Documents published in 2020 : Scipedia

Locking in the incompressible limit for the element-free Galerkin method
A. Huerta, S. Fernández-Méndez

Int. J. Numer. Meth. Engng. (2001). Vol. 51 (11), pp. 1361-1383

Abstract
Volumetric locking (locking in the incompressible limit) for linear elastic isotropic materials is studied in the context of the element-free Galerkin method. The modal analysis developed here shows that the number of non-physical locking modes is independent of the dilation parameter (support of the interpolation functions). Thus increasing the dilation parameter does not suppress locking. Nevertheless, an increase in the dilation parameter does reduce the energy associated with the non-physical locking modes; thus, in part, it alleviates the locking phenomena. This is shown for linear and quadratic orders of consistency. Moreover, the biquadratic order of consistency, as in finite elements, improves the locking behaviour. Although more locking modes are present in the element-free Galerkin method with quadratic consistency than with standard biquadratic finite elements. Finally, numerical examples are shown to validate the modal analysis. In particular, the conclusions of the modal analysis are also confirmed in an elastoplastic example.
Abstract
Volumetric locking (locking in the incompressible limit) for linear elastic isotropic materials is studied in the context of the element-free Galerkin method. The modal analysis [...]
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Arbitrary Lagrangian-Eulerian formulation for fluid-rigid body interaction
J. Sarrate, A. Huerta, J. Donea

Comput. Methods Appl. Mech. Engrg., (2001). Vol. 190 (24-25), pp. 3171-3188

Abstract
A new formulation for two-dimensional fluid–rigid body interaction problems is developed. In particular, vortex-induced oscillations of a rigid body in viscous incompressible flow are studied. The incompressible Navier–Stokes equations are used to describe the motion of the fluid, while it is assumed that the rigid body is mounted on a system consisting of a spring and a dashpot. An arbitrary Lagrangian–Eulerian formulation (ALE) is used in order to account for large boundary motion. A general formulation for the coupled problem is obtained by uncoupling the translation motion of the body from its rotational motion and developing a specific algorithm to efficiently handle the nonlinear dependence of the rotations. This general formulation can be easily applied to multi-body problems. Two numerical examples involving either translations and rotations are presented as an illustration of the proposed methodologies for fluid–rigid body interaction.
Abstract
A new formulation for two-dimensional fluid–rigid body interaction problems is developed. In particular, vortex-induced oscillations of a rigid body in viscous incompressible [...]
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An improved algorithm to smooth graded quadrilateral meshes preserving the prescribed element size
J. Sarrate, A. Huerta

Comput. Methods Appl. Mech. Engrg., (2001). Vol. 17 (2), pp. 89-99

Abstract
In the generation of quadrilateral unstructured meshes, special attention is focussed to the shape of the elements. This is because it is well known that the distortion of the elements and the accuracy of the analysis are closely related. However, in adaptive schemes it is also essential that the newly generated mesh meets the prescribed element sizes in order to obtain a solution with the desired precision. In 1982 Giuliani developed a robust rezoning algorithm based on geometrical criteria. It gives proven results in a smooth element size distribution, but elements do not verify the prescribed element size when sharp distributions appear. This paper presents a modification of the Giuliani method that generates non-distorted elements while preserving the element size. Similar to the original method, this modification can be extended to three-dimensional cases.
Abstract
In the generation of quadrilateral unstructured meshes, special attention is focussed to the shape of the elements. This is because it is well known that the distortion of [...]
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Error estimation and adaptivity for nonlocal damage models
A. Huerta, A. Rodríguez-Ferran

Int. J. Solids and Structures (2000). Vol. 37 (48-50), pp. 7501-7528

Abstract
Nonlocal damage models are typically used to model failure of quasi-brittle materials. Due to brittleness, the choice of a particular model or set of parameters can have a crucial influence on the structural response. To assess this influence, it is essential to keep finite element discretization errors under control. If not, the effect of these errors on the result of a computation could be erroneously interpreted from a constitutive viewpoint. To ensure the quality of the FE solution, an adaptive strategy based on error estimation is proposed here. It is based on the combination of a residual-type error estimator and quadrilateral h-remeshing. Another important consequence of brittleness is that it leads to structural responses of the snap-through or snap-back type. This requires the use of arc-length control, with a definition of the arc parameter that accounts for the localized nature of quasi-brittle failure. All these aspects are discussed for two particular nonlocal damage models (Mazars and modified von Mises) and for two tests: the Brazilian tensile splitting test and the single-edge notched beam test. For the latter test, the capability of the Mazars model to capture the curved crack pattern observed in experiments – a topic of debate in the literature – is confirmed.
Abstract
Nonlocal damage models are typically used to model failure of quasi-brittle materials. Due to brittleness, the choice of a particular model or set of parameters can have a [...]
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Enrichment and coupling of the finite element and meshless methods
A. Huerta, S. Fernández-Méndez

Int. J. Numer. Meth. Engng. (2000). Vol. 48 (11), pp. 1615-1636

Abstract
A mixed hierarchical approximation based on finite elements and meshless methods is presented. Two cases are considered. The first one couples regions where finite elements or meshless methods are used to interpolate: continuity and consistency is preserved. The second one enriches a finite element mesh with particles. Thus, there is no need to remesh in adaptive refinement processes. In both cases the same formulation is used, convergence is studied and examples are shown.
Abstract
A mixed hierarchical approximation based on finite elements and meshless methods is presented. Two cases are considered. The first one couples regions where finite elements [...]
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Efficient unstructured quadrilateral mesh generation
J. Sarrate, A. Huerta

Int. J. Numer. Meth. Engng. (2000). Vol. 49 (10), pp. 1327-1350

Abstract
This work is devoted to the description of an algorithm for automatic quadrilateral mesh generation. The technique is based on a recursive decomposition of the domain into quadrilateral elements. This automatically generates meshes composed entirely by quadrilaterals over complex geometries (there is no need for a previous step where triangles are generated). A background mesh with the desired element sizes allows to obtain the preferred sizes anywhere in the domain. The final mesh can be viewed as the optimal one given the objective function is defined. The recursive algorithm induces an efficient data structure which optimizes the computer cost. Several examples are presented to show the efficiency of this algorithm.
Abstract
This work is devoted to the description of an algorithm for automatic quadrilateral mesh generation. The technique is based on a recursive decomposition of the domain into [...]
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Numerical differentiation for local and global tangent operators in computational plasticity.
A. Pérez-Foguet, A. Rodríguez-Ferran, A. Huerta

Comput. Methods Appl. Mech. Engrg., (2000). Vol. 189 (1), pp. 277-296

Abstract
In this paper, numerical differentiation is applied to integrate plastic constitutive laws and to compute the corresponding consistent tangent operators. The derivatives of the constitutive equations are approximated by means of difference schemes. These derivatives are needed to achieve quadratic convergence in the integration at Gauss-point level and in the solution of the boundary value problem. Numerical differentiation is shown to be a simple, robust and competitive alternative to analytical derivatives. Quadratic convergence is maintained, provided that adequate schemes and stepsizes are chosen. This point is illustrated by means of some numerical examples.
Abstract
In this paper, numerical differentiation is applied to integrate plastic constitutive laws and to compute the corresponding consistent tangent operators. The derivatives of [...]
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Numerical differentiation for non-trivial consistent tangent matrices: an application to the MRS-lade model
A. Pérez-Foguet, A. Rodríguez-Ferran, A. Huerta

Int. J. Numer. Meth. Engng. (2000). Vol. 48 (2), pp. 159-184

Abstract
In a companion paper Pérez-Foguet, A., Rodríguez-Ferran, A. and Huerta, A. Numerical differentiation for local and global tangent operators in computational plasticity. Computer Methods in Applied Mechanics and Engineering, 2000, in press, the authors have shown that numerical differentiation is a competitive alternative to analytical derivatives for the computation of consistent tangent matrices. Relatively simple models were treated in that reference. The approach is extended here to a complex model: the MRS-Lade model. This plastic model has a cone-cap yield surface and exhibits strong coupling between the flow vector and the hardening moduli. Because of this, differentiating these quantities with respect to stresses and internal variables - the crucial step in obtaining consistent tangent matrices - is rather involved. Numerical differentiation is used here to approximate these derivatives. The approximated derivatives are then used to (1) compute consistent tangent matrices (global problem) and (2) integrate the constitutive equation at each Gauss point (local problem) with the Newton-Raphson method. The choice of the stepsize (i.e. the perturbation in the approximation schemes), based on the concept of relative stepsize, poses no difficulties. In contrast to previous approaches for the MRS-Lade model, quadratic convergence is achieved, for both the local and the global problems. The computational efficiency (CPU time) and robustness of the proposed approach is illustrated by means of several numerical examples, where the major relevant topics are discussed in detail.
Abstract
In a companion paper Pérez-Foguet, A., Rodríguez-Ferran, A. and Huerta, A. Numerical differentiation for local and global tangent operators in computational [...]
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High-order accurate time-stepping schemes for convection-diffusion problems
J. Donea, B. Roig, A. Huerta

Comput. Methods Appl. Mech. Engrg., (2000). Vol. 182 (3-4), pp. 249-275

Abstract
The paper discusses the formulation of high-order accurate time-stepping schemes for transient convection–diffusion problems to be combined with finite element methods of the least-squares type for a stable discretization of highly convective problems. Padé approximations of the exponential function are considered for deriving multi-stage time integration schemes involving first time derivatives only, thus easier to implement in conjunction with C0 finite elements than standard time-stepping schemes which incorporate higher-order time derivatives. After a brief discussion of the stability and accuracy properties of the multi-stage Padé schemes and having underlined the similarity between Padé and Runge–Kutta methods, the paper closes with the presentation of illustrative examples which indicate the effectiveness of the proposed methods.
Abstract
The paper discusses the formulation of high-order accurate time-stepping schemes for transient convection–diffusion problems to be combined with finite element methods [...]
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Adapting Broyden method to handle linear constraints imposed via Lagrange multipliers
A. Rodríguez-Ferran, A. Huerta

Int. J. Numer. Meth. Engng. (1999). Vol. 46 (12), pp. 2011-2026

Abstract
Various non-linear equation solvers are adapted to handle linear constraints via the Lagrange-multiplier technique. This adaptation process turns out to be quite straightforward for Newton-Raphson methods and rank-two Quasi-Newton methods (BFGS and DFP), but rather more involved for Broyden method. In fact, two Broyden methods can be obtained: the standard one and a modified one, better adapted to the Lagrange-multiplier environment. Some numerical examples are used to assess the relative performance of the various adapted solvers. These tests illustrate the superiority of the modified Broyden method over the standard one.
Abstract
Various non-linear equation solvers are adapted to handle linear constraints via the Lagrange-multiplier technique. This adaptation process turns out to be quite straightforward [...]
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FIC-FEM formulation for the multidimensional transient advection-diffusion-absorption equation (preprint)
A. Puigferrat, I. de-Pouplana, E. Oñate

Computer Methods in Applied Mechanics and Engineering (2020). Vol 365, pp. 112984, DOI: 10.1016/j.cma.2020.112984

Abstract
In this paper we present a stabilized FIC-FEM formulation for the multidimensional transient advection-diffusion-absorption equation. The starting point is the non-local form of the governing equations for the multidimensional transient advection-diffusion-absorption problems obtained via the Finite Increment Calculus (FIC) procedure. The FIC governing equations have a residual form that introduces a characteristic length vector that depends on streamline, absorption and shock capturing stabilization parameters, as well as on a characteristic element size that ensures a stabilized numerical solution using a standard Galerkin FEM. The value of the stabilization parameters is obtained as an extension of the steady-state form. The accuracy of the FIC-FEM formulation is verified in the solution of several transient advection-diffusion-absorption problems using regular meshes of 3-noded triangles and 4-noded quadrilaterals.
Abstract
In this paper we present a stabilized FIC-FEM formulation for the multidimensional transient advection-diffusion-absorption equation. The starting point is the non-local form [...]
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Accuracy of two stress update algorithms for shear-free large deformations paths
A. Rodríguez-Ferran, A. Huerta

Journal of Engineering Mechanics (1999). Vol. 125 (6), pp. 715-717

Abstract
The behavior of two stress update algorithms for shear-free large deformation paths is analyzed. The first algorithm has a truncation error of order 1. The second algorithm has a truncation error of order 2. As a consequence, the global performance of the second algorithm is clearly superior. However, for the particular case of shear-free deformation paths, the first algorithm correctly predicts null shear stresses, while the second one does not. This behavior was reported in a previous paper for an extension-rotation test. In this note a general shear-free deformation path is considered in full detail.
Abstract
The behavior of two stress update algorithms for shear-free large deformation paths is analyzed. The first algorithm has a truncation error of order 1. The second algorithm [...]
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Analysis of the vane test considering size and time effects
A. Pérez-Foguet, A. Ledesma, A. Huerta

Int. J. Numer. Anal. Meth. Geomech. (1999). Vol. 23 (5), pp. 383-412

Abstract
An analysis of the vane test using an Arbitrary Lagrangian-Eulerian formulation within a finite element framework is presented. This is suitable for soft clays for which the test is commonly used to measure in situ undrained shear strength. Constitutive laws are expressed in terms of shear stress-shear strain rates, and that permits the study of time effects in a natural manner. An analysis of the shear stress distributions on the failure surface according to the material model is presented. The effect of the constitutive law on the shear band amplitude and on the position of the failure surface is shown. In general, the failure surface is found at 1-1·01 times the vane radius, which is consistent with some experimental results. The problem depends on two dimensionless parameters that represent inertial and viscous forces. For usual vane tests, viscous forces are predominant, and the measured shear strength depends mainly on the angular velocity applied. That can explain some of the comparisons reported when using different vane sizes. Finally, the range of the shear strain rate applied to the soil is shown to be fundamental when comparing experimental results from vane, triaxial and viscosimeter tests. Appart from that, an experimental relation between undrained shear strength and vane angular velocity has been reproduced by this simulation.
Abstract
An analysis of the vane test using an Arbitrary Lagrangian-Eulerian formulation within a finite element framework is presented. This is suitable for soft clays for which the [...]
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Plastic flow potential for cone region on the MRS-Lade model
A. Pérez-Foguet, A. Huerta

Journal of Engineering Mechanics (1999). Vol. 125 (3), pp. 364-367

Abstract
The original formulation of the MRS-Lade model, with nonassociated flow rule on the meridian plane in the cone region, has a corner. In order to reduce the computational effort of corner solution algorithms, a modified plastic flow potential for the cone part is found in the literature. This modification may have a nonadmissible flip over of the flow vector in the cone-cap intersection if the plastic flow potential is not correctly defined. Here a corrected plastic flow potential for the cone region is defined to obtain a continuous transition of the flow vector.
Abstract
The original formulation of the MRS-Lade model, with nonassociated flow rule on the meridian plane in the cone region, has a corner. In order to reduce the computational effort [...]
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Adaptive analysis of yield line patterns in plates with the Arbitrary Lagrangian-Eulerian method
H. Askes, A. Rodríguez-Ferran, A. Huerta

Computers and Structures (1999). Vol. 70 (3), pp. 257-271

Abstract
Plasticity models provide suitable tools to describe the so-called yield line pattern that occurs with the failure of plates. However, in a Lagrangian description a huge number of finite elements are needed for accurate solutions. Accuracy can be combined with low computer costs by means of the arbitrary Lagrangian–Eulerian (ALE) method. With the ALE method, the finite element mesh is automatically refined in the yield lines. A new remesh indicator is proposed that captures newly appearing yield lines as well as already formed yield lines. Numerical examples show the effectiveness of this approach.
Abstract
Plasticity models provide suitable tools to describe the so-called yield line pattern that occurs with the failure of plates. However, in a Lagrangian description a huge number [...]
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ALE stress update for transient and quasistatic processes
A. Rodríguez-Ferran, F. Casadei, A. Huerta

Int. J. Numer. Meth. Engng. (1998). Vol. 43 (2), pp. 241-262

Abstract
A key issue in Arbitrary Lagrangian-Eulerian (ALE) non-linear solid mechanics is the correct treatment of the convection terms in the constitutive equation. These convection terms, which reflect the relative motion between the finite element mesh and the material, are found for both transient and quasistatic ALE analyses. It is shown in this paper that the same explicit algorithms can be employed to handle the convection terms of the constitutive equation for both types of analyses. The most attractive consequence of this fact is that a quasistatic simulation can be upgraded from Updated Lagrangian (UL) to ALE without significant extra computational cost. These ideas are illustrated by means of two numerical examples.
Abstract
A key issue in Arbitrary Lagrangian-Eulerian (ALE) non-linear solid mechanics is the correct treatment of the convection terms in the constitutive equation. These convection [...]
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Comparing two algorithms to add large strains to small-strain FE code
A. Rodríguez-Ferran, A. Huerta

Journal of Engineering Mechanics (1998). Vol. 124 (9), pp. 939-948

Abstract
Two algorithms for the stress update (i.e., time integration of the constitutive equation) in large-strain solid mechanics are discussed, with particular emphasis on two issues: (1) The incremental objectivity; and (2) the implementation aspects. It is shown that both algorithms are incrementally objective (i.e., they treat rigid rotations properly) and that they can be employed to add large-strain capabilities to a small-strain finite element (FE) code in a simple way. A set of benchmark tests, consisting of simple large deformation paths, have been used to test and compare the two algorithms, both for elastic and plastic analyses. These tests evidence different time-integration accuracy for each algorithm. However, it is also shown that the algorithm that is less accurate in general gives exact results for shear-free deformation paths.
Abstract
Two algorithms for the stress update (i.e., time integration of the constitutive equation) in large-strain solid mechanics are discussed, with particular emphasis on two issues: [...]
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Two stress update algorithms for large strains: accuracy analysis and numerical implementation
A. Rodríguez-Ferran, P. Pegon, A. Huerta

Int. J. Numer. Meth. Engng. (1997). Vol. 40 (23), pp. 4363-4404

Abstract
Two algorithms for the stress update (i.e., time integration of the constitutive equation) in large-strain solid mechanics are compared from an analytical point of view. The order of the truncation error associated to the numerical integration is deduced for each algorithm a priori, using standard numerical analysis. This accuracy analysis has been performed by means of a convected frame formalism, which also allows a unified derivation of both algorithms in spite of their inherent differences. Then the two algorithms are adapted from convected frames to a fixed Cartesian frame and implemented in a small-strain finite element code. The implementation is validated by means of a set of simple deformation paths (simple shear, extension, extension and compression, extension and rotation) and two benchmark tests in non-linear mechanics (the necking of a circular bar and a shell under ring loads). In these numerical tests, the observed order of convergence is in very good agreement with the theoretical order of convergence, thus corroborating the accuracy analysis.
Abstract
Two algorithms for the stress update (i.e., time integration of the constitutive equation) in large-strain solid mechanics are compared from an analytical point of view. The [...]
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A note on a numerical benchmark test: an axisymmetric shell under ring loads
A. Vila, A. Rodríguez-Ferran, A. Huerta

Comput. Methods Appl. Mech. Engrg., (1997). Vol. 13 (3), pp. 181-192

Abstract
In this paper, a well-known numerical benchmark test which is usually solved with displacement control for low values of the load eccentricity is examined for a complete range of eccentricities of the ring load. For a certain range of the eccentricity the response shows either snap-through or snap-back, depending on the controlled variable. Thus, in this range of eccentricities, the test can be used to verify implementations of arc-length algorithms, using the displacement controlled solution as a reference. Moreover, results are presented for large eccentricities beyond the applicability of displacement-controlled strategies.
Abstract
In this paper, a well-known numerical benchmark test which is usually solved with displacement control for low values of the load eccentricity is examined for a complete range [...]
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Arbitrary lagrangian-eulerian finite element analysis of strain localization in transient problems
A. Huerta, G. Pijaudier, L. Bodé

Int. J. Numer. Meth. Engng. (1995). Vol. 38 (24), pp. 4171-4191

Abstract
Non-local models guaranty that finite element computations on strain softening materials remain sound up to failure from a theoretical and computational viewpoint. The non-locality prevents strain localization with zero global dissipation of energy, and consequently finite element calculations converge upon mesh refinements to non-zero width localization zones. One of the major drawbacks of these models is that the element size needed in order to capture the localization zone must be smaller than the intemallength. Hence, the total number of degrees of freedom becomes rapidly prohibitive for most engineering applications and there is an obvious need for mesh adaptivity. This paper deals with the application of the arbitrary Lagrangian-Eulerian (ALE) formulation, well known in hydrodynamics and fluid-structure interaction problems, to transient strain localization in a non-local damageable material. It is shown that the ALE formulation which is employed in large boundary motion problems can also be well suited for non-linear transient analysis of softening materials where localization bands appear. The remeshing strategy is based on the equidistribution of an indicator that quantifies the interelement jump of a selected state variable. Two well known one-dimensional examples illustrate the capabilities of this technique: the first one deals with localization due to a propagating wave in a bar, and the second one studies the wave propagation in a hollow sphere.
Abstract
Non-local models guaranty that finite element computations on strain softening materials remain sound up to failure from a theoretical and computational viewpoint. The non-locality [...]
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New ALE applications in non-linear fast-transient solid dynamics
A. Huerta, F. Casadei

Engineering Computations (1994). Vol. 11 (4), pp. 317-345

Abstract
The arbitrary Lagrangian—Eulerian (ALE) formulation, which is already well established in the hydrodynamics and fluid-structure interaction fields, is extended to materials with memory, namely, non- linear path-dependent materials. Previous attempts to treat non- linear solid mechanics with the ALE description have, in common, the implicit interpolation technique employed. Obviously, this implies a numerical burden which may be uneconomical and may induce to give up this formulation, particularly in fast-transient dynamics where explicit algorithms are usually employed. Here, several applications are presented to show that if adequate stress updating techniques are implemented, the ALE formulation could be much more competitive than classical Lagrangian computations when large deformations are present. Moreover, if the ALE technique is interpreted as a simple interpolation enrichment, adequate—in opposition to distorted or locally coarse—meshes are employed. Notice also that impossible computations (or at least very involved numerically) with a Lagrangian code are easily implementable in an ALE analysis. Finally, it is important to observe that the numerical examples shown range from a purely academic test to real engineering simulations. They show the effective applicability of this formulation to non-linear solid mechanics and, in particular, to impact, coining or forming analysis.
Abstract
The arbitrary Lagrangian—Eulerian (ALE) formulation, which is already well established in the hydrodynamics and fluid-structure interaction fields, is extended to materials [...]
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Discretization influence on regularization by two localization limiters
A. Huerta, G. Pijaudier

Journal of Engineering Mechanics (1994). Vol. 120 (6), pp. 1198-1218

Abstract
In materials with a strain‐softening characteristic behavior, classical continuum mechanics favors uncontrolled strain localization in numerical analyses. Several methods have been proposed to regularize the problem. Two such localization limiters developed to overcome spurious instabilities in computational failure analysis are examined and compared. A disturbance analysis, on both models, is performed to obtain the closed‐form solution of propagating wave velocities as well as the velocities at which the energy travels. It also shows that in spite of forcing the same stress‐strain response, the wave equation does not yield similar results. Both propagations of waves are dispersive, but the internal length of each model is different when equivalent behavior is desired. In fact, the previously suggested derivations of gradient models from nonlocal integral models were not completely rigorous. The perturbation analysis is pursued in the discrete space where computations are done, and the closed form solutions are also obtained. The finite‐element discretization introduces an added dispersion associated to the regularization technique. Therefore, the influence of the discretization on the localization limiters can be evaluated. The element size must be smaller than the internal length of the models in order to obtain sufficient accuracy.
Abstract
In materials with a strain‐softening characteristic behavior, classical continuum mechanics favors uncontrolled strain localization in numerical analyses. Several methods [...]
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Numerical analysis of nonlinear large-strain consolidation and filling
A. Huerta, A. Rodríguez-Ferran

Computers and Structures (1992). Vol. 44 (1-2), pp. 357-365

Abstract
Finite strain consolidation and filling of soft sediments at high water level is a challenging problem because of its highly non-linear physical and mathematical aspects. Several numerical schemes designed for this problem are presented as well as simple numerical improvements for a better handling of the extremely high variations of the material properties with depth. The numerical algorithms developed are robust and verify convergence of the iterative schemes instead of the more classical approaches based on choosing time increments ‘sufficiently’ small and assuming convergence at every step. A set of computer programs has been developed to predict magnitude and rate of large-strain self-weight one-dimensional and pseudo bi-dimensional (i.e. one-dimensional deformation, bi-dimensional flux) consolidation during and after deposition, that is, coupling filling and consolidation phenomena. The actual life of the deposit can be numerically simulated combining filling periods and quiescent periods where surcharges (or capping) can exist. Consequently, they are a basic technique for the design of disposal ponds.
Abstract
Finite strain consolidation and filling of soft sediments at high water level is a challenging problem because of its highly non-linear physical and mathematical aspects. [...]
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Finite element analysis of bifurcation in nonlocal strain softening solids
G. Pijaudier, A. Huerta

Comput. Methods Appl. Mech. Engrg. (1991). Vol. 90 (1-3), pp. 905-919

Abstract
Progressive damage in brittle heterogeneous materials produces at the macroscopic level strain softening from which theoretical difficulties arise (e.g. ill-posedness and multiple bifurcation points). This characteristics behavior favours spurious strain localization in numerical analyses and calls for the implementation of localization limiters, for instance nonlocal damage constitutive relations. The issue of possible (stable or unstable) equilibrium paths, multiple localization zones, and of the detection of bifurcation points has, however, never been addressed in the context of nonlocal constitutive laws. We extend here the eigenmode analysis and perturbation method proposed by De Borst to the study of the bifurcation and post-bifurcation response of discrete nonlocal strain softening solids. Numerical applications on beams show that bifurcation and instability may occur in the post-peak regime. As opposed to the case of local constitutive relations, the number of possible solutions at a bifurcation point is restricted due to the constraint introduced by the localization limiter and these solutions are shown to be mesh independent.
Abstract
Progressive damage in brittle heterogeneous materials produces at the macroscopic level strain softening from which theoretical difficulties arise (e.g. ill-posedness and [...]
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Large-amplitude sloshing with submerged blocks
A. Huerta, W. Liu

Journal of pressure vessel technology (1990). Vol. 112 (1), pp. 104-108

Abstract
The computer simulation of forced vibrations induced on a water pool is presented in this paper. The complexity of the seismic fluid-structure interaction problem is accentuated by the large free surface motion. To overcome this difficulty, the arbitrary Lagrangian Eulerian (ALE) finite element formulation is employed. Moreover, the nonlinear behavior of the free surface motion is also taken into account. The results of the numerical simulation are compared with published experimental data and the effectiveness of the ALE algorithm is demonstrated
Abstract
The computer simulation of forced vibrations induced on a water pool is presented in this paper. The complexity of the seismic fluid-structure interaction problem [...]
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Viscous flow with large free surface motion
A. Huerta, W. Liu

Comput. Methods Appl. Mech. Engrg., (1988). Vol. 69 (3), pp. 277-324

Abstract
An arbitrary Lagrangian-Eulerian (ALE) Petrov-Galerkin finite element technique is developed to study nonlinear viscous fluids under large free surface wave motion. A review of the kinematics and field equations from an arbitrary reference is presented and since the major challenge of the ALE description lies in the mesh rezoning algorithm, various methods, including a new mixed formulation, are developed to update the mesh and map the moving domain in a more rational manner. Moreover, the streamline-upwind/Petrov-Galerkin formulation is implemented to accurately describe highly convective free surface flows. The effectiveness of the algorithm is demonstrated on a tsunami problem, the dam-break problem where the Reynolds number is taken as high as 3000, and a large-amplitude sloshing problem.
Abstract
An arbitrary Lagrangian-Eulerian (ALE) Petrov-Galerkin finite element technique is developed to study nonlinear viscous fluids under large free surface wave motion. A review [...]
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Permeability and compressibility of slurries from seepage-induced consolidation
A. Huerta, G. Kriegsmann, R. Krizek

Journal of geotechnical engineering (ASCE) (1988). Vol. 114 (5), pp. 614-627

Abstract
A one-dimensional mathematical model based on finite-strain theory is developed to solve the problem of seepage-induced consolidation in sedimented slurries or very soft clays. The direct solution employs known or assumed material property relationships to determine the final thickness of a soft sediment subjected to a constant piezometric head. It is useful for predicting the capacity of a disposal area and the time-dependent improvement in material properties. Alternatively, the inverse solution utilizes final settlement and steady-state flow data from laboratory or field tests to deduce permeability and compressibility relationships for soft sediments. This approach is especially helpful in the case of permeability determinations because it avoids some of the major problems associated with permeability testing of such materials. The resulting model shows that the coefficient of permeability influences both the time to reach the steady-state condition and the nature of the steady-state condition itself. An illustrative example is presented wherein data from a series of tests on a kaolinite slurry are used to establish material property relationships that are then used to predict the response of other tests on the same soil under different conditions
Abstract
A one-dimensional mathematical model based on finite-strain theory is developed to solve the problem of seepage-induced consolidation in sedimented slurries or very soft clays. [...]
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Viscous Flow Structure Interaction
A. Huerta, W. Liu

Journal of pressure vessel technology (1988). Vol. 110 (1), pp. 15-21

Abstract
Considerable research activities in vibration and seismic analysis for various fluid-structure systems have been carried out in the past two decades. Most of the approaches are formulated within the framework of finite elements, and the majority of work deals with inviscid fluids. However, there has been little work done in the area of fluid-structure interaction problems accounting for flow separation and nonlinear phenomenon of steady streaming. In this paper, the Arbitrary Lagrangian Eulerian (ALE) finite element method is extended to address the flow separation and nonlinear phenomenon of steady streaming for arbitrarily shaped bodies undergoing large periodic motion in a viscous fluid. The results are designed to evaluate the fluid force acting on the body; thus, the coupled rigid body-viscous flow problem can be simplified to a standard structural problem using the concept of added mass and added damping. Formulas for these two constants are given for the particular case of a cylinder immersed in an infinite viscous fluid. The finite element modeling is based on a pressure-velocity mixed formulation and a streamline upwind Petrov/Galerkin technique. All computations are performed using a personal computer.
Abstract
Considerable research activities in vibration and seismic analysis for various fluid-structure systems have been carried out in the past two decades. Most of the approaches [...]
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Converse flexoelectricity yields large piezoresponse force microscopy signals in non-piezoelectric materials
A. Abdollahi, N. Domingo, I. Arias, G. Catalan

Nature Communications (2019). Vol. 10 (1266), pp. 1-6

Abstract
Converse flexoelectricity is a mechanical stress induced by an electric polarization gradient. It can appear in any material, irrespective of symmetry, whenever there is an inhomogeneous electric field distribution. This situation invariably happens in piezoresponse force microscopy (PFM), which is a technique whereby a voltage is delivered to the tip of an atomic force microscope in order to stimulate and probe piezoelectricity at the nanoscale. While PFM is the premier technique for studying ferroelectricity and piezoelectricity at the nanoscale, here we show, theoretically and experimentally, that large effective piezoelectric coefficients can be measured in non-piezoelectric dielectrics due to converse flexoelectricity.
Abstract
Converse flexoelectricity is a mechanical stress induced by an electric polarization gradient. It can appear in any material, irrespective of symmetry, whenever there is an [...]
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Phase-field modeling of fracture in ferroelectric materials
A. Abdollahi, I. Arias

Archives of Comp. Meths. Engng. (2015). Vol. 22 (2), pp. 153-181 (Preprint)

Abstract
This paper presents a family of phase-field models for the coupled simulation of the microstructure formation and evolution, and the nucleation and propagation of cracks in single and polycrystalline ferroelectric materials. The first objective is to introduce a phase-field model for ferroelectric single crystals. The model naturally couples two existing energetic phase-field approaches for brittle fracture and ferroelectric domain formation and evolution. Simulations show the interactions between the microstructure and the crack under mechanical and electromechanical loadings. Another objective of this paper is to encode different crack face boundary conditions into the phase-field framework since these conditions strongly affect the fracture behavior of ferroelectrics. The smeared imposition of these conditions are discussed and the results are compared with that of sharp crack models to validate the proposed approaches. Simulations show the effects of different conditions and electromechanical loadings on the crack propagation. In a third step, the model is modified by introducing a crack non-interpenetration condition in the variational approach to fracture accounting for the asymmetric behavior in tension and compression. The modified model makes it possible to explain anisotropic crack growth in ferroelectrics under the Vickers indentation loading. This model is also employed for the fracture analysis of multilayer ferroelectric actuators, which shows the potential of the model for future applications. The coupled phase-field model is also extended to polycrystals by introducing realistic polycrystalline microstructures in the model. Inter- and trans-granular crack propagation modes are observed in the simulations. Finally, and for completeness, the phase-field theory is extended to the simulation of the propagation of conducting cracks under purely electrical loading and to the three-dimensional simulation of crack propagation in ferroelectric single crystals. Salient features of the crack propagation phenomenon predicted by the simulations of this paper are directly compared with experimental observations.
Abstract
This paper presents a family of phase-field models for the coupled simulation of the microstructure formation and evolution, and the nucleation and propagation of cracks in [...]
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Trends and clinico-epidemiological features of human rabies cases in Bangladesh 2006–2018
S. Ghosh, S. Ghosh

(2020). Scientific Reports 10 (1), 1-11, 2020
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Detection of highly pathogenic avian in waterfowl in Bangladesh
S. Ghosh

(2021).

Abstract
Bangladesh has reported repeated outbreaks of highly pathogenic avian inﬂuenza (HPAI) A(H5) viruses in poultry since 2007. Because of the large number of live poultry markets (LPM) relative to the population density of poultry throughout the country, these markets can serve as sentinel sites for HPAI A(H5) detection. Through active LPM surveillance during June 2016–June 2017, HPAI A(H5N6) viruses along with 14 other subtypes of inﬂuenza A viruses were detected. The HPAI A(H5N6) viruses belonged to clade 2.3.4.4 and were likely introduced into Bangladesh around March 2016. Human infections with inﬂuenza clade 2.3.4.4 viruses in Bangladesh have not been identiﬁed, but the viruses had several molecular markers associated with potential human infection. Vigilant surveillance at the animal-human interface is essential to identify emerging avian inﬂuenza viruses with the potential to threaten public and animal health.
Abstract
Bangladesh has reported repeated outbreaks of highly pathogenic avian inﬂuenza (HPAI) A(H5) viruses in poultry since 2007. Because of the large number of live poultry markets [...]
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Awareness of rabies and response to dog bites in a Bangladesh community
S. Ghosh

(2021).

Abstract
Community awareness regarding rabies and treatment seeking behaviours are critical both for the prevention and control of the disease in human and animals. We conducted a study to explore people’s awareness about rabies, their attitudes towards dogs and practices associated with treating dog bites in Satkhira Sadar, a southwestern sub-district of Bangladesh. Of the total 3200 households (HHs) surveyed, the majority of the respondents have heard about rabies (73%) and there was a high level of awareness that dog bite is the main cause of rabies (86%), and that rabies can be prevented by vaccination (85%). However, 59% of the dog bite victims first seek treatment from traditional healers instead of visiting the hospitals, 29% received the rabies vaccine, 2% practiced proper wound washing with soap and water, while 4.8% have not taken any measures. None of the victims have received rabies immunoglobulin (RIG). Of the respondents, 5.2% reported a history of dog bite in at least one family member, and 11.8% reported a history of dog bite in domestic animals during the previous year. The HHs having a higher number of family members (OR: 1.13, 95% CI: 1.07–1.2), having a pet dog (OR: 2.1, 95% CI: 1.4–3.2) and caring or feeding a community dog (OR: 2.1, 95% CI: 1.4–2.9) showed an increased risk of getting a dog bite. Among the bite victims, 3.6% (n= 6) humans and 15.8% (n = 60) animals died. As a measure for dog population management (DPM), 56% preferred sterilization while the rest preferred killing of dogs. The current treatment seeking behaviours of the respondents should be improved through additional education and awareness programme and better availability for the provision of post-exposure prophylaxis in Bangladesh. We recommend scaling up national mass dog vaccination and DPM to reduce the burden of rabies cases and dog bites in Bangladesh.
Abstract
Community awareness regarding rabies and treatment seeking behaviours are critical both for the prevention and control of the disease in human and animals. We conducted a [...]
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The Pattern of Highly Pathogenic Avian Influenza H5N1 Outbreaks in South Asia
S. Hossain, P. Ghosh, S. Ghosh, M. Hossain, C. Beard, M. and, S. Ghosh

(2021).

Abstract
ighly pathogenic avian influenza (HPAI) H5N1 has caused severe illnesses in poultry and in humans. More than 15,000 outbreaks in domestic birds from 2005 to 2018 and 861 human cases from 2003 to 2019 were reported across the world to OIE (Office International des Epizooties) and WHO (World Health Organization), respectively. We reviewed and summarized the spatial and temporal distribution of HPAI outbreaks in South Asia. During January 2006 to June 2019, a total of 1063 H5N1 outbreaks in birds and 12 human cases for H5N1 infection were reported to OIE and WHO, respectively. H5N1 outbreaks were detected more in the winter season than the summer season and PubMed to collect data from published articles using the following
Abstract
ighly pathogenic avian influenza (HPAI) H5N1 has caused severe illnesses in poultry and in humans. More than 15,000 outbreaks in domestic birds from 2005 to 2018 and 861 human [...]
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Trends and clinico-epidemiological features of human rabies cases in Bangladesh 2006–2018
S. Ghosh, S. Ghosh

(2021).
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Constructive and destructive interplay between piezoelectricity and flexoelectricity in flexural sensors and actuators
A. Abdollahi, I. Arias

Journal of Applied Mechanics (2015). Vol. 82 (12), pp. 121003-1/121003-4 (Preprint)

Abstract
Flexoelectricity is an electromechanical effect coupling polarization to strain gradients. It fundamentally differs from piezoelectricity because of its size-dependence and symmetry. Flexoelectricity is generally perceived as a small effect noticeable only at the nanoscale. Since ferroelectric ceramics have a particularly high flexoelectric coefficient, however, it may play a significant role as piezoelectric transducers shrink to the submicrometer scale. We examine this issue with a continuum model self-consistently treating piezo- and flexoelectricity. We show that in piezoelectric device configurations that induce strain gradients and at small but technologically relevant scales, the electromechanical coupling may be dominated by flexoelectricity. More importantly, depending on the device design flexoelectricity may enhance or reduce the effective piezoelectric effect. Focusing on bimorph configurations, we show that configurations that are equivalent at large scales exhibit dramatically different behavior for thicknesses below 100¿nm for typical piezoelectric materials. Our results suggest flexoelectric-aware designs for small-scale piezoelectric bimorph transducers.
Abstract
Flexoelectricity is an electromechanical effect coupling polarization to strain gradients. It fundamentally differs from piezoelectricity because of its size-dependence and [...]
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Three-dimensional simulation of crack propagation in ferroelectric polycrystals: Effect of combined toughening mechanisms
A. Abdollahi, I. Arias

Acta Materialia (2014). Vol. 65, pp. 106-117 (Preprint)

Abstract
We simulate the fracture processes of ferroelectric polycrystals in three dimensions using a phase-field model. In this model, the grain boundaries, cracks and ferroelectric domain walls are represented in a diffuse way by three phase-fields. We thereby avoid the difficulty of tracking the interfaces in three dimensions. The resulting model can capture complex interactions between the crack and the polycrystalline and ferroelectric domain microstructures. The simulation results show the effect of the microstructures on the fracture response of the material. Crack deflection, crack bridging, crack branching and ferroelastic domain switching are observed to act as the main fracture toughening mechanisms in ferroelectric polycrystals. Our fully 3-D simulations illustrate how the combination of these mechanisms enhances the fracture toughness of the material, and pave the way for further systematic studies, including fracture homogenization.
Abstract
We simulate the fracture processes of ferroelectric polycrystals in three dimensions using a phase-field model. In this model, the grain boundaries, cracks and ferroelectric [...]
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Conducting crack propagation driven by electric fields in ferroelectric ceramics
A. Abdollahi, I. Arias

Acta Materialia (2013). Vol. 61 (19), pp. 7087-7097 (Preprint)

Abstract
Ferroelectric ceramics are susceptible to fracture under high electric fields, which are commonly generated in the vicinity of electrodes or conducting layers. In the present work, we extend a phase-field model of fracture in ferroelectric single crystals to the simulation of the propagation of conducting cracks under purely electrical loading. This is done by introducing the electrical enthalpy of a diffuse conducting layer into the phase-field formulation. Simulation results show oblique crack propagation and crack branching from a conducting notch, forming a tree-like crack pattern in a ferroelectric sample under positive and negative electric fields. Microstructure evolution indicates the formation of tail-to-tail and head-to-head 90° domains, which results in charge accumulation around the crack. The charge accumulation, in turn, induces a high electric field and hence a high electrostatic energy, further driving the conducting crack. Salient features of the results are compared with experiments.
Abstract
Ferroelectric ceramics are susceptible to fracture under high electric fields, which are commonly generated in the vicinity of electrodes or conducting layers. In the present [...]
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Phase-field modeling of crack propagation in piezoelectric and ferroelectric materials with different electromechanical crack conditions
I. Arias, A. Abdollahi

Journal of the Mechanics and Physics of Solids (2012). Vol. 60 (12), pp. 2100-2126

Abstract
We present a family of phase-field models for fracture in piezoelectric and ferroelectric materials. These models couple a variational formulation of brittle fracture with, respectively, (1) the linear theory of piezoelectricity, and (2) a Ginzburg–Landau model of the ferroelectric microstructure to address the full complexity of the fracture phenomenon in these materials. In these models, both the cracks and the ferroelectric domain walls are represented in a diffuse way by phase-fields. The main challenge addressed here is encoding various electromechanical crack models (introduced as crack-face boundary conditions in sharp models) into the phase-field framework. The proposed models are verified through comparisons with the corresponding sharp-crack models. We also perform two dimensional finite element simulations to demonstrate the effect of the different crack-face conditions, the electromechanical loading and the media filling the crack gap on the crack propagation and the microstructure evolution. Salient features of the results are compared with experiments.
Abstract
We present a family of phase-field models for fracture in piezoelectric and ferroelectric materials. These models couple a variational formulation of brittle fracture with, [...]
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Crack initiation patterns at electrode edges in multilayer ferroelectric actuators
A. Abdollahi, I. Arias

Smart materials and structures (2012). Vol. 21 (9), pp. 094011

Abstract
In multilayer ferroelectric actuators, electrode edges are the main source of fracture due to the generation of non-uniform electric fields in their vicinity. The electric fields, in turn, induce incompatible strain fields and hence concentrated stresses, which may cause the ceramic to crack. In this paper, the crack initiation from the electrode edges is simulated using a phase-field model. This model is based on variational formulations of brittle crack propagation and domain evolution in ferroelectric materials. The simulation results show different crack initiation patterns depending on the bonding conditions between the ceramic and electrode layers. Three extreme conditions are considered, which are fully cofired, partially cofired, and separated layers. The crack initiation patterns can be either delimitation along the electrode–ceramic interface or oblique cracking from the electrode into the material. The calculations suggest a mechanism explaining the experimentally observed crack branches near the electrode edges. The effects of the ceramic layer thickness and length of the internal electrode on the crack initiation are also evaluated.
Abstract
In multilayer ferroelectric actuators, electrode edges are the main source of fracture due to the generation of non-uniform electric fields in their vicinity. The electric [...]
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Numerical simulation of intergranular and transgranular crack propagation in ferroelectric polycrystals
A. Abdollahi, I. Arias

International Journal of Fracture (2012). Vol. 174 (1), pp. 3-15

Abstract
We present a phase-field model to simulate intergranular and transgranular crack propagation in ferroelectric polycrystals. The proposed model couples three phase-fields describing (1) the polycrystalline structure, (2) the location of the cracks, and (3) the ferroelectric domain microstructure. Different polycrystalline microstructures are obtained from computer simulations of grain growth. Then, a phase-field model for fracture in ferroelectric single-crystals is extended to polycrystals by incorporating the differential fracture toughness of the bulk and the grain boundaries, and the different crystal orientations of the grains. Our simulation results show intergranular crack propagation in fine-grain microstructures, while transgranular crack propagation is observed in coarse grains. Crack deflection is shown as the main toughening mechanism in the fine-grain structure. Due to the ferroelectric domain switching mechanism, noticeable fracture toughness enhancement is also obtained for transgranular crack propagation. These observations agree with experiment.
Abstract
We present a phase-field model to simulate intergranular and transgranular crack propagation in ferroelectric polycrystals. The proposed model couples three phase-fields describing [...]
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Phase-field modeling of the coupled microstructure and fracture evolution in ferroelectric single crystals
A. Abdollahi, I. Arias

Acta Materialia (2011). Vol. 59 (12), pp. 4733-4746

Abstract
We propose a phase-field model for the coupled simulation of microstructure formation and evolution, and the nucleation and propagation of cracks in single-crystal ferroelectric materials. The model naturally couples two existing energetic phase-field approaches for brittle fracture and ferroelectric domain formation and evolution. The finite-element implementation of the theory in two dimensions (plane-polarization and plane-strain) is described. We perform, to the best of our knowledge, the first crack propagation calculations of ferroelectric single crystals, simultaneously allowing general microstructures to develop. Previously, the microstructure calculations were performed at fixed crack configurations or under the assumption of small-scale switching. Our simulations show that this assumption breaks down as soon as the crack-tip field interacts with the boundaries of the test sample (or, in general, obstacles such as defects or grain boundaries). Then, the microstructure induced by the presence of the crack propagates beyond its vicinity, leading to the formation of twins. Interactions between the twins and the crack are investigated under mechanical and electromechanical loadings, both for permeable and impermeable cracks, with an emphasis on fracture toughening due to domain switching, and compared with experiments
Abstract
We propose a phase-field model for the coupled simulation of microstructure formation and evolution, and the nucleation and propagation of cracks in single-crystal ferroelectric [...]
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Phase-field simulation of anisotropic crack propagation in ferroelectric single crystals: effect of microstructure on the fracture process
A. Abdollahi, I. Arias

Modeling and simulation in materials science and engineering (2011). Vol. 19 (7), pp. 1-13

Abstract
Crack propagation during the indentation test of a ferroelectric single crystal is simulated using a phase- eld model. This model is based on variational formulations of brittle crack propagation and domain evolution in ferroelectric materials. Due to the high compressive stresses near the indenter contact faces, a modi ed regularized formulation of the variational brittle fracture is coupled with the material model to prevent crack formation and interpenetration in the compressed regions. The simulation results show that the radial cracks perpendicular to the poling direction of the material propagate faster than the parallel ones, which is in agreement with experimental observations. This anisotropy in the crack propagation is due to interactions between the material microstructure and the radial cracks, as captured by the phase- eld simulation. Crack propagation during the indentation test of a ferroelectric single crystal is simulated using a phase-eld model. This model is based on variational formulations of brittle crack propagation and domain evolution in ferroelectric materials. Due to the high compressive stresses near the indenter contact faces, a modied regularized formulation of the variational brittle fracture is coupled with the material model to prevent crack formation and interpenetration in the compressed regions. The simulation results show that the radial cracks perpendicular to the poling direction of the material propagate faster than the parallel ones, which is in agreement with experimental observations. This anisotropy in the crack propagation is due to interactions between the material microstructure and the radial cracks, as captured by the phase-eld simulation.
Abstract
Crack propagation during the indentation test of a ferroelectric single crystal is simulated using a phase- eld model. This model is based on variational formulations of brittle [...]
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Experimental validation of large-scale simulations of dynamic fracture along weak planes
V. Chalivendra, S. Hong, I. Arias, J. Knap, A. Rosakis, M. Ortiz

Int. J. Impact Engineering (2009). Vol. 36 (7), pp. 888-898

Abstract
A well-controlled and minimal experimental scheme for dynamic fracture along weak planes is specifically designed for the validation of large-scale simulations using cohesive finite elements. The role of the experiments in the integrated approach is two-fold. On the one hand, careful measurements provide accurate boundary conditions and material parameters for a complete setup of the simulations without free parameters. On the other hand, quantitative performance metrics are provided by the experiments, which are compared a posteriori with the results of the simulations. A modified Hopkinson bar setup in association with notch-face loading is used to obtain controlled loading of the fracture specimens. An inverse problem of cohesive zone modeling is performed to obtain accurate mode-I cohesive zone laws from experimentally measured deformation fields. The speckle interferometry technique is employed to obtain the experimentally measured deformation field. Dynamic photoelasticity in conjunction with high-speed photography is used to capture experimental records of crack propagation. The comparison shows that both the experiments and the numerical simulations result in very similar crack initiation times and produce crack tip velocities which differ by less than 6%. The results also confirm that the detailed shape of the non-linear cohesive zone law has no significant influence on the numerical results.
Abstract
A well-controlled and minimal experimental scheme for dynamic fracture along weak planes is specifically designed for the validation of large-scale simulations using cohesive [...]
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Numerical modelling and experimental validation of dynamic fracture events along weak planes
I. Arias, J. Knap, J. Chalivendra, S. Hong, M. Ortiz, A. Rosakis

Comput. Methods Appl. Mech. Engrg., (2007). Vol. 196 (37-40), pp. 3833-3840

Abstract
The conceptual simplicity and the ability of cohesive finite element models to describe complex fracture phenomena makes them often the approach of choice to study dynamic fracture. These models have proven to reproduce some experimental features, but to this point, no systematic study has validated their predictive ability; the difficulty in producing a sufficiently complete experimental record, and the intensive computational requirements needed to obtain converged simulations are possible causes. Here, we present a systematic integrated numerical–experimental approach to the verification and validation (V&V) of simulations of dynamic fracture along weak planes. We describe the intertwined computational and the experimental sides of the work, present the V&V results, and extract general conclusions about this kind of integrative approach.
Abstract
The conceptual simplicity and the ability of cohesive finite element models to describe complex fracture phenomena makes them often the approach of choice to study dynamic [...]
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A phenomenological cohesive model of ferroelectric fatigue
I. Arias, S. Serebrinsky, M. Ortiz

Acta Materialia (2006). Vol. 54 (4), pp. 975-984

Abstract
We develop a phenomenological model of electro-mechanical ferroelectric fatigue based on a ferroelectric cohesive law that couples mechanical displacement and electric-potential discontinuity to mechanical tractions and surface-charge density. The ferroelectric cohesive law exhibits a monotonic envelope and loading–unloading hysteresis. The model is applicable whenever the changes in properties leading to fatigue are localized in one or more planar-like regions, modeled by the cohesive surfaces. We validate the model against experimental data for a simple test configuration consisting of an infinite slab acted upon by an oscillatory voltage differential across the slab and otherwise stress free. The model captures salient features of the experimental record including: the existence of a threshold nominal field for the onset of fatigue; the dependence of the threshold on the applied-field frequency; the dependence of fatigue life on the amplitude of the nominal field; and the dependence of the coercive field on the size of the component, or size effect. Our results, although not conclusive, indicate that planar-like regions affected by cycling may lead to the observed fatigue in tetragonal PZT.
Abstract
We develop a phenomenological model of electro-mechanical ferroelectric fatigue based on a ferroelectric cohesive law that couples mechanical displacement and electric-potential [...]
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Rayleigh wave correction for the BEM analysis of two-dimensional elastodynamic problems in a half-space
I. Arias, J. Achenbach

Int. J. Numer. Meth. Engng. (2004). Vol. 60 (13), pp. 2131-2146

Abstract
A simple, elegant approach is proposed to correct the error introduced by the truncation of the infinite boundary in the BEM modelling of two-dimensional wave propagation problems in elastic half-spaces. The proposed method exploits the knowledge of the far-field asymptotic behaviour of the solution to adequately correct the BEM displacement system matrix for the truncated problem to account for the contribution of the omitted part of the boundary. The reciprocal theorem of elastodynamics is used for a convenient computation of this contribution involving the same boundary integrals that form the original BEM system. The method is formulated for a two-dimensional homogeneous, isotropic, linearly elastic half-space and its implementation in a frequency domain boundary element scheme is discussed in some detail. The formulation is then validated for a free Rayleigh pulse travelling on a half-space and successfully tested for a benchmark problem with a known approximation to the analytical solution. This is the pre-peer reviewed version of the following article: Arias, I.; Achenbach, J. Rayleigh wave correction for the BEM analysis of two-dimensional elastodynamic problems in a half-space.
Abstract
A simple, elegant approach is proposed to correct the error introduced by the truncation of the infinite boundary in the BEM modelling of two-dimensional wave propagation [...]
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Use of reciprocity considerations for the two-dimensional BEM analysis of wave propagation in an elastic half-space with applications to acoustic emission
I. Arias, J. Achenbach

Wave Motion (2004). Vol. 39 (4), pp. 281-294

Abstract
A simple numerical treatment of the infinite boundary in the BEM analysis of two-dimensional wave propagation problems in elastic half-spaces is proposed to avoid the spurious reflections of non-decaying Rayleigh waves introduced by the truncation of the boundary. The proposed method exploits the knowledge of the far-field asymptotic behavior of the solution to adequately correct the BEM displacement system matrix for the truncated problem to account for the contribution of the omitted part of the boundary. The reciprocal theorem of elastodynamics is used for a convenient computation of this contribution exclusively in terms of the boundary integrals of the original BEM system. The method is applied to the study of the acoustic emission from nucleating and propagating surface-breaking and buried cracks in a two-dimensional elastic half-space. It is shown to be particularly advantageous since it allows for an accurate calculation of the generated signal even when the observation point is located far from the acoustic emission source.
Abstract
A simple numerical treatment of the infinite boundary in the BEM analysis of two-dimensional wave propagation problems in elastic half-spaces is proposed to avoid the spurious [...]
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A model for the ultrasonic detection of surface-breaking cracks by the scanning laser source technique
I. Arias, J. Achenbach

Wave Motion (2004). Vol. 39 (1), pp. 61-75

Abstract
A model for the scanning laser source (SLS) technique is presented. The SLS is a novel laser-based inspection method for the ultrasonic detection of small surface-breaking cracks. The generated ultrasonic signal is monitored as a line-focused laser is scanned over the defect. Characteristic changes in the amplitude and the frequency content are observed. The modeling approach is based on the decomposition of the field generated by the laser in a cracked two-dimensional half-space, by virtue of linear superposition, into the incident and the scattered fields. The incident field is that generated by laser illumination of a defect-free half-space. A thermoelastic model has been used which takes account of the effect of thermal diffusion, as well as the finite width and duration of the laser source. The scattered field incorporates the interactions of the incident field with the surface-breaking crack. It has been analyzed numerically by a direct frequency domain boundary element method. A comparison with an experiment for a large defect shows that the model captures the observed phenomena. A simulation for a small crack illustrates the ability of the SLS technique to detect defects smaller than the wavelength of the generated Rayleigh wave.
Abstract
A model for the scanning laser source (SLS) technique is presented. The SLS is a novel laser-based inspection method for the ultrasonic detection [...]
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Thermoelastic generation of ultrasound by line-focused laser irradiation
I. Arias, J. Achenbach

Int. J. Solids and Structures (2003). Vol. 40 (25), pp. 6917-6935

Abstract
A two-dimensional theoretical model for the field generated in the thermoelastic regime by line-focused laser illumination of a homogeneous, isotropic, linearly elastic half-space is presented. The model accounts for the effects of thermal diffusion and optical penetration, as well as the finite width and duration of the laser source. The model is obtained by solving the thermoelastic problem in plane strain, rather than by integrating available solutions for the point-source, leading to a lower computational effort. The well-known dipole model follows from appropriate limits. However, it is shown that, by simple elasticity arguments, the strength of the dipole can be related a-priori to the heat input and certain material properties. The strength is found to be smaller than that of the dipoles equivalent to a buried source due to the effect of the free surface. This fact has been overlooked by some previous researchers. Excellent quantitative agreement with experimental observations provides validation for the model. Some representative results are presented to illustrate the generated field and provide insight into the relevance of the different mechanisms taken into account in the model.
Abstract
A two-dimensional theoretical model for the field generated in the thermoelastic regime by line-focused laser illumination of a homogeneous, isotropic, linearly elastic half-space [...]
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D2.4 First Release of the mesh generation/adaptation capabilities
L. Cirrottola, A. Froehly, B. Keith, S. Warnakulasuriya, R. Rossi, C. Soriano

Open Access Repository of the ExaQUte project: Deliverables (2021). 12

Abstract
This document presents a description of the parallel mesh adaptation library for the rst actual software release. Regarding the octree mesh-generation capabilities, the reader can refers to Deliverable 2.2. As it is discussed in Section 1.3.2 of part B of the project proposal there are two parallel research lines aimed at developing scalable adaptive mesh renement (AMR) algorithms and implementations. The rst one is based on using octree-based mesh generation and adaptation for the whole simulation in combination with untted nite element methods (FEMs) and the use of algebraic constraints to deal with non-conformity of spaces. On the other hand the second strategy is based on the use of an initial octree mesh that, aftermaking it conformal through the addition of template-based tetrahedral renements, is adapted anisotropically during the calculation.
Abstract
This document presents a description of the parallel mesh adaptation library for the rst actual software release. Regarding the octree mesh-generation capabilities, the [...]
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D8.3 Report on exploitation activities
C. Soriano, A. Apostolatos, R. Rossi

Open Access Repository of the ExaQUte project: Deliverables (2021). 13

Abstract
This deliverable describes the exploitation activities carried our in ExaQUte in the framework of WP9.
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D8.2 Report on dissemination activities
C. Soriano, R. Rossi

Open Access Repository of the ExaQUte project: Deliverables (2021). 14

Abstract
This deliverable descritves the Dissemination activities in ExaQUte
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D4.3 Benchmarking report as tested on the available infrastructure
T. Karasek, S. Böhm, B. Keith, R. Amela, R. Badia, R. Rossi, C. Soriano

Open Access Repository of the ExaQUte project: Deliverables (2021). 15

Abstract
The main focus of this deliverable is testing and benchmarking the available infrastructure using the execution frameworks PyCOMPSs and HyperLoom. A selected benchmark employing the Multi Level Monte Carlo (MLMC) algorithm was run on two systems: TIER-0 (MareNostrum4) and TIER-1 (Salomon) supercomputers. In both systems, good performance scalability was achieved.
Abstract
The main focus of this deliverable is testing and benchmarking the available infrastructure using the execution frameworks PyCOMPSs and HyperLoom. A selected benchmark [...]
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Phase field modeling of brittle fracture in an Euler–Bernoulli beam accounting for transverse part-through cracks
W. Lai, J. Gao, Y. Li, M. Arroyo, Y. Shen

Comput. Methods Appl. Mech. Engrg., (2020). Vol. 361, pp. 112787

Abstract
We present a phase field model to simulate brittle fracture in an initially straight Euler–Bernoulli beam, with generalization to curved beams. We start from formulating the problem with the principle of minimum potential energy in a 3D solid, with the displacement field and the phase field as primary arguments. We then select, for each cross section, representative fields that characterize the said cross section, including the beam deflection and rotation, and two independent ansatz variables within the cross section to represent the phase field. The problem then reduces to a minimization with only one-dimensional field variables. A feature of the proposed method is, without discretizing the phase field within the cross section, it can represent its variation within the cross section, allowing to simulate cracks partially going through the thickness due to bending as well as axial loads.
Abstract
We present a phase field model to simulate brittle fracture in an initially straight Euler–Bernoulli beam, with generalization to curved beams. We start from formulating [...]
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Approximation of tensor fields on surfaces of arbitrary topology based on local Monge parametrizations
A. Torres-Sánchez, D. Santos-Oliván, M. Arroyo

Journal of Computational Physics (2020). Vol. 405, pp. 109168

Abstract
We introduce a new method, the Local Monge Parametrizations (LMP) method, to approximate tensor fields on general surfaces given by a collection of local parametrizations, e.g. as in finite element or NURBS surface representations. Our goal is to use this method to solve numerically tensor-valued partial differential equations (PDEs) on surfaces. Previous methods use scalar potentials to numerically describe vector fields on surfaces, at the expense of requiring higher-order derivatives of the approximated fields and limited to simply connected surfaces, or represent tangential tensor fields as tensor fields in 3D subjected to constraints, thus increasing the essential number of degrees of freedom. In contrast, the LMP method uses an optimal number of degrees of freedom to represent a tensor, is general with regards to the topology of the surface, and does not increase the order of the PDEs governing the tensor fields. The main idea is to construct maps between the element parametrizations and a local Monge parametrization around each node. We test the LMP method by approximating in a least-squares sense different vector and tensor fields on simply connected and genus-1 surfaces. Furthermore, we apply the LMP method to two physical models on surfaces, involving a tension-driven flow (vector-valued PDE) and nematic ordering (tensor-valued PDE), on different topologies. The LMP method thus solves the long-standing problem of the interpolation of tensors on general surfaces with an optimal number of degrees of freedom.
Abstract
We introduce a new method, the Local Monge Parametrizations (LMP) method, to approximate tensor fields on general surfaces given by a collection of local parametrizations, [...]
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Surface tension controls the hydraulic fracture of adhesive interfaces bridged by molecular bonds
D. Kaurin, M. Arroyo

Physical review letters (2019). Vol. 123 (22), pp. 1-6 (Preprint)

Abstract
Biological function requires cell-cell adhesions to tune their cohesiveness; for instance, during the opening of new fluid-filled cavities under hydraulic pressure. To understand the physical mechanisms supporting this adaptability, we develop a stochastic model for the hydraulic fracture of adhesive interfaces bridged by molecular bonds. We find that surface tension strongly enhances the stability of these interfaces by controlling flaw sensitivity, lifetime, and optimal architecture in terms of bond clustering. We also show that bond mobility embrittles adhesions and changes the mechanism of decohesion. Our study provides a mechanistic background to understand the biological regulation of cell-cell cohesion and fracture.
Abstract
Biological function requires cell-cell adhesions to tune their cohesiveness; for instance, during the opening of new fluid-filled cavities under hydraulic pressure. To understand [...]
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Out-of-equilibrium mechanochemistry and self-organization of fluid membranes interacting with curved proteins
C. Tozzi, N. Walani, M. Arroyo

New journal of physics (2019). Vol. 21, pp. 1-23

Abstract
The function of biological membranes is controlled by the interaction of the fluid lipid bilayer with various proteins, some of which induce or react to curvature. These proteins can preferentially bind or diffuse towards curved regions of the membrane, induce or stabilize membrane curvature and sequester membrane area into protein-rich curved domains. The resulting tight interplay between mechanics and chemistry is thought to control organelle morphogenesis and dynamics, including traffic, membrane mechanotransduction, or membrane area regulation and tension buffering. Despite all these processes are fundamentally dynamical, previous work has largely focused on equilibrium and a self-consistent theoretical treatment of the dynamics of curvature sensing and generation has been lacking. Here, we develop a general theoretical and computational framework based on a nonlinear Onsager’s formalism of irreversible thermodynamics for the dynamics of curved proteins and membranes. We develop variants of the model, one of which accounts for membrane curving by asymmetric crowding of bulky off-membrane protein domains. As illustrated by a selection of test cases, the resulting governing equations and numerical simulations provide a foundation to understand the dynamics of curvature sensing, curvature generation, and more generally membrane curvature mechano-chemistry.
Abstract
The function of biological membranes is controlled by the interaction of the fluid lipid bilayer with various proteins, some of which induce or react to curvature. These proteins [...]
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Modelling fluid deformable surfaces with an emphasis on biological interfaces
A. Torres-Sánchez, D. Millán, M. Arroyo

Journal of fluid mechanics (2019). Vol. 872, pp. 218-271 (Preprint)

Abstract
Fluid deformable surfaces are ubiquitous in cell and tissue biology, including lipid bilayers, the actomyosin cortex or epithelial cell sheets. These interfaces exhibit a complex interplay between elasticity, low Reynolds number interfacial hydrodynamics, chemistry and geometry, and govern important biological processes such as cellular traffic, division, migration or tissue morphogenesis. To address the modelling challenges posed by this class of problems, in which interfacial phenomena tightly interact with the shape and dynamics of the surface, we develop a general continuum mechanics and computational framework for fluid deformable surfaces. The dual solid–fluid nature of fluid deformable surfaces challenges classical Lagrangian or Eulerian descriptions of deforming bodies. Here, we extend the notion of arbitrarily Lagrangian–Eulerian (ALE) formulations, well-established for bulk media, to deforming surfaces. To systematically develop models for fluid deformable surfaces, which consistently treat all couplings between fields and geometry, we follow a nonlinear Onsager formalism according to which the dynamics minimizes a Rayleighian functional where dissipation, power input and energy release rate compete. Finally, we propose new computational methods, which build on Onsager’s formalism and our ALE formulation, to deal with the resulting stiff system of higher-order partial differential equations. We apply our theoretical and computational methodology to classical models for lipid bilayers and the cell cortex. The methods developed here allow us to formulate/simulate these models in their full three-dimensional generality, accounting for finite curvatures and finite shape changes. This article has been published in a revised form in Journal of fluid mechanics,
Abstract
Fluid deformable surfaces are ubiquitous in cell and tissue biology, including lipid bilayers, the actomyosin cortex or epithelial cell sheets. These interfaces exhibit a [...]
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The plasma membrane as a mechanochemical transducer
A. Roux, X. Quiroga, N. Walani, M. Arroyo, P. Roca

Philosophical transaction of the Royal Society B. Diological sciences (2019). Vol. 374, pp. 1-15

Abstract
Cells are constantly submitted to external mechanical stresses, which they must withstand and respond to. By forming a physical boundary between cells and their environment that is also a biochemical platform, the plasma membrane (PM) is a key interface mediating both cellular response to mechanical stimuli, and subsequent biochemical responses. Here, we review the role of the PM as a mechanosensing structure. We first analyse how the PM responds to mechanical stresses, and then discuss how this mechanical response triggers downstream biochemical responses. The molecular players involved in PM mechanochemical transduction include sensors of membrane unfolding, membrane tension, membrane curvature or membrane domain rearrangement. These sensors trigger signalling cascades fundamental both in healthy scenarios and in diseases such as cancer, which cells harness to maintain integrity, keep or restore homeostasis and adapt to their external environment. This article is part of a discussion meeting issue ‘Forces in cancer: interdisciplinary approaches in tumour mechanobiology’.
Abstract
Cells are constantly submitted to external mechanical stresses, which they must withstand and respond to. By forming a physical boundary between cells and their environment [...]
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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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