Scipedia: Documents published in 2020

Extraction of a crack opening from a continuous approach using regularized damage models

María Jesús Samper — Tue, 10 Mar 2020 13:32:02 +0100

Crack opening governs many transfer properties that play a pivotal role in durability analyses. Instead of trying to combine continuum and discrete models in computational analyses, it would be attractive to derive from the continuum approach an estimate of crack opening, without considering the explicit description of a discontinuous displacement field in the computational model. This is the prime objective of this contribution. The derivation is based on the comparison between two continuous variables: the distribution if the effective non local strain that controls damage and an analytical distribution of the effective non local variable that derives from a strong discontinuity analysis. Close to complete failure, these distributions should be very close to each other. Their comparison provides two quantities: the displacement jump across the crack [U] and the distance between the two profiles. This distance is an error indicator defining how close the damage distribution is from that corresponding to a crack surrounded by a fracture process zone. It may subsequently serve in continuous/discrete models in order to define the threshold below which the continuum approach is close enough to the discrete one in order to switch descriptions. The estimation of the crack opening is illustrated on a one-dimensional example and the error between the profiles issued from discontinuous and FE analyses is found to be of a few percents close to complete failure.

NURBS-enhanced finite element method (NEFEM)

María Jesús Samper — Tue, 10 Mar 2020 13:15:39 +0100

An improvement to the classical finite element (FE) method is proposed. It is able to exactly represent the geometry by means of the usual CAD description of the boundary with non-uniform rational B-splines (NURBS). Here, the 2D case is presented. For elements not intersecting the boundary, a standard FE interpolation and numerical integration are used. But elements intersecting the NURBS boundary need a specifically designed piecewise polynomial interpolation and numerical integration. A priori error estimates are also presented. Finally, some examples demonstrate the applicability and benefits of the proposed methodology. NURBS-enhanced finite element method (NEFEM) is at least one order of magnitude more precise than the corresponding isoparametric FE in every numerical example shown. This is the case for both continuous and discontinuous Galerkin formulations. Moreover, for a desired precision, NEFEM is also more computationally efficient, as shown in the numerical examples. The use of NEFEM is strongly recommended in the presence of curved boundaries and/or when the boundary of the domain has complex geometric details. The possibility of computing an accurate solution with coarse meshes and high-order interpolations makes NEFEM a more efficient strategy than classical isoparametric FE.

Upper and lower bounds in limit analysis: adaptive meshing strategies and discontinuous loading

María Jesús Samper — Tue, 10 Mar 2020 13:05:07 +0100

Upper and lower bounds of the collapse load factor are here obtained as the optimum values of two discrete constrained optimization problems. The membership constraints for Von Mises and Mohr–Coulomb plasticity criteria are written as a set of quadratic constraints, which permits one to solve the optimization problem using specific algorithms for Second‐Order Conic Program (SOCP). From the stress field at the lower bound and the velocities at the upper bound, we construct a novel error estimate based on elemental and edge contributions to the bound gap. These contributions are employed in an adaptive remeshing strategy that is able to reproduce fan‐type mesh patterns around points with discontinuous surface loading. The solution of this type of problems is analysed in detail, and from this study some additional meshing strategies are also described. We particularise the resulting formulation and strategies to two‐dimensional problems in plane strain and we demonstrate the effectiveness of the method with a set of numerical examples extracted from the literature.

NURBS-enhanced finite element method for Euler equations

María Jesús Samper — Tue, 10 Mar 2020 11:57:50 +0100

In this work, the NURBS-enhanced finite element method (NEFEM) is combined with a discontinuous Galerkin (DG) formulation for the numerical solution of Euler equations of gas dynamics. With NEFEM, numerical fluxes along curved boundaries are computed much more accurately due to the exact geometric representation of the computational domain. The proper implementation of the wall boundary condition and the exact geometry provide accurate results even with a linear approximation of the solution. A detailed comparison of NEFEM in front of isoparametric finite elements is presented, demonstrating the superiority of NEFEM approach for both linear and higher-order computations

Discontinuous Galerkin methods for the Stokes equations using divergence-free approximations

María Jesús Samper — Tue, 10 Mar 2020 11:52:36 +0100

A discontinuous Galerkin (DG) method with solenoidal approximation for the simulation of incompressible flow is proposed. It is applied to the solution of the Stokes equations. The interior penalty method is employed to construct the DG weak form. For every element, the approximation space for the velocity field is decomposed as the direct sum of a solenoidal space and an irrotational space. This allows to split the DG weak form into two uncoupled problems: the first one solves for the velocity and the hybrid pressure (pressure along the mesh edges) and the second one allows the computation of the pressure in the element interior. Furthermore, the introduction of an extra penalty term leads to an alternative DG formulation for the computation of solenoidal velocities with no presence of pressure terms. Pressure can then be computed as a post-process of the velocity solution. Numerical examples demonstrate the applicability of the proposed methodologies.

Stability of incompressible formulations enriched with X-FEM

María Jesús Samper — Tue, 10 Mar 2020 11:41:26 +0100

The treatment of (near-)incompressibility is a major concern for applications involving rubber-like materials, or when important plastic ows occurs as in forming processes. The use of mixed nite element methods is known to prevent the locking of the nite element approximation in the incompressible limit. However, it also introduces a critical condition for the stability of the formulation, called the infsup or LBB condition. Recently, the nite element method has evolved with the introduction of the partition of unity. The eXtended Finite Element Method (XFEM) uses the partition of unity to remove the need to mesh physical surfaces or to remesh them as they evolve. The enrichment of the displacement eld makes it possible to treat surfaces of discontinuity inside nite elements. In this paper, some strategies are proposed for the enrichment of mixed nite element approximations in the incompressible setting. The case of holes, material interfaces and cracks are considered. Numerical examples show that for well chosen enrichment strategies, the nite element convergence rate is preserved and the inf-sup condition is passed.

Mathematical e-Learning: state of the art and experiences at the Open University of Catalonia

María Jesús Samper — Tue, 10 Mar 2020 11:10:03 +0100

In this article we present a review of the state of the art in mathematical e-learning and some personal experiences on this area developed during the last eleven years at the Open University of Catalonia (UOC), a completely online university located in Spain. The article discusses important aspects related to online mathematics courses offered in higher education programs, including: benefits and challenges, universities offering this type of education, methodological considerations, emergent technologies, learning projects and environments, etc. Also, key aspects of the UOC mathematical e-learning model and its historical evolution are described and analysed. Special attention is paid to mathematical curricula in computer sciences degrees, where a lot of work needs to be done in order to adapt mathematics courses to the continuously changing educational necessities of students. A curricula design proposal, based on a top-down approach, is presented as a best practice. Finally, some trends and future perspectives on the subject are suggested.

Hydraulic behaviour of a representative structural volume for containment buildings

María Jesús Samper — Tue, 10 Mar 2020 10:58:52 +0100

For particular structures like containment buildings of nuclear power plants, the study of the hydraulic behaviour is of great concern. These structures are indeed the third barrier used to protect the environment in case of accidents. The evolution of the leaking rate through the porous medium is closely related to the changes in the permeability during the ageing process of the structure. It is thus essential to know the relation between concrete degradation and the transfer property when the consequences of a mechanical loading on the hydraulic behaviour have to be evaluated. A chained approach is designed for this purpose. The mechanical behaviour is described by an elastic plastic damage formulation, where damage is responsible for the softening evolution while plasticity accounts for the development of irreversible strains. The drying process is evaluated according to a non-linear equation of diffusion. From the knowledge of the damage and the degree of saturation, a relation is proposed to calculate the permeability of concrete. Finally, the non-homogeneous distribution of the hydraulic conductivity is included in the hydraulic problem which is in fact the association of the mass balance equation for gas phase and Darcy law. From this methodology, it is shown how an indicator for the hydraulic flows can be deduced.

Goal oriented error estimation for the element free Galerkin method

María Jesús Samper — Tue, 10 Mar 2020 10:54:49 +0100

A novel approach for implicit residual-type error estimation in meshfree methods is presented. This allows to compute upper and lower bounds of the error in energy norm with the ultimate goal of obtaining bounds for outputs of interest. The proposed approach precludes the main drawbacks of standard residual type estimators circumventing the need of flux-equilibration and resulting in a simple implementation that avoids integrals on edges/sides of a domain decomposition (mesh). This is especially interesting for mesh-free methods.

Stabilized updated Lagrangian corrected SPH for explicit dynamic problems

María Jesús Samper — Tue, 10 Mar 2020 10:46:15 +0100

Smooth Particle Hydrodynamics with a total Lagrangian formulation are, in general, more robust than nite elements for large distortion problems. Nevertheless, updating the reference con¯guration may still be necessary in some problems involving extremely large distortions. However, as discussed here a standard updated formulation suffers the presence of zero energy modes that are activated and may spoil completely the solution. It is important to note that, unlike an Eulerian formulation,the updated Lagrangian does not present tension instability but only zero energy modes. Here an stabilization technique is incorporated to the updated formulation to obtain an improved method without mechanisms and capable to solve problems with extremely large distortions.

Updated Lagrangian formulation for corrected smooth particle hydrodynamics

María Jesús Samper — Tue, 10 Mar 2020 10:40:53 +0100

Smooth Particle Hydrodynamics (SPH) are, in general, more robust than finite elements for large distortion problems. Nevertheless, updating the reference configuration may be necessary in some problems involving extremely large distortions. If a standard updated formulation is implemented in SPH zero energy modes are activated and spoil the solution. It is important to note that the updated Lagrangian does not present tension instability but only zero energy modes. Here an stabilization technique is incorporated to the updated formulation to obtain an improved method without mechanisms.

An elastic plastic damage formulation for concrete: application to elementary and structural tests

María Jesús Samper — Tue, 10 Mar 2020 10:35:17 +0100

Pure elastic damage models or pure elastic plastic constitutive laws are not totally satisfactory to describe the behaviour of concrete. They indeed fail to reproduce the unloading slopes during cyclic loading which define experimentally the value of the damage in the material. When coupled effects are considered, in particular in hydro-mechanical problems, the capability of numerical models to reproduce the unloading behaviour is essential, because an accurate value of the damage, which controls the material permeability, is needed. In the context of very large size calculations that are needed for 3D massive structures heavily reinforced and pre-stressed (such as containment vessels), constitutive relations ought also to be as simple as possible. Here an elastic plastic damage formulation is proposed to circumvent the disadvantages of pure plastic and pure damage approaches. It is based on an isotropic damage model combined with a hardening yield plastic surface in order to reach a compromise as far as simplicity is concerned. Three elementary tests are first considered for validation. A tension test, a cyclic compression test and triaxial tests illustrate the improvements achieved by the coupled law compared to a simple damage model (plastic strains, change of volumetric behaviour, decrease in the elastic slope under hydrostatic pressures). Finally, one structural application is also considered: a concrete column wrapped in a steel tube.

Étude de la stabilité d'une formulation incompressible traitée par X-FEM

María Jesús Samper — Mon, 09 Mar 2020 17:33:20 +0100

The treatment of (near-)incompressibility is a major concern for the simulation of rubber-like parts, or forming processes. The use of mixed finite element methods is known to prevent the locking of the F.E. approximation in the incompressible limit. However, the stability of these formulations is conditionned by the fullfilment of the inf-sup condition. Recently, finite elements method has evolved with the introduction of the partition of unity. The X-FEM uses it to remove the need to mesh (and remesh) physical surfaces. In this paper, a strategy is proposed for the treatment of holes within X-FEM in the incompressible setting. Numerical examples show that F.E. convergence rate is preserved and that the inf-sup condition is passed.

Mesh projection between parametric surfaces

María Jesús Samper — Mon, 09 Mar 2020 17:21:05 +0100

This paper presents a new algorithm to map a given mesh over a source surface onto a target surface. This projection is determined by means of a least-squares approximation of a transformation defined between the loops of boundary nodes of the cap surfaces in the parametric spaces. Once the new mesh is obtained on the parametric space of the target surface, it is mapped to the target surface according to its parameterization. Therefore, in contrast with the usual techniques, the developed algorithm does not require solving any root finding problem to ensure that the projected nodes are on the target surface. Finally, this projection algorithm is extended to three-dimensional cases and included in a sweep meshing tool in order to generate the inner layers of elements in the physical space.

The computation of bounds for linear-functional outputs of weak solutions to the two-dimensional elasticity equations

María Jesús Samper — Mon, 09 Mar 2020 17:11:31 +0100

We present a method for the computation of upper and lower bounds for linear-functional outputs of the exact solutions to the two dimensional elasticity equations. The method can be regarded as a generalization of the well known complementary energy principle. The desired output is cast as the supremum of a quadratic-linear convex functional over an infinite dimensional domain. Using duality the computation of an upper bound for the output of interest is reduced to a feasibility problem for the complementary, or dual, problem. In order to make the problem tractable from a computational perspective two additional relaxations that preserve the bounding properties are introduced. First, the domain is triangulated and a domain decomposition strategy is used to generate a sequence of independent problems to be solved over each triangle. The Lagrange multipliers enforcing continuity are approximated using piecewise linear functions over the edges of the triangulation. Second, the solution of the adjoint problem is approximated over the triangulation using a standard Galerkin finite element approach. A lower bound for the output of interest is computed by repeating the process for the negative of the output. Reversing the sign of the computed upper bound for the negative of the output yields a lower bound for the actual output. The method can be easily generalized to three dimensions. However, a constructive proof for the existence of feasible solutions for the outputs of interest is only given in two dimensions. The computed bound gaps are found to converge optimally, that is, at the same rate as the finite element approximation. An attractive feature of the proposed approach is that it allows for a data set to be generated that can be used to certify and document the computed bounds. Using this data set and a simple algorithm, the correctness of the computed bounds can be established without recourse to the original code used to compute them. In the present paper, only computational domains whose boundary is made up of straight sided segments and polynomially varying loads are considered. Two examples are given to illustrate the proposed methodology.

Continuous blending of SPH with finite elements

María Jesús Samper — Mon, 09 Mar 2020 16:41:03 +0100

This paper proposes a methodology for the continuous blending of the finite element method and smooth particle hydrodynamics. The coupled approximation with finite elements and particles, and the discretization of the boundary value problem with a coupled integration, are described. An integration correction is also proposed to stabilize the solution. Some numerical examples demonstrate the applicability of the method.

A new damage model based on non-local displacements

María Jesús Samper — Mon, 09 Mar 2020 16:34:18 +0100

A new non-local damage model is presented. Non-locality (of integral or gradient type) is incorporated into the model by means of non-local displacements. This contrasts with existing damage models, where a non-local strain or strain-related state variable is used. The new model is very attractive from a computational viewpoint, especially regarding the computation of the consistent tangent matrix needed to achieve quadratic convergence in Newton iterations. At the same time, its physical response is very similar to that of the standard models, including its regularization capabilities. All these aspects are discussed in detail and illustrated by means of numerical examples.

Benchmarks for the validation of a non local model

María Jesús Samper — Mon, 09 Mar 2020 16:26:43 +0100

The aim of this contribution is to present a series of organised benchmarks that helps at validating the robustness of the FE implementation of a constitutive relation, its pertinence with respect to experiments, and quantitative and qualitative comparisons of structural elements. It is applied to an isotropic damage model used for concrete, coupled with a non local gradient formulation to avoid a spurious description of strain localisation. After the elementary (uniaxial monotonic, cyclic or triaxial loading) and structural (three point bending tests) simulations, an industrial application is presented in the form of a representative structural volume of a containment building for French nuclear power plants.

Efficient and reliable nonlocal damage models

María Jesús Samper — Mon, 09 Mar 2020 15:35:32 +0100

We present an efficient and reliable approach for the numerical modelling of failure with nonlocal damage models. The two major numerical challenges––the strongly nonlinear, highly localized and parameter-dependent structural response of quasi-brittle materials, and the interaction between nonadjacent finite elements associated to nonlocality––are addressed in detail. Reliability of the numerical results is ensured by an h-adaptive strategy based on error estimation. We use a residual-type error estimator for nonlinear FE analysis based on local computations, which, at the same time, accounts for the nonlocality of the damage model. Efficiency is achieved by a proper combination of load-stepping control technique and iterative solver for the nonlinear equilibrium equations. A major issue is the computation of the consistent tangent matrix, which is nontrivial due to nonlocal interaction between Gauss points. With computational efficiency in mind, we also present a new nonlocal damage model based on the nonlocal average of displacements. For this new model, the consistent tangent matrix is considerably simpler to compute than for current models. The various ideas discussed in the paper are illustrated by means of three application examples: the uniaxial tension test, the three-point bending test and the single-edge notched beam test.

A comparison of two formulations to blend finite elements and mesh-free methods

María Jesús Samper — Mon, 09 Mar 2020 15:28:34 +0100

Mesh-free methods have since their early developments been blended to the finite element formulation in order to benefit from the advantages of both numerical techniques. In this paper, two recently proposed formulations to couple mesh-free and finite element methods are discussed and compared.

Imposing essential boundary conditions in mesh-free methods

María Jesús Samper — Mon, 09 Mar 2020 15:23:21 +0100

Imposing essential boundary conditions is a key issue in mesh-free methods. The mesh-free interpolation does not verify the Kronecker delta property and, therefore, the imposition of prescribed values is not as straightforward as for the finite element method. The aim of this paper is to present a general overview on the existing techniques to enforce essential boundary conditions in Galerkin based mesh-free methods. Special attention is paid to the mesh-free coupling with finite elements for the imposition of prescribed values and to methods based on a modification of the Galerkin weak form. Particular examples are used to analyze and compare their performance in different situations.

Pseudo-divergence-free element free Galerkin method for incompressible fluid flow

María Jesús Samper — Mon, 09 Mar 2020 15:17:05 +0100

Incompressible modeling in finite elements has been a major concern since its early developments and has been extensively studied. However, incompressibility in mesh-free methods is still an open topic. Thus, instabilities or locking can preclude the use of mesh-free approximations in such problems. Here, a novel mesh-free formulation is proposed for incompressible flow. It is based on defining a pseudo-divergence-free interpolation space. That is, the finite dimensional interpolation space approaches a divergence-free space when the discretization is refined. Note that such an interpolation does not include any overhead in the computations. The numerical evaluations are performed using the inf–sup numerical test and two well-known benchmark examples for Stokes flow.

Computing bounds for linear functionals of exact weak solutions to Poisson's equation

María Jesús Samper — Mon, 09 Mar 2020 15:04:33 +0100

We present a method for Poisson’s equation that computes guaranteed upper and lower bounds for the values of piecewise-polynomial linear functional outputs of the exact weak solution of the infinite-dimensional continuum problem with piecewise-polynomial forcing. The method results from exploiting the Lagrangian saddle point property engendered by recasting the output problem as a constrained minimization problem. Localization is achieved by Lagrangian relaxation and the bounds are computed by appeal to a local dual problem. The proposed method computes approximate Lagrange multipliers using traditional finite element approximations to calculate a primal and an adjoint solution along with well known hybridization techniques to calculate interelement continuity multipliers. The computed bounds hold uniformly for any level of refinement, and in the asymptotic convergence regime of the finite element method, the bound gap decreases at twice the rate of the energy norm measure of the error in the finite element solution. Given a finite element solution and its output adjoint solution, the method can be used to provide a certificate of precision for the output with an asymptotic complexity that is linear in the number of elements in the finite element discretization. The elemental contributions to the bound gap are always positive and hence lend themselves to be used as adaptive indicators, as we demonstrate with a numerical example.

Numerical modelling of void inclusions in porous media

María Jesús Samper — Mon, 09 Mar 2020 14:43:32 +0100

Numerical modelling of porous flow in a low‐permeability matrix with high‐permeability inclusions is a challenging task because the large ratio of permeabilities ill‐conditions the finite element system of equations. We propose a coupled model where Darcy flow is used for the porous matrix and potential flow is used for the inclusions. We discuss appropriate interface conditions in detail and show that the head drop in the inclusions can be prescribed in a very simple way. Algorithmic aspects are treated in full detail. Numerical examples show that this coupled approach precludes ill‐conditioning and is more efficient than heterogeneous Darcy flow.

Locking in the incompressible limit: pseudo-divergence-free element free Galerkin

María Jesús Samper — Mon, 09 Mar 2020 14:37:04 +0100

Locking in finite elements has been a major concern since its early developments. It appears because poor numerical interpolation leads to an over-constrained system. This paper proposes a new formulation that asymptotically suppresses locking for the element free Galerkin (EFG) method in incompressible limit, i.e. the so-called volumetric locking. Originally it was claimed that EFG did not present volumetric locking. However, recently, performing a modal analysis, the senior author has shown that EFG presents volumetric locking. In fact, it is concluded that an increase of the dilation parameter attenuates, but never suppresses, the volumetric locking and that, as in standard finite elements, an increase in the order of reproducibility (interpolation degree) reduces the relative number of locking modes. Here an improved formulation of the EFG method is proposed in order to alleviate volumetric locking.Diffuse derivatives are defined in the thesis of the second author and their convergence to the derivatives of the exact solution, when the radius of the support goes to zero (for a fixed dilation parameter), it is proved. Therefore, diffuse divergence converges to the exact divergence. Since the diffuse divergence-free condition can be imposed a priori, new interpolation functions are defined that asymptotically verify the incompressibility condition. Modal analysis and numerical results for classical benchmark tests in solids corroborate this issue.

Numerical representation of the quality measures of triangles and triangular meshes

María Jesús Samper — Mon, 09 Mar 2020 14:26:56 +0100

In this note a new procedure to represent the quality measure for triangles is proposed. The triangles are identified by their three angles and are represented in a bounded domain, called angle representation region, according to the area co-ordinates, which are common and well known by finite element users. The developed representation can also be used in order to visualize the characteristics of any quality measure. This new procedure is extended to graphically represent triangular meshes in the angle representation region.

Efficient and accurate approach for powder compaction problems

María Jesús Samper — Mon, 09 Mar 2020 14:18:19 +0100

In this paper, a new approach for powder cold compaction simulations is presented. A density-dependent plastic model within the framework of finite strain multiplicative hyperelastoplasticity is used to describe the highly nonlinear material behaviour; the Coulomb dry friction model is used to capture friction effects at die-powder contact; and an Arbitrary Lagrangian–Eulerian (ALE) formulation is used to avoid the (usual) excessive distortion of Lagrangian meshes caused by large mass fluxes. Several representative examples, involving structured and unstructured meshes are simulated. The results obtained agree with the experimental data and other numerical results reported in the literature. It is shown that, contrary to other Lagrangian and adaptive h-remeshing approaches recently reported for this type of problems, the present approach verifies the mass conservation principle with very low relative errors (less than 1% in all ALE examples and exactly in the pure Lagrangian examples). Moreover, thanks to the use of an ALE formulation and in contrast with other simulations, the presented density distributions do not present spurious oscillations.

Time accurate consistently stabilized mesh-free methods for convection dominated problems

María Jesús Samper — Mon, 09 Mar 2020 14:10:33 +0100

The behaviour of high‐order time stepping methods combined with mesh‐free methods is studied for the transient convection–diffusion equation. Particle methods, such as the element‐free Galerkin (EFG) method, allow to easily increase the order of consistency and, thus, to formulate high‐order schemes in space and time. Moreover, second derivatives of the EFG shape functions can be constructed with a low extra cost and are well defined, even for linear interpolation. Thus, consistent stabilization schemes can be considered without loss in the convergence rates.

Locking in the incompressible limit: pseudo-divergence-free element free Galerkin

María Jesús Samper — Mon, 09 Mar 2020 13:58:06 +0100

Locking in finite elements has been a major concern since its early developments and has been extensively studied. However, locking in mesh-free methods is still an open topic. Until now the remedies proposed in the literature are extensions of already developed methods for finite elements. Here a new approach is explored and an improved formulation that asymptotically suppresses volumetric locking for the EFG method is proposed. The diffuse divergence converges to the exact divergence. Since the diffuse divergence-free condition can be imposed a priori, new interpolation functions are defined that asymptotically verify the incompressibility condition. Modal analysis and numerical results for classical benchmark tests in solids and fluids corroborate this issue.

The efficient computation of bounds for functionals of finite element solutions in large strain elasticity

María Jesús Samper — Mon, 09 Mar 2020 13:47:03 +0100

We present an implicit a posteriori finite element procedure to compute bounds for functional outputs of finite element solutions in large strain elasticity. The method proposed relies on the existence of a potential energy functional whose local minima, over a space of suitably chosen continuous functions, corresponds to the problem solution. The output of interest is cast as a constrained minimization problem over an enlarged discontinuous finite element space. A Lagrangian is formed were the multipliers are an adjoint solution, which enforces equilibrium, and hybrid fluxes, which constrain the solution to be continuous. By computing approximate values for the multipliers on a coarse mesh, strict upper and lower bounds for the output of interest on a suitably refined mesh, are obtained. This requires a minimization over a discontinuous space, which can be carried out locally at low cost. The computed bounds are uniformly valid regardless of the size of the underlying coarse discretization. The method is demonstrated with two applications involving large strain plane stress incompressible neo-Hookean hyperelasticity.

Time‐accurate solution of stabilized convection–diffusion–reaction equations: II. Accuracy analysis and examples

María Jesús Samper — Mon, 09 Mar 2020 13:39:18 +0100

The paper addresses the development of time‐accurate methods for solving transient convection–diffusion –reaction problems using finite elements. The accuracy characteristics of the spatially stabilized implicit multi‐stage time‐stepping schemes developed in a companion paper (Part I of this work) are analysed and compared here. This is done by means of a Fourier analysis. An important improvement is observed when the order of the method is increased. Moreover, the stabilization techniques proposed (streamline‐upwind Petrov–Galerkin (SUPG), Galerkin least‐square (GLS), sub‐grid scale (SGS) and least squares) do not degrade the phase accuracy. Finally, some examples are presented to show the applicability of these schemes.

Time-accurate solution of stabilized convection-difusion-reaction equations: I. Time and space discretization

María Jesús Samper — Mon, 09 Mar 2020 13:19:46 +0100

The paper addresses the development of time-accurate methods for solving transient convection-diffusion-reaction problems using finite elements. Multi-stage time-stepping schemes of high accuracy are used. They are first combined with a Galerkin formulation to briefly recall the time-space discretization. Then spatial stabilization techniques are combined with high-order time-stepping schemes. Moreover, a least-squares formulation is also developed for these high-order time schemes combined with C0 finite elements (in spite of the diffusion operator and without reducing the strong form into a system of first-order differential equations). The weak forms induced by the SUPG, GLS, SGS and least-squares formulations are presented and compared. In a companion paper (Part II of this work), the phase and damping properties of the developed schemes are analysed and numerical examples are included to confirm the effectiveness of the proposed methodology for solving time-dependent convection-diffusion-reaction problems.

Quantitative analysis of microvascular invasion preoperative prediction in solitary small hepatocellular carcinoma on dynamic enhancement MRI

Xueyan Zhou — Fri, 06 Mar 2020 08:16:05 +0100

The purpose of this study is to predict preoperatively microvascular invasion (MVI) of solitary small hepatocellular cancer (sHCC) by using the kinetic parameters analysis on dynamic enhancement magnetic resonance imaging (MRI). Patients (n = 61) with known solitary sHCC(≤3cm) were preoperatively examined with Gd-EOB-DTPA-enhanced MRI first before hepatic resection. The arterial peritumoral enhancement measured from the dynamic enhancement-MRI was analyzed by using quantitative kinetic parameters, including initial enhancement (E1), peak enhancement (E''peak''), and enhancement ratio (E''R'') calculated. Correlations between quantitative kinetic parameters and MVI were evaluated and differences between MVI positive and negative groups were assessed. Histopathological analysis of liver resection confirmed that 19 patients had sHCC with MVI and that 42 patients had sHCC without MVI. Average (± standard deviation) E1 is 0.36±0.12 and 0.46±0.09, E''peak'' is 0.78±0.24 and 0.74±0.18, and E''R'' is 0.42±0.20 and 0.56±0.17 for negative and positive group, respectively. Statistical analysis showed that average E1 and ER for the positive group were significantly higher (p less than 0.05) than the negative group. The receiver operating characteristics (ROC) analysis between the two groups had area under the curve of 0.74 and 0.71 for E1 and E''R'', respectively. Quantitative kinetic parameters analysis for the arterial peritumoral enhancement is feasibility to the prediction and assist diagnosis of MVI in clinical practice.

Error estimation and adaptivity for nonlinear FE analysis

María Jesús Samper — Thu, 05 Mar 2020 09:47:29 +0100

An adaptive strategy for nonlinear finite-element analysis, based on the combination of error estimation and h-remeshing, is presented. Its two main ingredients are a residual-type error estimator and an unstructured quadrilateral mesh generator. The error estimator is based on simple local computations over the elements and the so-called patches. In contrast to other residual estimators, no flux splitting is required. The adaptive strategy is illustrated by means of a complex nonlinear problem: the failure analysis of a single-edge notched beam. The quasi-brittle response of concrete is modelled by means of a nonlocal damage model.

Arbitrary Lagrangian-Eulerian (ALE) formulation for hyperelastoplasticity

María Jesús Samper — Wed, 04 Mar 2020 16:40:55 +0100

The arbitrary Lagrangian–Eulerian (ALE) description in non‐linear solid mechanics is nowadays standard for hypoelastic–plastic models. An extension to hyperelastic–plastic models is presented here. A fractional‐step method—a common choice in ALE analysis—is employed for time‐marching: every time‐step is split into a Lagrangian phase, which accounts for material effects, and a convection phase, where the relative motion between the material and the finite element mesh is considered. In contrast to previous ALE formulations of hyperelasticity or hyperelastoplasticity, the deformed configuration at the beginning of the time‐step, not the initial undeformed configuration, is chosen as the reference configuration. As a consequence, convecting variables are required in the description of the elastic response. This is not the case in previous formulations, where only the plastic response contains convection terms. In exchange for the extra convective terms, however, the proposed ALE approach has a major advantage: only the quality of the mesh in the spatial domain must be ensured by the ALE remeshing strategy; in previous formulations, it is also necessary to keep the distortion of the mesh in the material domain under control. Thus, the full potential of the ALE description as an adaptive technique can be exploited here. These aspects are illustrated in detail by means of three numerical examples: a necking test, a coining test and a powder compaction test.

Coupling finite elements and particles for adaptivity: an application to consistently stabilized convection–diffusion

María Jesús Samper — Wed, 04 Mar 2020 16:33:26 +0100

A mixed approximation coupling finite elements and mesh-less methods is presented. It allows selective refinement of the finite element solution without remeshing cost. The distribution of particles can be arbitrary. Continuity and consistency is preserved. The behaviour of the mixed interpolation in the resolution of the convection-diffusion equation is analyzed.

Arbitrary Lagrangian-Eulerian simulation of powder compaction processes

María Jesús Samper — Wed, 04 Mar 2020 15:30:24 +0100

In this paper, a new strategy for the simulation of quasi-static cold compaction processes of powders is presented. A material model formulated within the framework of isotropic finite strain multiplicative hyperelastoplasticity is used. An elliptic plastic model expressed in terms of the Kirchhoff stresses and the relative density models the transition between the loose powder and the compacted sample. The Coulomb dry friction model is used to capture friction effects at powder-die contact. Excessive distortion of Lagrangian meshes due to large mass fluxes is usual in powder compaction problems. Moreover, Lagrangian approaches cannot deal properly with mass fluxes around sharp corners. For these reasons, an Arbitrary Lagrangian-Eulerian (ALE) formulation is used here. The present results illustrate that this approach allows simulating highly demanding powder compaction processes without mesh distortion and spurious oscillations in the results. Moreover, it is shown that the mass conservation principle is verified with a low relative error.

Consistent tangent matrices for density-dependent finite plasticity models

María Jesús Samper — Wed, 04 Mar 2020 15:16:41 +0100

The consistent tangent matrix for density-dependent plastic models within the theory of isotropic multiplicative hyperelastoplasticity is presented here. Plastic equations expressed as general functions of the Kirchhoff stresses and density are considered. They include the Cauchy-based plastic models as a particular case. The standard exponential return-mapping algorithm is applied, with the density playing the role of a fixed parameter during the nonlinear plastic corrector problem. The consistent tangent matrix has the same structure as in the usual density-independent plastic models. A simple additional term takes into account the influence of the density on the plastic corrector problem. Quadratic convergence results are shown for several representative examples involving geomaterial and powder constitutive models.

Consistent tangent matrices for substepping schemes

María Jesús Samper — Wed, 04 Mar 2020 15:05:53 +0100

A very simple and general expression of the consistent tangent matrix for substepping time-integration schemes is presented. If needed, the derivatives required for the computation of the consistent tangent moduli can be obtained via numerical differentiation. These two strategies (substepping and numerical differentiation) lead to quadratic convergence in complex nonlinear inelasticity problems.

Adaptive analysis based on error estimation for nonlocal damage models

María Jesús Samper — Wed, 04 Mar 2020 14:51:59 +0100

An adaptive finite element strategy for nonlocal damage computations is presented. The proposed approach is based on the combination of a residual-type error estimator and quadrilateral h-remeshing. A distinctive feature of the error estimator is that it consists in solving simple local problems over elements and so-called patches. The paper focuses on how the nonlocality of the constitutive model should be accounted for when solving these local problems. It is shown that the nonlocal damage models must be slightly modified. The resulting adaptive strategy is illustrated by means of some numerical examples involving the single-edge notched beam test.

Locking in the incompressible limit for the element-free Galerkin method

María Jesús Samper — Wed, 04 Mar 2020 14:42:40 +0100

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.

Arbitrary Lagrangian-Eulerian formulation for fluid-rigid body interaction

María Jesús Samper — Wed, 04 Mar 2020 14:36:00 +0100

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.

An improved algorithm to smooth graded quadrilateral meshes preserving the prescribed element size

María Jesús Samper — Wed, 04 Mar 2020 14:29:17 +0100

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.

Error estimation and adaptivity for nonlocal damage models

María Jesús Samper — Wed, 04 Mar 2020 14:24:26 +0100

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.

Enrichment and coupling of the finite element and meshless methods

María Jesús Samper — Wed, 04 Mar 2020 14:15:06 +0100

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.

Efficient unstructured quadrilateral mesh generation

María Jesús Samper — Wed, 04 Mar 2020 13:55:11 +0100

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.

Numerical differentiation for local and global tangent operators in computational plasticity.

María Jesús Samper — Tue, 03 Mar 2020 16:15:58 +0100

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.

Numerical differentiation for non-trivial consistent tangent matrices: an application to the MRS-lade model

María Jesús Samper — Tue, 03 Mar 2020 15:26:02 +0100

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.

High-order accurate time-stepping schemes for convection-diffusion problems

María Jesús Samper — Tue, 03 Mar 2020 15:14:27 +0100

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.

Adapting Broyden method to handle linear constraints imposed via Lagrange multipliers

María Jesús Samper — Tue, 03 Mar 2020 15:03:27 +0100

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.

FIC-FEM formulation for the multidimensional transient advection-diffusion-absorption equation (preprint)

María Jesús Samper — Tue, 03 Mar 2020 15:03:05 +0100

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.

Accuracy of two stress update algorithms for shear-free large deformations paths

María Jesús Samper — Tue, 03 Mar 2020 14:56:25 +0100

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.

Analysis of the vane test considering size and time effects

María Jesús Samper — Tue, 03 Mar 2020 14:47:58 +0100

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.

Plastic flow potential for cone region on the MRS-Lade model

María Jesús Samper — Tue, 03 Mar 2020 14:35:13 +0100

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.

Adaptive analysis of yield line patterns in plates with the Arbitrary Lagrangian-Eulerian method

María Jesús Samper — Tue, 03 Mar 2020 14:26:46 +0100

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.

ALE stress update for transient and quasistatic processes

María Jesús Samper — Tue, 03 Mar 2020 14:19:23 +0100

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.

Comparing two algorithms to add large strains to small-strain FE code

María Jesús Samper — Tue, 03 Mar 2020 14:10:33 +0100

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.

Two stress update algorithms for large strains: accuracy analysis and numerical implementation

María Jesús Samper — Tue, 03 Mar 2020 14:03:53 +0100

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.

A note on a numerical benchmark test: an axisymmetric shell under ring loads

María Jesús Samper — Tue, 03 Mar 2020 13:58:58 +0100

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.

Arbitrary lagrangian-eulerian finite element analysis of strain localization in transient problems

María Jesús Samper — Tue, 03 Mar 2020 13:52:03 +0100

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.

New ALE applications in non-linear fast-transient solid dynamics

María Jesús Samper — Tue, 03 Mar 2020 13:32:26 +0100

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.

Discretization influence on regularization by two localization limiters

María Jesús Samper — Tue, 03 Mar 2020 13:25:47 +0100

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.

Numerical analysis of nonlinear large-strain consolidation and filling

María Jesús Samper — Tue, 03 Mar 2020 13:18:13 +0100

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.

Finite element analysis of bifurcation in nonlocal strain softening solids

María Jesús Samper — Tue, 03 Mar 2020 12:50:23 +0100

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.

Large-amplitude sloshing with submerged blocks

María Jesús Samper — Tue, 03 Mar 2020 11:50:28 +0100

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

Viscous flow with large free surface motion

María Jesús Samper — Tue, 03 Mar 2020 11:42:38 +0100

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.

Permeability and compressibility of slurries from seepage-induced consolidation

María Jesús Samper — Tue, 03 Mar 2020 11:39:30 +0100

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

Viscous Flow Structure Interaction

María Jesús Samper — Tue, 03 Mar 2020 11:07:52 +0100

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.

Converse flexoelectricity yields large piezoresponse force microscopy signals in non-piezoelectric materials

María Jesús Samper — Tue, 03 Mar 2020 09:50:42 +0100

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.

Phase-field modeling of fracture in ferroelectric materials

María Jesús Samper — Tue, 03 Mar 2020 09:28:43 +0100

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.

Trends and clinico-epidemiological features of human rabies cases in Bangladesh 2006–2018

Sumon Ghosh — Tue, 03 Mar 2020 07:26:02 +0100

Detection of highly pathogenic avian in waterfowl in Bangladesh

Sumon Ghosh — Tue, 03 Mar 2020 07:20:06 +0100

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.

Awareness of rabies and response to dog bites in a Bangladesh community

Sumon Ghosh — Tue, 03 Mar 2020 07:20:03 +0100

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.

The Pattern of Highly Pathogenic Avian Influenza H5N1 Outbreaks in South Asia

Sumon Ghosh — Tue, 03 Mar 2020 07:19:02 +0100

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

Trends and clinico-epidemiological features of human rabies cases in Bangladesh 2006–2018

Sumon Ghosh — Tue, 03 Mar 2020 07:17:02 +0100

Constructive and destructive interplay between piezoelectricity and flexoelectricity in flexural sensors and actuators

María Jesús Samper — Mon, 02 Mar 2020 16:47:56 +0100

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.

Three-dimensional simulation of crack propagation in ferroelectric polycrystals: Effect of combined toughening mechanisms

María Jesús Samper — Mon, 02 Mar 2020 16:28:28 +0100

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.

Conducting crack propagation driven by electric fields in ferroelectric ceramics

María Jesús Samper — Mon, 02 Mar 2020 15:35:55 +0100

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.

Phase-field modeling of crack propagation in piezoelectric and ferroelectric materials with different electromechanical crack conditions

María Jesús Samper — Mon, 02 Mar 2020 15:26:34 +0100

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.

Crack initiation patterns at electrode edges in multilayer ferroelectric actuators

María Jesús Samper — Mon, 02 Mar 2020 14:54:48 +0100

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.

Numerical simulation of intergranular and transgranular crack propagation in ferroelectric polycrystals

María Jesús Samper — Mon, 02 Mar 2020 14:24:16 +0100

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.

Phase-field modeling of the coupled microstructure and fracture evolution in ferroelectric single crystals

María Jesús Samper — Mon, 02 Mar 2020 14:10:10 +0100

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

Phase-field simulation of anisotropic crack propagation in ferroelectric single crystals: effect of microstructure on the fracture process

María Jesús Samper — Mon, 02 Mar 2020 13:54:18 +0100

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.

Experimental validation of large-scale simulations of dynamic fracture along weak planes

María Jesús Samper — Mon, 02 Mar 2020 13:28:39 +0100

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.

Numerical modelling and experimental validation of dynamic fracture events along weak planes

María Jesús Samper — Mon, 02 Mar 2020 13:14:46 +0100

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.

A phenomenological cohesive model of ferroelectric fatigue

María Jesús Samper — Mon, 02 Mar 2020 13:04:59 +0100

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.

Rayleigh wave correction for the BEM analysis of two-dimensional elastodynamic problems in a half-space

María Jesús Samper — Mon, 02 Mar 2020 12:20:03 +0100

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.

Use of reciprocity considerations for the two-dimensional BEM analysis of wave propagation in an elastic half-space with applications to acoustic emission

María Jesús Samper — Mon, 02 Mar 2020 12:06:39 +0100

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.

A model for the ultrasonic detection of surface-breaking cracks by the scanning laser source technique

María Jesús Samper — Mon, 02 Mar 2020 12:00:56 +0100

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.

Thermoelastic generation of ultrasound by line-focused laser irradiation

María Jesús Samper — Mon, 02 Mar 2020 11:12:08 +0100

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.

D2.4 First Release of the mesh generation/adaptation capabilities

Cecilia Soriano — Thu, 27 Feb 2020 16:43:02 +0100

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.

D8.3 Report on exploitation activities

Cecilia Soriano — Thu, 27 Feb 2020 16:40:02 +0100

This deliverable describes the exploitation activities carried our in ExaQUte in the framework of WP9.

D8.2 Report on dissemination activities

Cecilia Soriano — Thu, 27 Feb 2020 16:36:02 +0100

This deliverable descritves the Dissemination activities in ExaQUte

D4.3 Benchmarking report as tested on the available infrastructure

Cecilia Soriano — Thu, 27 Feb 2020 16:31:02 +0100

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.

Phase field modeling of brittle fracture in an Euler–Bernoulli beam accounting for transverse part-through cracks

María Jesús Samper — Thu, 27 Feb 2020 14:48:59 +0100

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.

Approximation of tensor fields on surfaces of arbitrary topology based on local Monge parametrizations

María Jesús Samper — Thu, 27 Feb 2020 14:43:07 +0100

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.

Surface tension controls the hydraulic fracture of adhesive interfaces bridged by molecular bonds

María Jesús Samper — Thu, 27 Feb 2020 14:34:16 +0100

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.

Out-of-equilibrium mechanochemistry and self-organization of fluid membranes interacting with curved proteins

María Jesús Samper — Thu, 27 Feb 2020 14:14:57 +0100

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.

Modelling fluid deformable surfaces with an emphasis on biological interfaces

María Jesús Samper — Thu, 27 Feb 2020 14:07:03 +0100

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,

The plasma membrane as a mechanochemical transducer

María Jesús Samper — Thu, 27 Feb 2020 14:02:37 +0100

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’.