear, does not assume predefined shapes, and can access a wide range of time and length scales. We validate it with the well understood tether extension. We investigate the tubular lipid transport between cells, the dynamics of bud absorption by a planar membrane, and the fate of a localized lipid density asymmetry in vesicles. These axisymmetric examples bear biological relevance and highlight the diversity of dynamical regimes that bilayers can experience.
Abstract
Biological membranes are continuously brought out of equilibrium, as they shape organelles, package and transport cargo, or respond to external actions. Even the dynamics [...]
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Thin-shell theory based analysis of radially pressurized multiwall carbon nanotubes
H. Shima, M. Arroyo, K. Iiboshi, M. Sato

Computational Materials Science (2012). Vol. 52 (1), pp. 90-94

Abstract
The radial deformation of multiwall carbon nanotubes (MWNTs) under hydrostatic pressure is investi gated within the continuum elastic approximation. A thin shell theory, with accurate elastic constants and interwall couplings, allows us to estimate the critical pressure above which the original circular cross section transforms into radially corrugated ones. The emphasis is placed on the rigorous formula tion of the van der Waals interaction between adjacent walls, which we analyze using two different approaches. Possible consequences of the radial corrugation in the physical properties of pressurized MWNTs are also discussed.
Abstract
The radial deformation of multiwall carbon nanotubes (MWNTs) under hydrostatic pressure is investi gated within the continuum elastic approximation. A thin shell theory, with [...]
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Thin shell analysis from scattered points with maximum-entropy approximants
D. Milan, A. Rosolen, M. Arroyo

Int. J. Numer. Meth. Engng. (2011). Vol. 85 (6), pp. 723-751

Abstract
We present a method to process embedded smooth manifolds using sets of points alone. This method avoids any global parameterization and hence is applicable to surfaces of any genus. It combines three ingredients: (1) the automatic detection of the local geometric structure of the manifold by statistical learning methods; (2) the local parameterization of the surface using smooth meshfree (here maximum-entropy) approximants; and (3) patching together the local representations by means of a partition of unity. Mesh-based methods can deal with surfaces of complex topology, since they rely on the element-level parameterizations, but cannot handle high-dimensional manifolds, whereas previous meshfree methods for thin shells consider a global parametric domain, which seriously limits the kinds of surfaces that can be treated. We present the implementation of the method in the context of Kirchhoff–Love shells, but it is applicable to other calculations on manifolds in any dimension. With the smooth approximants, this fourth-order partial differential equation is treated directly. We show the good performance of the method on the basis of the classical obstacle course. Additional calculations exemplify the flexibility of the proposed approach in treating surfaces of complex topology and geometry.
Abstract
We present a method to process embedded smooth manifolds using sets of points alone. This method avoids any global parameterization and hence is applicable to surfaces of [...]
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On the optimum support size in meshfree methods: a variational adaptivity approach with maximum-entropy approximants
D. Millán, A. Rosolen, M. Arroyo

Int. J. Numer. Meth. Engng. (2010). Vol. 82 (7), pp. 868-895

Abstract
We present a method for the automatic adaption of the support size of meshfree basis functions in the context of the numerical approximation of boundary value problems stemming from a minimum principle. The method is based on a variational approach, and the central idea is that the variational principle selects both the discretized physical fields and the discretization parameters, here those defining the support size of each basis function. We consider local maximum-entropy approximation schemes, which exhibit smooth basis functions with respect to both space and the discretization parameters (the node location and the locality parameters). We illustrate by the Poisson, linear and non-linear elasticity problems the effectivity of the method, which produces very accurate solutions with very coarse discretizations and finds unexpected patterns of the support size of the shape functions.
Abstract
We present a method for the automatic adaption of the support size of meshfree basis functions in the context of the numerical approximation of boundary value problems stemming [...]
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Diverse corrugation pattern in radially shrinking carbon nanotubes
H. Shima, M. Sato, K. Iiboshi, S. Ghosh, M. Arroyo

Physical review B: condensed matter and material physics (2010). Vol. 82 (8), pp. 085401

Abstract
Stable cross sections of multiwalled carbon nanotubes subjected to electron-beam irradiation are investigated in the realm of the continuum mechanics approximation. The self-healing nature of sp2 graphitic sheets implies that selective irradiation of the outermost walls causes their radial shrinkage with the remaining inner walls undamaged. The shrinking walls exert high pressure on the interior part of nanotubes, yielding a wide variety of radial-corrugation patterns (i.e. circumferentially wrinkling structures) in the cross section. All corrugation patterns can be classified into two deformation phases for which the corrugation amplitudes of the innermost wall differ significantly.
Abstract
Stable cross sections of multiwalled carbon nanotubes subjected to electron-beam irradiation are investigated in the realm of the continuum mechanics approximation. The self-healing [...]
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Elastic bending modulus of monolayer graphene
Q. Lu, M. Arroyo, R. Huang

Journal of physics D: Applied physics (2009). Vol. 42 (10), pp. 1-6

Abstract
An analytic formula is derived for the elastic bending modulus of monolayer graphene based on an empirical potential for solid-state carbon atoms. Two physical origins are identified for the non-vanishing bending stiffness of the atomically thin graphene sheet, one due to the bond-angle effect and the other resulting from the bond-order term associated with the dihedral angles. The analytical prediction compares closely with ab initio energy calculations. Pure bending of graphene monolayers into cylindrical tubes is simulated by a molecular mechanics approach, showing slight nonlinearity and anisotropy in the tangent bending modulus as the bending curvature increases. An intrinsic coupling between bending and in-plane strain is noted for graphene monolayers rolled into carbon nanotubes.
Abstract
An analytic formula is derived for the elastic bending modulus of monolayer graphene based on an empirical potential for solid-state carbon atoms. Two physical origins are [...]
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Smooth, second order, non-negative meshfree approximants selected by maximum entropy
C. Cyron, M. Arroyo, M. Ortiz

Int. J. Numer. Meth. Engng. (2009). Vol. 79 (13), pp. 1605-1632

Abstract
We present a family of approximation schemes, which we refer to as second-order maximum-entropy (max-ent) approximation schemes, that extends the first-order local max-ent approximation schemes to second-order consistency. This method retains the fundamental properties of first-order max-ent schemes, namely the shape functions are smooth, non-negative, and satisfy a weak Kronecker-delta property at the boundary. This last property makes the imposition of essential boundary conditions in the numerical solution of partial differential equations trivial. The evaluation of the shape functions is not explicit, but it is very efficient and robust. To our knowledge, the proposed method is the first higher-order scheme for function approximation from unstructured data in arbitrary dimensions with non-negative shape functions. As a consequence, the approximants exhibit variation diminishing properties, as well as an excellent behavior in structural vibrations problems as compared with the Lagrange finite elements, MLS-based meshfree methods and even B-Spline approximations, as shown through numerical experiments. When compared with usual MLS-based second-order meshfree methods, the shape functions presented here are much easier to integrate in a Galerkin approach, as illustrated by the standard benchmark problems.
Abstract
We present a family of approximation schemes, which we refer to as second-order maximum-entropy (max-ent) approximation schemes, that extends the first-order local max-ent [...]
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Relaxation dynamics of fluid membranes
M. Arroyo, A. DeSimone

Physical review E: statistical, nonlinear and soft matter physics (2009). Vol. 79 (3), pp. 031915-1/031915-17

Abstract
We study the effect of membrane viscosity in the dynamics of liquid membranes{possibly with free or internal boundaries{ driven by conservative forces (curvature elasticity and line tension) and dragged by the bulk dissipation of the ambient fluid and the friction occurring when the amphiphilic molecules move relative to each other. To this end, we formulate a continuum model which includes a new form of the governing equations for a two-dimensional viscous fluid moving on a curved, time-evolving surface. The effect of membrane viscosity has received very limited attention in previous continuum studies of the dynamics of fluid membranes, although recent coarse-grained discrete simulations suggest its importance. By applying our model to the study of vesiculation and membrane fusion in a simpli ed geometry, we conclude that membrane viscosity plays a dominant role in the relaxation dynamics of fluid membranes of sizes comparable to those found in eukaryotic cells, and is not negligible in many large synthetic systems of current interest.
Abstract
We study the effect of membrane viscosity in the dynamics of liquid membranes{possibly with free or internal boundaries{ driven by conservative forces (curvature elasticity [...]
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Effective coarse-grained simulations of super-thick multi-walled carbon nanotubes under torsion
Z. Jian, X. Huang, M. Arroyo, S. Zhang

Journal of Applied Physics (2009). Vol. 105 (3), pp. 33516/33516-8

Abstract
Under torsion and beyond the buckling point, multi-walled carbon nanotubes (MWCNTs) develop a periodic wave-like rippling morphology. Here, we show that torsional rippling deformations can be accurately described by a simple sinusoidal shape function. Combining this observation with the geometry optimization, we develop an effective coarse-grained model that reproduces the complex nonlinear mechanical responses of thick MWCNTs under torsion predicted by large-scale atomistic simulations. Furthermore, the model allows us to simulate super-thick tubes, inaccessible by other coarse-grained methods. With this effective coarse-grained model, we show from an energetic analysis that the rippling deformation is a result of in-plane strain energy relaxation, penalized by the increase in the interlayer van der Waals interaction energy. Our simulations reveal that the torsional response of MWCNTs with up to 100 layers approximately follows a simple bilinear law, and the ratio of the torsional rigidities in the pre- and post-buckling regimes is nearly a constant, independent of the tube radius. In contrast, the bifurcation torsional strain powerly scales with the tube radius. We also find that the wave number in the circumferential direction linearly increases with tube radius, while the wavelength monotonically increases with tube radius, and approaches a constant in the limit of bulk graphite. The bilinear constitutive relation, together with the scaling law of the bifurcation torsional strain, furnishes a simple nonlinear beam theory, which facilitates the analysis of MWCNT bundles and networks.
Abstract
Under torsion and beyond the buckling point, multi-walled carbon nanotubes (MWCNTs) develop a periodic wave-like rippling morphology. Here, we show that torsional rippling [...]
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Optimization of a novel micro-opto-X-ray imaging lens
H. Ostadi, M. Arroyo, P. Prewett, K. Jiang, S. Huq

Microelestronic engineering (2008). Vol. 85 (5-6), pp. 1086-1088

Abstract
A mechanically deformable reflection transmission MOEMS system is capable of focusing X-rays to sub micron spots. This paper considers the geometry of the proposed deformed slotted microcantilever lens element under thermally derived strain, using finite element analysis. The work shows that an optimized MOEMS design using a slotted polyimide/gold thermal bimorph cantilever is capable of achieving ideal geometry with a larger than expected number of focusing slots – up to 111 at 2 μm width.
Abstract
A mechanically deformable reflection transmission MOEMS system is capable of focusing X-rays to sub micron spots. This paper considers the geometry of the proposed deformed [...]
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Rippling and a phase-transforming mesoscopic model for multiwalled carbon nanotubes
M. Arroyo, I. Arias

Journal of the Mechanics and Physics of Solids (2008). Vol. 56 (4), pp. 1124-1244

Abstract
We propose to model thick multiwalled carbon nanotubes as beams with non-convex curvature energy. Such models develop stressed phase mixtures composed of smoothly bent sections and rippled sections. This model is motivated by experimental observations and large-scale atomistic-based simulations. The model is analyzed, validated against large-scale simulations, and exercised in examples of interest. It is shown that modelling MWCNTs as linear elastic beams can result in poor approximations that overestimate the elastic restoring force considerably, particularly for thick tubes. In contrast, the proposed model produces very accurate predictions both of the restoring force and of the phase pattern. The size effect in the bending response of MWCNTs is also discussed.
Abstract
We propose to model thick multiwalled carbon nanotubes as beams with non-convex curvature energy. Such models develop stressed phase mixtures composed of smoothly bent sections [...]
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Size-dependent nonlinear elastic scaling of multiwalled carbon nanotubes
I. Arias, M. Arroyo

Physical review letters (2008). Vol. 100 (8), pp. 085503-1/085503-4

Abstract
We characterize through large-scale simulations the nonlinear elastic response of multi-walled carbon nanotubes (MWNCNTs) in torsion and bending. We identify a unified law consisting of two distinct power-law regimes in the energy-deformation relation. This law encapsulates the complex mechanics of rippling and is described in terms of elastic constants, a critical length-scale and an anharmonic energy-deformation exponent. The mechanical response of MWCNTs is found to be strongly size-dependent, in that the critical strain beyond which they behave nonlinearly scales as the inverse of their diameter. These predictions are consistent with available experimental observations.
Abstract
We characterize through large-scale simulations the nonlinear elastic response of multi-walled carbon nanotubes (MWNCNTs) in torsion and bending. We identify a unified law [...]
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List of publications of Aula CIMNE UPCT
L. Almunia

Repository of Aula CIMNE ETSINO (2020). 1

Abstract
List of publications of Aula CIMNE UPCT
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R&D Projects of Aula CIMNE UPCT
L. Almunia

Repository of Aula CIMNE ETSINO (2020). 2

Abstract
R&D Projects of Aula CIMNE UPCT
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On the geometric character of stress in continuum mechanics
E. Kanso, M. Arroyo, Y. Tong, J. Marsden, M. Desbrun

Zeitschrift für angewandte Mathematik und Physik (2007). Vol. 58 (5), pp. 843-856

Abstract
This paper shows that the stress field in the classical theory of continuum mechanics may be taken to be a covector-valued differential two-form. The balance laws and other fundamental laws of continuum mechanics may be neatly rewritten in terms of this geometric stress. A geometrically attractive and covariant derivation of the balance laws from the principle of energy balance in terms of this stress is presented.
Abstract
This paper shows that the stress field in the classical theory of continuum mechanics may be taken to be a covector-valued differential two-form. The balance laws and other [...]
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Prueba
H. Tabares-Ospina

Héctor Tabares-Ospina's personal collection (2020). 1

Abstract
This
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Active vibration control analysis in smart composite structures using ANSYS
A. Shakir, A. Saber

Rev. int. métodos numér. cálc. diseño ing. (2020). Vol. 36, (2), 26

Abstract
Piezoelectric Macro-Fiber Composite (MFC) utilization is increasing in engineering fields due to its strong actuation forces and high flexibility. In this paper, piezoelectric ( ) type (M8528-P1) patches are applied for active control of a cantilever composite beam. A linear coupled ﬁnite element model for piezoelectric MFC actuation of the composite beam was developed based on the APDL-ANSYS codes by using linear piezoelectric constitutive equations to study smart composite beam behavior in open and closed-loop cases. Active vibration control response of laminated composite beams with various stacking sequence configurations was examined, and the results were compared. In this, the proportional type (kp) of control algorithms is utilized, and in the summary of work refined two sets of finite element models. The first set their laminates to have an orientation (0 with 90), and others have an orientation (0 with 45). When the control signal applied with the gain (kp) to a system increases, the rise time generally decreases, the actuator voltages for different control gain for all cases are observed with the increase in the proportional constant. The findings of this study indicate that the composite beams composed from (0/90) stacking sequence sets had reached stability state faster than the composite beams composed from (0/45) stacking sequence sets.
Abstract
Piezoelectric Macro-Fiber Composite (MFC) utilization is increasing in engineering fields due to its strong actuation forces and high flexibility. In this paper, piezoelectric [...]
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Local maximum‐entropy approximation schemes: a seamless bridge between finite elements and meshfree methods
M. Arroyo, M. Ortiz

Int. J. Numer. Meth. Engng. (2006). Vol. 65 (13), pp. 2167-2202

Abstract
We present a one‐parameter family of approximation schemes, which we refer to as local maximum‐entropy approximation schemes, that bridges continuously two important limits: Delaunay triangulation and maximum‐entropy (max‐ent) statistical inference. Local max‐ent approximation schemes represent a compromise—in the sense of Pareto optimality—between the competing objectives of unbiased statistical inference from the nodal data and the definition of local shape functions of least width. Local max‐ent approximation schemes are entirely defined by the node set and the domain of analysis, and the shape functions are positive, interpolate affine functions exactly, and have a weak Kronecker‐delta property at the boundary. Local max‐ent approximation may be regarded as a regularization, or thermalization, of Delaunay triangulation which effectively resolves the degenerate cases resulting from the lack or uniqueness of the triangulation. Local max‐ent approximation schemes can be taken as a convenient basis for the numerical solution of PDEs in the style of meshfree Galerkin methods. In test cases characterized by smooth solutions we find that the accuracy of local max‐ent approximation schemes is vastly superior to that of finite elements.
Abstract
We present a one‐parameter family of approximation schemes, which we refer to as local maximum‐entropy approximation schemes, that bridges continuously two important [...]
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Continuum mechanics modeling and simulation of carbon nanotubes
M. Arroyo, T. Belytschko

Meccanica (2005). Vol. 40 (4-6), pp. 455-469

Abstract
The understanding of the mechanics of atomistic systems greatly benefits from continuum mechanics. One appealing approach aims at deductively constructing continuum theories starting from models of the interatomic interactions. This viewpoint has become extremely popular with the quasicontinuum method. The application of these ideas to carbon nanotubes presents a peculiarity with respect to usual crystalline materials: their structure relies on a two-dimensional curved lattice. This renders the cornerstone of crystal elasticity, the Cauchy–Born rule, insufficient to describe the effect of curvature. We discuss the application of a theory which corrects this deficiency to the mechanics of carbon nanotubes (CNTs). We review recent developments of this theory, which include the study of the convergence characteristics of the proposed continuum models to the parent atomistic models, as well as large scale simulations based on this theory. The latter have unveiled the complex nonlinear elastic response of thick multiwalled carbon nanotubes (MWCNTs), with an anomalous elastic regime following an almost absent harmonic range.
Abstract
The understanding of the mechanics of atomistic systems greatly benefits from continuum mechanics. One appealing approach aims at deductively constructing continuum theories [...]
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Finite crystal elasticity of carbon nanotubes based on the exponential Cauchy-Born rule
M. Arroyo, T. Belytschko

Physical review B: condensed matter and material physics (2004). Vol. 69 (11), pp. 115415-1, 115415-11

Abstract
A finite deformation continuum theory is derived from interatomic potentials for the analysis of the mechanics of carbon nanotubes. This nonlinear elastic theory is based on an extension of the Cauchy-Born rule called the exponential Cauchy-Born rule. The continuum object replacing the graphene sheet is a surface without thickness. The method systematically addresses both the characterization of the small strain elasticity of nanotubes and the simulation at large strains. Elastic moduli are explicitly expressed in terms of the functional form of the interatomic potential. The expression for the flexural stiffness of graphene sheets, which cannot be obtained from standard crystal elasticity, is derived. We also show that simulations with the continuum model combined with the finite element method agree very well with zero temperature atomistic calculations involving severe deformations.
Abstract
A finite deformation continuum theory is derived from interatomic potentials for the analysis of the mechanics of carbon nanotubes. This nonlinear elastic theory is based [...]
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Finite element methods for the non-linear mechanics of crystalline sheets and nanotubes
M. Arroyo, T. Belytschko

Int. J. Numer. Meth. Engng. (2004). Vol. 59 (3), pp. 419-456

Abstract
The formulation and finite element implementation of a finite deformation continuum theory for the mechanics of crystalline sheets is described. This theory generalizes standard crystal elasticity to curved monolayer lattices by means of the exponential Cauchy–Born rule. The constitutive model for a two‐dimensional continuum deforming in three dimensions (a surface) is written explicitly in terms of the underlying atomistic model. The resulting hyper‐elastic potential depends on the stretch and the curvature of the surface, as well as on internal elastic variables describing the rearrangements of the crystal within the unit cell. Coarse grained calculations of carbon nanotubes (CNTs) are performed by discretizing this continuum mechanics theory by finite elements. A smooth discrete representation of the surface is required, and subdivision finite elements, proposed for thin‐shell analysis, are used. A detailed set of numerical experiments, in which the continuum/finite element solutions are compared to the corresponding full atomistic calculations of CNTs, involving very large deformations and geometric instabilities, demonstrates the accuracy of the proposed approach. Simulations for large multi‐million systems illustrate the computational savings which can be achieved
Abstract
The formulation and finite element implementation of a finite deformation continuum theory for the mechanics of crystalline sheets is described. This theory generalizes standard [...]
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Nonlinear mechanical response and rippling of thick multi-walled carbon nanotubes
M. Arroyo, T. Belytschko

Physical review letters (2003). Vol. 91 (21), pp. 215505-1, 221505-4

Abstract
The measured drop of the effective bending stiffness of multiwalled carbon nanotubes (MWCNTs) with increasing diameter is investigated by a generalized local quasicontinuum method. The previous hypothesis that this reduction is due to a rippling mode is confirmed by the calculations. The observed ripples result from a complex three-dimensional deformation similar to theYoshimura buckling pattern. It is found that thick MWCNTs exhibit a well-defined nonlinear moment-curvature relation, even for small deformations, governed by the interplay of strain energy relaxation and intertube interactions. Rippling deformations are also predicted for MWCNTs subject to torsion, resulting in an effective torsional modulus much smaller than that predicted by linear elasticity.
Abstract
The measured drop of the effective bending stiffness of multiwalled carbon nanotubes (MWCNTs) with increasing diameter is investigated by a generalized local quasicontinuum [...]
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A finite deformation membrane based on inter-atomic potentials for the transverse mechanics of nanotubes
M. Arroyo, T. Belytschko

Mechanics of materials (2003). Vol. 35 (3-6), pp. 193-215

Abstract
A finite deformation hyper-elastic membrane theory based on inter-atomic potentials for crystalline films composed of a single atomic layer is developed. For this purpose, an extension of the standard Born rule that exploits the differential geometry concept of the exponential map is proposed to deal with the curvature of surfaces. The exponential map is approximated locally and strain measures based on the stretch and the curvature of the membrane arise. The methodology is first particularized to atomic chains in two dimensions, and then to graphene sheets. A reduced model for the transverse mechanics of carbon nanotubes is developed in detail. This model is a hyper-elastic constrained membrane which fully exploits the symmetry of the transverse deformation. Additionally, a continuum version of the non-bonded interactions is provided. The continuum model is discretized using finite elements and very good agreement with molecular mechanics simulations is obtained. Finally, several simulations illustrate the strong effect of the van der Waals interactions in the transverse deformation of carbon nanotubes.
Abstract
A finite deformation hyper-elastic membrane theory based on inter-atomic potentials for crystalline films composed of a single atomic layer is developed. For this purpose, [...]
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An atomistic-based finite deformation membrane for single layer crystalline films
M. Arroyo, T. Belytschko

Journal of the Mechanics and Physics of Solids (2002). Vol. 50 (9), pp. 1941-1977

Abstract
A general methodology to develop hyper-elastic membrane models applicable to crystalline films one-atom thick is presented. In this method, an extension of the Born rule based on the exponential map is proposed. The exponential map accounts for the fact that the lattice vectors of the crystal lie along the chords of the curved membrane, and consequently a tangent map like the standard Born rule is inadequate. In order to obtain practical methods, the exponential map is locally approximated. The effectiveness of our approach is demonstrated by numerical studies of carbon nanotubes. Deformed configurations as well as equilibrium energies of atomistic simulations are compared with those provided by the continuum membrane resulting from this method discretized by finite elements.
Abstract
A general methodology to develop hyper-elastic membrane models applicable to crystalline films one-atom thick is presented. In this method, an extension of the Born rule based [...]
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A generic finite element framework on parallel tree-based adaptive meshes
S. Badia, A. Martín, E. Neiva, F. Verdugo

(2019). Under review

Abstract
We present highly scalable parallel distributed-memory algorithms and associated data structures for a generic finite element framework that supports h-adaptivity on computational domains represented as multiple connected adaptive trees—forest-of-trees—, thus providing multi-scale resolution on problems governed by partial differential equations.The framework is grounded on a rich representation of the adaptive mesh suitable for generic finite elements that is built on top of a low-level, light-weight forest-oftrees data structure handled by a specialized, highly parallel adaptive meshing engine. Along the way, we have identified the requirements that the forest-of-trees layer must fulfill to be coupled into our framework. Essentially, it must be able to describe neighboring relationships between cells in the adapted mesh (apart from hierarchical relationships) across the lower-dimensional objects at the boundary of the cells. Atop this two-layered mesh representation, we build the rest of data structures required for the numerical integration and assembly of the discrete system of linear equations.We consider algorithms that are suitable for both subassembled and fully-assembled distributed data layouts of linear system matrices. The proposed framework has been implemented within the FEMPAR scientific software library, using p4est as a practical forest-of-octrees demonstrator. A comprehensive strong scaling study of this implementation when applied to Poisson and Maxwell problems reveals remarkable scalability up to 32.2K CPU cores and 482.2M degrees of freedom. Besides, the implementation in FEMPAR of the proposed approach is up to 2.6 and 3.4 times faster than the state-of-the-art deal.II finite element software in the h-adaptive approximation of a Poisson problem with firstand second-order Lagrangian finite elements, respectively (excluding the linear solver step from the comparison).
Abstract
We present highly scalable parallel distributed-memory algorithms and associated data structures for a generic finite element framework that supports h-adaptivity on computational [...]
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Embedded multilevel Monte Carlo for uncertainty quantification in random domains
S. Badia, J. Hampton, J. Principe

(2019). Under review

Abstract
The multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty quantification in PDE models. It combines approximations at different levels of accuracy using a hierarchy of meshes in a similar way as multigrid. The generation of body-fitted mesh hierarchies is only possible for simple geometries. On top of that, MLMC for random domains involves the generation of a mesh for every sample. Instead, here we consider the use of embedded methods which make use of simple background meshes of an artificial domain (a bounding-box) for which it is easy to define a mesh hierarchy, thus eliminating the need of body-fitted unstructured meshes, but can produce ill-conditioned discrete problems. To avoid this complication, we consider the recent aggregated finite element method (AgFEM). In particular, we design an embedded MLMC framework for (geometrically and topologically) random domains implicitly defined through a random level-set function, which makes use of a set of hierarchical background meshes and the AgFEM. Performance predictions from existing theory are verified statistically in three numerical experiments, namely the solution of the Poisson equation on a circular domain of random radius, the solution of the Poisson equation on a topologically identical but more complex domain, and the solution of a heat-transfer problem in a domain that has geometric and topological uncertainties. Finally, the use of AgFE is statistically demonstrated to be crucial for complex and uncertain geometries in terms of robustness and computational cost. Date: November 28, 2019.
Abstract
The multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty quantification in PDE models. It combines approximations [...]
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A modified Finite Element formulation for the imposition of the slip boundary condition over embedded volumeless geometries
R. Zorrilla, A. Larese, R. Rossi

Comput. Methods Appl. Mech. Engrg., (2019). (Preprint) Vol. 353, pp. 123-157

Abstract
This work describes a novel formulation for the simulation of Navier-Stokes problems including embedded objects. The new proposal is based on the use of a modified finite element space, which replaces the standard one within the elements intersected by the immersed geometry. The modified space is able to exactly reproduce the jumps happening at the embedded boundary while preserving the conformity across the faces intersected by the embedded object. The paper focuses particularly on the imposition of a slip boundary condition on the surface of the embedded geometry, proposing a new technique for the application of such constraint. The new proposal is carefully benchmarked using the results of a body fitted technique and of an alternative embedded approach. Potential applications of interest are also presented.
Abstract
This work describes a novel formulation for the simulation of Navier-Stokes problems including embedded objects. The new proposal is based on the use of a modified finite [...]
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Computational modeling of the fluid flow in type B aortic dissection using a modified finite element embedded formulation
R. Zorrilla, E. Soudah, R. Rossi

Biomechanics and Modeling in Mechanobiology (2020). (Preprint)

Abstract
This work explores the use of an embedded computational fluid dynamics method to study the type B aortic dissection. The use of the proposed technique makes it possible to easily test different intimal flap configurations without any need of remeshing. To validate the presented methodology, we take as reference test case an in vitro experiment present in the literature. This experiment, which considers several intimal flap tear configurations (number, size and location), mimics the blood flow in a real type B aortic dissection. We prove the correctness and suitability of the presented approach by comparing the pressure values and waveform. The obtained results exhibit a remarkable similarity with the experimental reference data. Complementary, we present a feasible surgical application of the presented computer method. The aim is to help the clinicians in the decision making before the type B aortic dissection surgical fenestration. The capabilities of the proposed technique are exploited to efficiently create artificial reentry tear configurations. We highlight that only the radius and center of the reentry tear need to be specified by the clinicians, without any need to modify neither the model geometry nor the mesh. The obtained computational surgical fenestration results are in line with the medical observations in similar clinical studies.
Abstract
This work explores the use of an embedded computational fluid dynamics method to study the type B aortic dissection. The use of the proposed technique makes it possible to [...]
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Parallel unstructured mesh adaptation using iterative remeshing and repartitioning
L. Cirrattola, A. Froehly

(2019). RR-9307, INRIA Bordeaux, équipe CARDAMOM

Abstract
Mesh adaptation has proven to be a powerful tool for increasing the accuracy ofnumerical simulations whenever the solution exhibits strong non-uniform features over the com-putational domain. Sequential remeshing currently represents a bottleneck for parallel solvers. Tothis aim, we present a parallel remeshing algorithm that enables the reuse of existing sequential remeshing libraries, a non-intrusive linkage with third-party solvers, and an efficient exploitationof distributed parallel environments. The numerical procedure is implemented in the open sourceParMmg software package.
Abstract
Mesh adaptation has proven to be a powerful tool for increasing the accuracy ofnumerical simulations whenever the solution exhibits strong non-uniform features over the com-putational [...]
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Balancing domain decomposition by constraints associated with subobjects
S. Badia, A. Martín, H. Nguyen

Applied Mathematics Letters (2019). (preprint) Vol. 87, pp. 93-100

Abstract
A simple variant of the BDDC preconditioner in which constraints are imposed on a selected set of subobjects (subdomain subedges, subfaces and vertices between pairs of subedges) is presented. We are able to show that the condition number of the preconditioner is bounded by C 1 + log(L/h)2, where C is a constant, and h and L are the characteristic sizes of the mesh and the subobjects, respectively. As L can be chosen almost freely, the condition number can theoretically be as small as O(1). We will discuss the pros and cons of the preconditioner and its application to heterogeneous problems. Numerical results on supercomputers are provided.
Abstract
A simple variant of the BDDC preconditioner in which constraints are imposed on a selected set of subobjects (subdomain subedges, subfaces and vertices between pairs of subedges) [...]
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Distributed-memory parallelization of the aggregated unfitted finite element method
F. Verdugo, A. Martín, S. Badia

Comput. Methods Appl. Mech. Engrg., (2019). (Preprint) Vol. 357, pp. 112583

Abstract
The aggregated unfitted finite element method (AgFEM) is a methodology recently introduced in order to address conditioning and stability problems associated with embedded, unfitted, or extended finite element methods. The method is based on removal of basis functions associated with badly cut cells by introducing carefully designed constraints, which results in well-posed systems of linear algebraic equations, while preserving the optimal approximation order of the underlying finite element spaces. The specific goal of this work is to present the implementation and performance of the method on distributed-memory platforms aiming at the efficient solution of large-scale problems. In particular, we show that, by considering AgFEM, the resulting systems of linear algebraic equations can be effectively solved using standard algebraic multigrid preconditioners. This is in contrast with previous works that consider highly customized preconditioners in order to allow one the usage of iterative solvers in combination with unfitted techniques. Another novelty with respect to the methods available in the literature is the problem sizes that can be handled with the proposed approach. While most of previous references discussing linear solvers for unfitted methods are based on serial non-scalable algorithms, we propose a parallel distributed-memory method able to efficiently solve problems at large scales. This is demonstrated by means of a weak scaling test defined on complex 3D domains up to 300M degrees of freedom and one billion cells on 16K CPU cores in the Marenostrum-IV platform. The parallel implementation of the AgFEM method is available in the large-scale finite element package FEMPAR.
Abstract
The aggregated unfitted finite element method (AgFEM) is a methodology recently introduced in order to address conditioning and stability problems associated with embedded, [...]
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The surrogate matrix methodology: A reference implementation for low-cost assembly in isogeometric analysis
D. Drzisga, B. Keith, B. Wohlmuth

(2019). Under review

Abstract
A reference implementation of a new method in isogeometric analysis (IGA) is presented. It delivers lowcost variable-scale approximations (surrogates) of the matrices which IGA conventionally requires to be computed by element-scale quadrature. To generate surrogate matrices, quadrature must only be performed on a fraction of the elements in the computational domain. In this way, quadrature determines only a subset of the entries in the final matrix. The remaining matrix entries are computed by a simple B-spline interpolation procedure. We present the modifications and extensions required for a reference implementation in the open-source IGA software library GeoPDEs. The exposition is fashioned to help facilitate similar modifications in other contemporary software libraries. Method name: Surrogate matrix method for isogeometric analysis
Abstract
A reference implementation of a new method in isogeometric analysis (IGA) is presented. It delivers lowcost variable-scale approximations (surrogates) of the matrices which [...]
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The surrogate matrix methodology: Low-cost assembly for isogeometric analysis
D. Drzisga, B. Keith, B. Wohlmuth

Computer Methods in Applied Mechanics and Engineering (2020). Vol. 361,1, 112776 (preprint)

Abstract
A new methodology in isogeometric analysis (IGA) is presented. This methodology delivers low-cost variable-scale approximations (surrogates) of the matrices which IGA conventionally requires to be computed from element-scale quadrature formulas. To generate surrogate matrices, quadrature must only be performed on certain elements in the computational domain. This, in turn, determines only a subset of the entries in the final matrix.The remaining matrix entries are computed by a simple B-spline interpolation procedure. Poisson’s equation, membrane vibration, plate bending, and Stokes’ flow problems are studied. In these problems, the use of surrogate matrices has a negligible impact on solution accuracy. Because only a small fraction of the original quadrature must be performed, we are able to report beyond a fifty-fold reduction in overall assembly time in the same software. The capacity for even further speed-ups is clearly demonstrated. The implementation used here was achieved by a small number of modifications to the open-source IGA software library GeoPDEs. Similar modifications could be made to other present-day software libraries.
Abstract
A new methodology in isogeometric analysis (IGA) is presented. This methodology delivers low-cost variable-scale approximations (surrogates) of the matrices which IGA conventionally [...]
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The surrogate matrix methodology: a priori error estimation
D. Drzisga, B. Keith, B. Wohlmuth

SIAM Journal on Scientific Computing (2019). Vol 41(6), pp. A3806–A3838 (preprint)

Abstract
We give the first mathematically rigorous analysis of an emerging approach to finite element analysis (see, e.g., Bauer et al. [Appl. Numer. Math., 2017]), which we hereby refer to as the surrogate matrix methodology. This methodology is based on the piece-wise smooth approximation of the matrices involved in a standard finite element discretization. In particular, it relies on the projection of smooth so-called stencil functions onto high-order polynomial subspaces. The performance advantage of the surrogate matrix methodology is seen in constructions where each stencil function uniquely determines the values of a significant collection of matrix entries. Such constructions are shown to be widely achievable through the use of locally-structured meshes. Therefore, this methodology can be applied to a wide variety of physically meaningful problems, including nonlinear problems and problems with curvilinear geometries. Rigorous a priori error analysis certifies the convergence of a novel surrogate method for the variable coefficient Poisson equation. The flexibility of the methodology is also demonstrated through the construction of novel methods for linear elasticity and nonlinear diffusion problems. In numerous numerical experiments, we demonstrate the efficacy of these new methods in a matrix-free environment with geometric multigrid solvers. In our experiments, up to a twenty-fold decrease in computation time is witnessed over the classical method with an otherwise identical implementation.
Abstract
We give the first mathematically rigorous analysis of an emerging approach to finite element analysis (see, e.g., Bauer et al. [Appl. Numer. Math., 2017]), which we hereby [...]
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AutoParallel: A Python module for automatic parallelization and distributed execution of affine loop nests
C. Ramon-Cortes, R. Amela, J. Ejarque, P. Clauss, R. Badia

(2020). Under review

Abstract
The last improvements in programming languages, programming models, and frameworks have focused on abstracting the users from many programming issues. Among others, recent programming frameworks include simpler syntax, automatic memory management and garbage collection, which simplifies code re-usage through library packages, and easily configurable tools for deployment. For instance, Python has risen to the top of the list of the programming languages due to the simplicity of its syntax, while still achieving a good performance even being an interpreted language. Moreover, the community has helped to develop a large number of libraries and modules, tuning them to obtain great performance. However, there is still room for improvement when preventing users from dealing directly with distributed and parallel computing issues. This paper proposes and evaluates AutoParallel, a Python module to automatically find an appropriate task-based parallelization of affine loop nests to execute them in parallel in a distributed computing infrastructure. This parallelization can also include the building of data blocks to increase task granularity in order to achieve a good execution performance. Moreover, AutoParallel is based on sequential programming and only contains a small annotation in the form of a Python decorator so that anyone with little programming skills can scale up an application to hundreds of cores.
Abstract
The last improvements in programming languages, programming models, and frameworks have focused on abstracting the users from many programming issues. Among others, recent [...]
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Quantitative investment model based on data mining
D. Wang

Rev. int. métodos numér. cálc. diseño ing. (2020). Vol. 36, (1), 22

Abstract
Quantitative investment is the process of establishing mathematical models using statistics, information technology, and mathematics to quantify and implement risks, returns, and traditional investment concepts. However, due to the backwardness of computing tools in the past, quantitative investment has not received much recognition. With the improvement of computer science and quantitative analysis theory, traditional fundamental analysis and the use of sampling statistical technology to build advanced mathematical models for investment analysis have failed to meet the requirements of investors. Therefore, the Quantitative investment strategies based on data mining technology are receiving more and more attention. In this paper, we uses MATLAB software to capture big data from financial and economic websites, and then uses neural network training models to predict the trend of stock changes, and finally establishes a suitable quantitative stock selection model. The simulation results show that only by using quantitative stock selection strategies to curb risks and selecting a suitable investment portfolio can achieve the ideal goals in the stock market.
Abstract
Quantitative investment is the process of establishing mathematical models using statistics, information technology, and mathematics to quantify and implement risks, returns, [...]
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Explicit finite deformation stress integration of the elasto-plastic constitutive equations
L. Monforte, M. Arroyo, A. Gens, J. Puigbó

(2014). Computer Methods and Recent Advances in Geomechanics - Proceedings of the 14th Int. Conference of International Association for Computer Methods and Recent Advances in Geomechanics, IACMAG 2014". Kyoto: CRC Press Taylor & Francis Group, p. 267-272.

Abstract
In this work, an explicit integration scheme for hyperelastic-based finite strains elasto-plasticity is presented. One step update equations are obtained from the large deformation multiplicative elasto-plasticity theory, where an exponential variation of the plastic deformation gradient is assumed. In addition, the material tangent matrix is presented and has the same formal structure as the usual small strains elasto-plastic tangent matrix. In purely elastic regime, the proposal reduces to the usual large deformation elasticity equations. Routines to alleviate the main drawbacks of explicit methods are outlined, such as a yield surface drift correction scheme and an adaptive substepping method. Several examples of typical geotechnical tests using the Houlsby hyperelastic model along with the Modified Cam Clay plastic model are discussed. Results from a convergence test suggest that, using an adaptive substepping scheme, the error of the local problem is independent of the step size.
Abstract
In this work, an explicit integration scheme for hyperelastic-based finite strains elasto-plasticity is presented. One step update equations are obtained from the large deformation [...]
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Evaluation of Multilayer Pavement Viscoelastic Properties from Falling Weight Deflectometer using Neural Networks
J. González, J. Puigbó, W. Bijsterveld

(2016). Chapters 16. In Materials and Infrastructures 1 (eds J.‐M. Torrenti and F. La Torre).

Abstract
The surface deflection caused by the falling weight deflectometer (FWD) is a dynamic problem usually treated as a static problem. This chapter presents a dynamic solution of the backcalculation problem using a viscoelastic model, introducing a viscosity variable. The calibration process is based on the numerical simulation of the FWD test to approximate the deflection curves obtained in the road track. Description of the experimental curves and the hypothesis of the numerical problem assumed are also described. The samples used to train and validate the artificial neural network (ANN) are conformed by four values per curve times the number of geophones, the input data, while the output data are five Young moduli and five viscosities. The backcalculation process is based on experimental tests from the FWD and calibrated using an FEM simulation of the problem.
Abstract
The surface deflection caused by the falling weight deflectometer (FWD) is a dynamic problem usually treated as a static problem. This chapter presents a dynamic solution [...]
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The particle finite element method (PFEM) in thermo‐mechanical problems
J. Rodríguez, J. Puigbó, J. Cante, J. Oliver

Int. J. Numer. Meth. Engng. (2015). (preprint) Vol. 107 (9), pp. 733-785

Abstract
The aim of this work is to develop a numerical framework for accurately and robustly simulating the different conditions exhibited by thermo‐mechanical problems. In particular, the work will focus on the analysis of problems involving large strains, rotations, multiple contacts, large boundary surface changes, and thermal effects. The framework of the numerical scheme is based on the particle finite element method (PFEM) in which the spatial domain is continuously redefined by a distinct nodal reconnection, generated by a Delaunay triangulation. In contrast to classical PFEM calculations, in which the free boundary is obtained by a geometrical procedure (α − shape method), in this work, the boundary is considered as a material surface, and the boundary nodes are removed or inserted by means of an error function. The description of the thermo‐mechanical constitutive model is based on the concepts of large strains plasticity. The plastic flow condition is assumed nearly incompressible, so a u‐p mixed formulation, with a stabilization of the pressure term via the polynomial pressure projection, is proposed. One of the novelties of this work is the use of a combination between the isothermal split and the so‐called IMPL‐EX hybrid integration technique to enhance the robustness and reduce the typical iteration number of the fully implicit Newton–Raphson solution algorithm. The new set of numerical tools implemented in the PFEM algorithm, including new discretization techniques, the use of a projection of the variables between meshes, and the insertion and removal of points allows us to eliminate the negative Jacobians present during large deformation problems, which is one of the drawbacks in the simulation of coupled thermo‐mechanical problems. Finally, two sets of numerical results in 2D are stated. In the first one, the behavior of the proposed locking‐free element type and different time integration schemes for thermo‐mechanical problems is analyzed. The potential of the method for modeling more complex coupled problems as metal cutting and metal forming processes is explored in the last example.
Abstract
The aim of this work is to develop a numerical framework for accurately and robustly simulating the different conditions exhibited by thermo‐mechanical problems. In particular, [...]
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Numerical simulation of undrained insertion problems in geotechnical engineering with the Particle Finite Element Method (PFEM)
L. Monforte, M. Arroyo, J. Puigbó, A. Gens

Computers and Geotechnics (2017). (preprint)Vol. 82, pp. 144-156

Abstract
The paper presents total-stress numerical analyses of large-displacement soil-structure interaction problems in geomechanics using the Particle Finite Element Method (PFEM). This method is characterized by frequent remeshing and the use of low order finite elements to evaluate the solution. Several important features of the method are: (i) a mixed formulation (displacement-mean pressure) stabilized numerically to alleviate the volumetric locking effects that are characteristic of low order elements when the medium is incompressible, (ii) a penalty method to prescribe the contact constraints between a rigid body and a deformable media combined with an implicit scheme to solve the tangential contact constraint, (iii) an explicit algorithm with adaptive substepping and correction of the yield surface drift to integrate the finite-strain multiplicative elasto-plastic constitutive relationship, and (iv) the mapping schemes to transfer information between successive discretizations. The performance of the method is demonstrated by several numerical examples, of increasing complexity, ranging from the insertion of a rigid strip footing to a rough cone penetration test. It is shown that the proposed method requires fewer computational resources than other numerical approaches addressing the same type of problems.
Abstract
The paper presents total-stress numerical analyses of large-displacement soil-structure interaction problems in geomechanics using the Particle Finite [...]
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Damage analysis of masonry structures subjected to rockfalls
O. Mavrouli, P. Giannopoulos, J. Puigbó, C. Syrmakezis

Landslides (2017). (preprint) Vol. 14 (3), pp. 891-904

Abstract
Masonry structures present substantial vulnerability to rockfalls. The methodologies for the damage quantification of masonry structures subjected to rockfalls are scarce. An analytical procedure for the damage assessment of masonry structures is presented. The procedure comprises three stages: (1) determination of the rockfall impact actions which are applied to a masonry structure, in terms of external forces, using the particle finite element method (PFEM), (2) evaluation of the mechanical properties, modelling of the masonry structure, and calculation of the internal stresses, using the finite element method (FEM), (3) assessment of the damage due to the rockfall actions, applying a failure criterion adapted to masonries, and calculation of the damage in terms of the percentage of the damaged wall surface. Three real rockfall events and their impact on buildings are analysed. A sensitivity analysis of the proposed procedure is then used to identify the variables that mostly affect the extent of the wall damage, which are the masonry width, the tensile strength, the block diameter and lastly, velocity.
Abstract
Masonry structures present substantial vulnerability to rockfalls. The methodologies for the damage quantification of masonry structures subjected to rockfalls are scarce. [...]
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Performance of mixed formulations for the particle finite element method in soil mechanics problems
L. Monforte, J. Puigbó, M. Arroyo, A. Gens

Comp. Part. Mech (2016). (Preprint) Vol. 4 (3), pp. 269-284

Abstract
This paper presents a computational framework for the numerical analysis of fluid-saturated porous media at large strains. The proposal relies, on one hand, on the particle finite element method (PFEM), known for its capability to tackle large deformations and rapid changing boundaries, and, on the other hand, on constitutive descriptions well established in current geotechnical analyses (Darcy’s law; Modified Cam Clay; Houlsby hyperelasticity). An important feature of this kind of problem is that incompressibility may arise either from undrained conditions or as a consequence of material behaviour; incompressibility may lead to volumetric locking of the low-order elements that are typically used in PFEM. In this work, two different three-field mixed formulations for the coupled hydromechanical problem are presented, in which either the effective pressure or the Jacobian are considered as nodal variables, in addition to the solid skeleton displacement and water pressure. Additionally, several mixed formulations are described for the simplified single-phase problem due to its formal similitude to the poromechanical case and its relevance in geotechnics, since it may approximate the saturated soil behaviour under undrained conditions. In order to use equal-order interpolants in displacements and scalar fields, stabilization techniques are used in the mass conservation equation of the biphasic medium and in the rest of scalar equations. Finally, all mixed formulations are assessed in some benchmark problems and their performances are compared. It is found that mixed formulations that have the Jacobian as a nodal variable perform better.
Abstract
This paper presents a computational framework for the numerical analysis of fluid-saturated porous media at large strains. The proposal relies, on one hand, on the particle [...]
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Continuous chip formation in metal cutting processes using the Particle Finite Element Method (PFEM)
J. Rodríguez, J. Puigbó, J. Cante, J. Oliver

Int. J. Solids and Structures (2017). Vol. 120, pp. 81-120

Abstract
This paper presents a study on the metal cutting simulation with a particular numerical technique, the Particle Finite Element Method (PFEM) with a new modified time integration algorithm and incorporating a contact algorithm capability . The goal is to reproduce the formation of continuous chip in orthogonal machining. The paper tells how metal cutting processes can be modelled with the PFEM and which new tools have been developed to provide the proper capabilities for a successful modelling. The developed method allows for the treatment of large deformations and heat conduction, workpiece-tool contact including friction effects as well as the full thermo-mechanical coupling for contact. The difficulties associated with the distortion of the mesh in areas with high deformation are solved introducing new improvements in the continuous Delaunay triangulation of the particles. The employment of adaptative insertion and removal of particles at every new updated configuration improves the mesh quality allowing for resolution of finer-scale features of the solution. The performance of the method is studied with a set of different two-dimensional tests of orthogonal machining. The examples consider, from the most simple case to the most complex case, different assumptions for the cutting conditions and different material properties. The results have been compared with experimental tests showing a good competitiveness of the PFEM in comparison with other available simulation tools.
Abstract
This paper presents a study on the metal cutting simulation with a particular numerical technique, the Particle Finite Element Method (PFEM) with a new modified time integration [...]
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Coronal advanced flap in combination with a connective tissue graft. Is the thickness of the flap a predictor for root coverage? A prospective clinical study
T. Garces-McIntyre, L. Vallcorba, A. Santos, C. Valles, J. Nart

Journal of Clinical Periodontology (2017). Vol. 44 (9), pp. 933-940

Abstract
Aim Evaluate if there is any relationship between the flap thickness (FT) and the presence of complete root coverage (CRC) when performing coronally advanced flaps in combination with a connective tissue graft (CTG). Materials and methods Prospective clinical study, in which multiple Miller class I and II recessions were treated with a coronally advanced flap and a CTG standardized at 1 mm of thickness. Individual stents permitted repeated measurements of conventional periodontal parameters at the same point. The primary outcome variable was CRC. Secondary outcomes were recession reduction, gingival thickness and width of keratinized tissue (KT) achieved at 6 months post‐surgery. Results Forty‐five recessions (2.4 ± 0.75 mm) were treated in 20 patients. Mean root coverage was 93.4 ± 10.98%; 65% achieved CRC. The mean FT was 1.01 mm ± 0.64 mm and 1.01 ± 0.61 mm at 2 and 5 mm from the gingival margin, respectively. No relationship could be found between FT and CRC (p > .05). Statistical significant changes (p < .05) were observed for recession depth, clinical attachment level, KT and soft tissue thickness at the end of the study. Conclusions Flap thickness seems not to be a predictor for CRC when performing a coronally advanced flap plus a CTG. This technique may be of choice when treating thin biotypes.
Abstract
Aim Evaluate if there is any relationship between the flap thickness (FT) and the presence of complete root coverage (CRC) when performing coronally advanced flaps in [...]
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