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See detailComputational homogenization of cellular materials with propagation of instabilities through the scales
Nguyen, Van Dung ULg; Noels, Ludovic ULg

Conference (2014, August 29)

The aim of this work is to develop an efficient multi–scale finite element framework to capture the buckling instabilities in cellular materials. As a classical multi–scale computational homogenization ... [more ▼]

The aim of this work is to develop an efficient multi–scale finite element framework to capture the buckling instabilities in cellular materials. As a classical multi–scale computational homogenization scheme looses accuracy with the apparition of the macroscopic localizations resulting from the micro–buckling, the second–order multi–scale computational homogenization scheme1 is considered. This second–order computational framework is herein enhanced with the following novelties so that it can be used for cellular materials. First, at the microscopic scale, the periodic boundary condition is used because of its efficiency. As the meshes generated from cellular materials exhibit a large void part on the boundaries and are not conforming in general, the classical enforcement based on the matching nodes cannot be applied. A new method based on the polynomial interpolation2 without the requirement of the matching mesh condition on opposite boundaries of the representative volume element (RVE) is developed. Next, in order to solve the underlying macroscopic Mindlin strain gradient continuum of this second–order scheme by the displacement–based finite element framework, the treatment of high order terms is based on the discontinuous Galerkin (DG) method to weakly impose the C1-continuity3. Finally, as the instability phenomena are considered at both scales of the cellular materials, the path following technique is adopted to solve both the macroscopic and microscopic problems4. The micro–buckling leading to the macroscopic localization and the size effect phenomena can be captured within the proposed framework. In particular it is shown that results are not dependent on the mesh size at the macroscopic scale during the softening response, and that they agree well with the direct numerical simulations. [less ▲]

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See detailStreamable Laguerre-Voronoi Tessellation Model for Tomographic Images
Leblanc, Christophe ULg; Nguyen, Van Dung ULg; Wan, Fangyi et al

Conference (2014, July 25)

Introduction. Nowadays, the interest in foam materials is growing in several engineering fields [1]. Foams can exhibit a nonlinear mechanical behavior [2], which is highly depen- dent on their ... [more ▼]

Introduction. Nowadays, the interest in foam materials is growing in several engineering fields [1]. Foams can exhibit a nonlinear mechanical behavior [2], which is highly depen- dent on their microstructure [3]. Thus designing foams with specific mechanical properties can be very challenging. The present contribution is part of the ARC-Bridging project [4], whose objective is to predict the mechanical behavior of complex microstructured mate- rials via numerical simulations. A possible classification of foam models into two groups is: random models and deterministic models [5]. The random models frequently require statistical estimations of their parameters [6], whereas the deterministic models generally require numerically expensive image analyse. Indeed, classical analysis steps involve a distance tranform, a watershed and, optionally, a h-minima transform [5, p. 22], which can be computationally demanding [7, 8, 9]. Contribution. In the present Laguerre–Voronoi tessellation model, the image analysis part neither involes the watershed transform, nor the h-minima transform. Instead, fol- lowing the original idea of A.M. Lopez-Reina et E. Béchet [10], these two transforms are respectively replaced by a Hessian-based removal of spurious extrema and a clustering of the remaining maxima. This substitution allows the processing of large 3D-images by slices, i.e. “streaming”. The only limitation is enforced by the distance transform: the “feature” voxel of a given voxel should belong to the same slice. For foam images, this condition is fulfilled as long as the slice’s thickness is larger than the maximal foam cell’s size. Conclusion and perspectives. The aim of this contribution is to provide an efficient tessellation model for tomographic images of foams. From input tomographic images, this model provides a geometry model which will be used as an input for finite element simulations under the ARC-Briding project [4]. Simulation results will be compared with experimental measures. [less ▲]

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See detailMuti-scale methods with strain-softening: damage-enhanced MFH for composite materials and computational homogenization for cellular materials with micro-buckling
Wu, Ling ULg; Nguyen, Van Dung ULg; Adam, Laurent et al

Conference (2014, June 06)

In this work, multi-scale methods with strain softening are developed in the contexts of damage modeling for composite laminates and of buckling analyses in cellular materials. First, an anisotropic ... [more ▼]

In this work, multi-scale methods with strain softening are developed in the contexts of damage modeling for composite laminates and of buckling analyses in cellular materials. First, an anisotropic gradient–enhanced continuum damage model is embedded in a mean–field homogenization (MFH) process for elasto-plastic composites. The homogenization procedure is based on the newly developed incremental secant mean-field homogenization formulation, for which the residual stress and strain states reached in the phases upon a fictitious elastic unloading are considered as starting point to apply the secant method. The mean stress fields in the phases are then computed using isotropic secant tensors, which are naturally used to define the Linear Comparison–Composite The resulting multi– scale model is then applied to study the damage process at the meso–scale of laminates, and in particular the damaging of plies in a composite stack. By using the gradient–enhanced continuum damage model, the problem of losing uniqueness upon strain softening is avoided. Second, an efficient multi–scale finite element framework capturing the buckling instabilities in cellular materials is developed. As a classical multi–scale computational homogenization scheme loses accuracy with the apparition of the macroscopic localizations resulting from the micro–buckling, the second order multi–scale computational homogenization scheme is considered. This second–order computational framework is enhanced with the following novelties so that it can be used for cellular materials. At the microscopic scale, the periodic boundary condition is used because of its efficiency. As the meshes generated from cellular materials exhibit a large void part on the boundaries and are not conforming in general, the classical enforcement based on the matching nodes cannot be applied. A new method based on the polynomial interpolation2 without the requirement of the matching mesh condition on opposite boundaries of the representative volume element (RVE) is developed. Next, in order to solve the underlying macroscopic Mindlin strain gradient continuum of this second–order scheme by the displacement–based finite element framework, the treatment of high order terms is based on the discontinuous Galerkin (DG) method to weakly impose the C1-continuity. Finally, as the instability phenomena are considered at both scales of the cellular materials, the path following technique is adopted to solve both the macroscopic and microscopic problems. [less ▲]

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See detailPrediction of macroscopic mechanical properties of a polycrystalline microbeam subjected to material uncertainties
Lucas, Vincent ULg; Wu, Ling ULg; Arnst, Maarten ULg et al

in Cunha, Álvaro; Caetano, Elsa; Ribeiro, Pedro (Eds.) et al Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 (2014, June)

The first resonance frequency is a key performance characteristic of MEMS vibrometers. In batch fabrication, this first resonance frequency can exhibit scatter owing to various sources of manufacturing ... [more ▼]

The first resonance frequency is a key performance characteristic of MEMS vibrometers. In batch fabrication, this first resonance frequency can exhibit scatter owing to various sources of manufacturing variability involved in the fabrication process. The aim of this work is to develop a stochastic multiscale model for predicting the first resonance frequency of MEMS microbeams constituted of polycrystals while accounting for the uncertainties in the microstructure due to the grain orientations. At the finest scale, we model the microstructure of polycrystaline materials using a random Voronoï tessellation, each grain being assigned a random orientation. Then, we apply a computational homogenization procedure on statistical volume elements to obtain a stochastic characterization of the elasticity tensor at the second scale of interest, the meso-scale. In the future, using a stochastic finite element method, we will propagate these meso-scale uncertainties to the first resonance frequency at the coarser scale. [less ▲]

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See detailComputational homogenization of cellular materials
Nguyen, Van Dung ULg; Noels, Ludovic ULg

in International Journal of Solids and Structures (2014), 51(11-12), 2183-2203

In this work we propose to study the behavior of cellular materials using a second–order multi–scale computational homogenization approach. During the macroscopic loading, micro-buckling of thin ... [more ▼]

In this work we propose to study the behavior of cellular materials using a second–order multi–scale computational homogenization approach. During the macroscopic loading, micro-buckling of thin components, such as cell walls or cell struts, can occur. Even if the behavior of the materials of which the micro–structure is made remains elliptic, the homogenized behavior can lose its ellipticity. In that case, a localization band is formed and propagates at the macro–scale. When the localization occurs, the assumption of local action in the standard approach, for which the stress state on a material point depends only on the strain state at that point, is no–longer suitable, which motivates the use of the second-order multi–scale computational homogenization scheme. At the macro–scale of this scheme, the discontinuous Galerkin method is chosen to solve the Mindlin strain gradient continuum. At the microscopic scale, the classical finite element resolutions of representative volume elements are considered. Since the meshes generated from cellular materials exhibit voids on the boundaries and are not conforming in general, the periodic boundary conditions are reformulated and are enforced by a polynomial interpolation method. With the presence of instability phenomena at both scales, the arc–length path following technique is adopted to solve both macroscopic and microscopic problems. [less ▲]

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See detailMuti-scale methods with strain-softening: damage-enhanced MFH for composite materials and computational homogenization for cellular materials with micro-buckling
Wu, Ling ULg; Nguyen, Van Dung ULg; Doghri, Issam et al

Scientific conference (2014, April 28)

Materials used in the aerospace industry, as composite or foamed materials are multiscale in nature. To predict the macroscopic behaviour of structures made of such materials, the micro-scopic responses ... [more ▼]

Materials used in the aerospace industry, as composite or foamed materials are multiscale in nature. To predict the macroscopic behaviour of structures made of such materials, the micro-scopic responses should also be computed within a nested scheme. This is particularly true when non-linear behaviours are modelled, or when the failure and post failure analyses are sought. In this work, multi-scale methods with strain softening are developed in the contexts of damage modelling for composite laminates and of buckling analyses in cellular materials. First, an anisotropic gradient–enhanced continuum damage model is embedded in a mean–field homogenization (MFH) process for elasto-plastic composites. The homogenization procedure is based on the newly developed incremental secant mean-field homogenization formulation, for which the residual stress and strain states reached in the phases upon a fictitious elastic unloading are considered as starting point to apply the secant method. The mean stress fields in the phases are then computed using isotropic secant tensors, which are naturally used to define the Linear Comparison–Composite The resulting multi– scale model is then applied to study the damage process at the meso–scale of laminates, and in particular the damaging of plies in a composite stack. By using the gradient–enhanced continuum damage model, the problem of losing uniqueness upon strain softening is avoided. Second, an efficient multi–scale finite element framework capturing the buckling instabilities in cellular materials is developed. As a classical multi–scale computational homogenization scheme loses accuracy with the apparition of the macroscopic localizations resulting from the micro–buckling, the second order multi–scale computational homogenization scheme is considered. This second–order computational framework is enhanced with the following novelties so that it can be used for cellular materials. At the microscopic scale, the periodic boundary condition is used because of its efficiency. As the meshes generated from cellular materials exhibit a large void part on the boundaries and are not conforming in general, the classical enforcement based on the matching nodes cannot be applied. A new method based on the polynomial interpolation2 without the requirement of the matching mesh condition on opposite boundaries of the representative volume element (RVE) is developed. Next, in order to solve the underlying macroscopic Mindlin strain gradient continuum of this second–order scheme by the displacement–based finite element framework, the treatment of high order terms is based on the discontinuous Galerkin (DG) method to weakly impose the C1-continuity. Finally, as the instability phenomena are considered at both scales of the cellular materials, the path following technique is adopted to solve both the macroscopic and microscopic problems. [less ▲]

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See detailMuti-scale methods with strain-softening: damage-enhanced MFH for composite materials and computational homogenization for cellular materials with micro-buckling
Noels, Ludovic ULg; Nguyen, Van Dung ULg; Wu, Ling ULg et al

Scientific conference (2014, April 14)

Materials used in the aerospace industry, as composite or foamed materials are multiscale in nature. To predict the macroscopic behaviour of structures made of such materials, the micro-scopic responses ... [more ▼]

Materials used in the aerospace industry, as composite or foamed materials are multiscale in nature. To predict the macroscopic behaviour of structures made of such materials, the micro-scopic responses should also be computed within a nested scheme. This is particularly true when non-linear behaviours are modelled, or when the failure and post failure analyses are sought. In this work, multi-scale methods with strain softening are developed in the contexts of damage modelling for composite laminates and of buckling analyses in cellular materials. First, an anisotropic gradient–enhanced continuum damage model is embedded in a mean–field homogenization (MFH) process for elasto-plastic composites. The homogenization procedure is based on the newly developed incremental secant mean-field homogenization formulation, for which the residual stress and strain states reached in the phases upon a fictitious elastic unloading are considered as starting point to apply the secant method. The mean stress fields in the phases are then computed using isotropic secant tensors, which are naturally used to define the Linear Comparison–Composite The resulting multi– scale model is then applied to study the damage process at the meso–scale of laminates, and in particular the damaging of plies in a composite stack. By using the gradient–enhanced continuum damage model, the problem of losing uniqueness upon strain softening is avoided. Second, an efficient multi–scale finite element framework capturing the buckling instabilities in cellular materials is developed. As a classical multi–scale computational homogenization scheme loses accuracy with the apparition of the macroscopic localizations resulting from the micro–buckling, the second order multi–scale computational homogenization scheme is considered. This second–order computational framework is enhanced with the following novelties so that it can be used for cellular materials. At the microscopic scale, the periodic boundary condition is used because of its efficiency. As the meshes generated from cellular materials exhibit a large void part on the boundaries and are not conforming in general, the classical enforcement based on the matching nodes cannot be applied. A new method based on the polynomial interpolation2 without the requirement of the matching mesh condition on opposite boundaries of the representative volume element (RVE) is developed. Next, in order to solve the underlying macroscopic Mindlin strain gradient continuum of this second–order scheme by the displacement–based finite element framework, the treatment of high order terms is based on the discontinuous Galerkin (DG) method to weakly impose the C1-continuity. Finally, as the instability phenomena are considered at both scales of the cellular materials, the path following technique is adopted to solve both the macroscopic and microscopic problems. [less ▲]

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See detailComputational homogenization of cellular materials capturing micro-buckling, macro-localization and size effects
Nguyen, Van Dung ULg

Doctoral thesis (2014)

The objective of this thesis is to develop an efficient multi-scale finite element framework to capture the macroscopic localization due to the micro-buckling of cell walls and the size effect phenomena ... [more ▼]

The objective of this thesis is to develop an efficient multi-scale finite element framework to capture the macroscopic localization due to the micro-buckling of cell walls and the size effect phenomena arising in structures made of cellular materials. Under the compression loading, the buckling phenomenon (so--called micro--buckling) of the slender components (cell walls, cell faces) of cellular solids can occur. Even if the tangent operator of the material of which the micro--structure is made, is still elliptic, the presence of the micro--buckling can lead to the loss of ellipticity of the resulting homogenized tangent operator. In that case, localization bands are formed and propagate in the macroscopic structure. Moreover, when considering a cellular structure whose dimensions are close to the cell size, the size effect phenomenon cannot be neglected since deformations are characterized by a strain gradient. On the one hand, a classical multi-scale computational homogenization scheme (so-called first-order scheme) looses accuracy with the apparition of the macroscopic localization or the high strain gradient arising in cellular materials because the underlying assumption of the local action principle, in which the stress state on a macroscopic material point depends only on the strain state at that point, is no--longer suitable. On the other hand, the second-order multi-scale computational homogenization scheme proposed by Kouznetsova exhibits a good ability to capture such phenomena. Thus this second--order scheme is improved in this thesis with the following novelties so that it can be used for cellular materials. First, at the microscopic scale, the periodic boundary condition is used because of its efficiency. As the meshes generated from cellular materials exhibit a large void part on the boundaries and are not conforming in general, the classical enforcement based on the matching nodes cannot be applied. A new method based on the polynomial interpolation without the requirement of the matching mesh condition on opposite boundaries of the representative volume element (RVE) is developed. Next, in order to solve the underlying macroscopic Mindlin strain gradient continuum of this second-order scheme by the displacement-based finite element framework, the presence of high order terms (related to the higher stress and strain) leads to many complications in the numerical treatment. Indeed, the resolution requires the continuities not only of the displacement field but also of its first derivatives. This work uses the discontinuous Galerkin (DG) method to weakly impose these continuities. This proposed second--order DG--based FE2 scheme appears to be easily integrated into conventional parallel finite element codes. Finally, the proposed second-order DG-based FE2 scheme is used to model cellular materials. As the instability phenomena are considered at both scales, the path following technique is adopted to solve both the macroscopic and microscopic problems. The micro--buckling leading to the macroscopic localization and the size effect phenomena can be captured within the proposed framework. [less ▲]

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See detailHomogenization with propagation of instabilities through the different scales
Noels, Ludovic ULg; Wu, Ling ULg; Nguyen, Van Dung ULg et al

Scientific conference (2014, January 31)

In this work, multi-scale methods with strain softening are developed in the contexts of damage modeling for composite laminates and of buckling analyses in cellular materials. First, an anisotropic ... [more ▼]

In this work, multi-scale methods with strain softening are developed in the contexts of damage modeling for composite laminates and of buckling analyses in cellular materials. First, an anisotropic gradient–enhanced continuum damage model is embedded in a mean–field homogenization (MFH) process for elasto-plastic composites. The homogenization procedure is based on the newly developed incremental secant mean-field homogenization formulation, for which the residual stress and strain states reached in the phases upon a fictitious elastic unloading are considered as starting point to apply the secant method. The mean stress fields in the phases are then computed using isotropic secant tensors, which are naturally used to define the Linear Comparison–Composite The resulting multi– scale model is then applied to study the damage process at the meso–scale of laminates, and in particular the damaging of plies in a composite stack. By using the gradient–enhanced continuum damage model, the problem of losing uniqueness upon strain softening is avoided. Second, an efficient multi–scale finite element framework capturing the buckling instabilities in cellular materials is developed. As a classical multi–scale computational homogenization scheme loses accuracy with the apparition of the macroscopic localizations resulting from the micro–buckling, the second order multi–scale computational homogenization scheme is considered. This second–order computational framework is enhanced with the following novelties so that it can be used for cellular materials. At the microscopic scale, the periodic boundary condition is used because of its efficiency. As the meshes generated from cellular materials exhibit a large void part on the boundaries and are not conforming in general, the classical enforcement based on the matching nodes cannot be applied. A new method based on the polynomial interpolation2 without the requirement of the matching mesh condition on opposite boundaries of the representative volume element (RVE) is developed. Next, in order to solve the underlying macroscopic Mindlin strain gradient continuum of this second–order scheme by the displacement–based finite element framework, the treatment of high order terms is based on the discontinuous Galerkin (DG) method to weakly impose the C1-continuity. Finally, as the instability phenomena are considered at both scales of the cellular materials, the path following technique is adopted to solve both the macroscopic and microscopic problems. [less ▲]

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See detailMulti-scale studies of foamed materials
Nguyen, Van Dung ULg; Noels, Ludovic ULg

Conference (2013, September)

We propose a multi-scale study to predict micro-buckling that could happen in foamed materials. At the macroscopic scale, when localization occurs, the characteristic size of macroscopic deformation is ... [more ▼]

We propose a multi-scale study to predict micro-buckling that could happen in foamed materials. At the macroscopic scale, when localization occurs, the characteristic size of macroscopic deformation is the same order of the microscopic size. The assumption of material action in standard multi-scale computational homogenization approach where the stress only depends on the strain at this point is no-longer suitable, which motivates the uses of the second-order scheme. In this work, an implementation of the second-order continuum based on a discontinuous Galerkin approximation is shown to be particularly efficient to constrain weakly the continuities of the displacement field and of its gradient. At the microscopic scale, classical finite element resolutions of RVEs are considered. To enforce the periodic boundary condition of this micro problem, we propose an efficient method, which is based on the polynomial interpolation, and allows applying the periodic boundary condition without requiring conformal meshes. The micro-macro transition follows the second-order computational homogenization scheme. With the proposed framework it is shown that, during the macroscopic loading, the micro- buckling of the thin components of the foamed structure (cell walls and edges) can occur even if the tangent modulus of micro-material is still elliptic since the homogenized tangent modulus at macro-scale can lose its ellipticity. In that case, the localization occurs at macro- scale and can be captured by the model. [less ▲]

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See detailMultiscale computational homogenization methods with a gradient enhanced scheme based on the discontinuous Galerkin formulation
Nguyen, Van Dung ULg; Becker, Gauthier ULg; Noels, Ludovic ULg

in Computer Methods in Applied Mechanics & Engineering (2013), 260

When considering problems of dimensions close to the characteristic length of the material, the size e ects can not be neglected and the classical (so–called first–order) multiscale computational ... [more ▼]

When considering problems of dimensions close to the characteristic length of the material, the size e ects can not be neglected and the classical (so–called first–order) multiscale computational homogenization scheme (FMCH) looses accuracy, motivating the use of a second–order multiscale computational homogenization (SMCH) scheme. This second–order scheme uses the classical continuum at the micro–scale while considering second–order continuum at the macro–scale. Although the theoretical background of the second–order continuum is increasing, the implementation into a finite element code is not straightforward because of the lack of high–order continuity of the shape functions. In this work, we propose a SMCH scheme relying on the discontinuous Galerkin (DG) method at the macro–scale, which simplifies the implementation of the method. Indeed, the DG method is a generalization of weak formulations allowing for inter-element discontinuities either at the C0 level or at the C1 level, and it can thus be used to constrain weakly the C1 continuity at the macro–scale. The C0 continuity can be either weakly constrained by using the DG method or strongly constrained by using usual C0 displacement–based finite elements. Therefore, two formulations can be used at the macro–scale: (i) the full–discontinuous Galerkin formulation (FDG) with weak C0 and C1 continuity enforcements, and (ii) the enriched discontinuous Galerkin formulation (EDG) with high–order term enrichment into the conventional C0 finite element framework. The micro–problem is formulated in terms of standard equilibrium and periodic boundary conditions. A parallel implementation in three dimensions for non–linear finite deformation problems is developed, showing that the proposed method can be integrated into conventional finite element codes in a straightforward and e cient way. [less ▲]

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See detailMulti-scale modelling
Noels, Ludovic ULg; Becker, Gauthier; Mulay, Shantanu Shashikant ULg et al

Scientific conference (2013, March 11)

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See detailMulti-scale computational homogenization analysis of foams with micro-buckling
Nguyen, Van Dung ULg; Noels, Ludovic ULg

Conference (2012, July)

When studying the behavior of foams by multi-scale computational homogenization procedure, the micro-buckling may occur at the cell walls and edges and reduces the effective stiffness of the structures at ... [more ▼]

When studying the behavior of foams by multi-scale computational homogenization procedure, the micro-buckling may occur at the cell walls and edges and reduces the effective stiffness of the structures at macro-scale. This instability can be enhanced by plastic deformation at micro-scale. At sufficiently large value of macro-strain, even if the micro-tangent moduli of micro-material is still elliptic, the homogenized tangent moduli at macro-scale can lose its ellipticity that implies the localization occurs at macro-scale. When localization occurs, the characteristic size of macro- scopic deformation is the same order of the microscopic size. The assumption of material action in standard multi-scale computational homogenization approach where the stress only depends on the strain at this point is no-longer suitable. And the material behavior at given point depends also on the neighborhood of this point. To cover this problem, the second-order multi-scale computational homogenization is suitably used. At macroscopic problem, the high-order stress and the high-order strain are enhanced to the standard formulation by using the Discontinuous-Galerkin formulation while at the micro-scale, the standard continuum formulation is still used. By this procedure, the influence of micro-buckling of foams on structural behaviour is studied. [less ▲]

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See detailImposing periodic boundary condition on arbitrary meshes by polynomial interpolation
Nguyen, Van Dung ULg; Béchet, Eric ULg; Geuzaine, Christophe ULg et al

in Computational Materials Science (2012), 55

In order to predict the effective properties of heterogeneous materials using the finite element approach, a boundary value problem (BVP) may be defined on a representative volume element (RVE) with ... [more ▼]

In order to predict the effective properties of heterogeneous materials using the finite element approach, a boundary value problem (BVP) may be defined on a representative volume element (RVE) with appropriate boundary conditions, among which periodic boundary condition is the most efficient in terms of convergence rate. The classical method to impose the periodic boundary condition requires the identical meshes on opposite RVE boundaries. This condition is not always easy to satisfy for arbitrary meshes. This work develops a new method based on polynomial interpolation that avoids the need of matching mesh condition on opposite RVE boundaries. [less ▲]

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See detailNon-linear mechanical solvers for GMSH
Noels, Ludovic ULg; Becker; Nguyen, Van Dung ULg et al

Scientific conference (2012, March)

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See detailImposing periodic boundary condition on arbitrary meshes by polynomial interpolation
Nguyen, Van Dung ULg; Béchet, Eric ULg; Geuzaine, Christophe ULg et al

in Hogge, Michel; Van Keer, Roger; Dick, Erik (Eds.) et al Proceedings of the 5th International Conference on Advanded COmputational Methods in Engineering (ACOMEN2011) (2011, November)

In order to predict the effective properties of heterogeneous materials using the finite element approach, a boundary value problem (BVP) may be defined on a representative volume element (RVE) with ... [more ▼]

In order to predict the effective properties of heterogeneous materials using the finite element approach, a boundary value problem (BVP) may be defined on a representative volume element (RVE) with appropriate boundary conditions, among which periodic boundary condition is the most efficient in terms of convergence rate. The classical method to impose the periodic boundary condition requires identical meshes on opposite RVE boundaries. This condition is not always easy to satisfy for arbitrary meshes. This work develops a new method based on polynomial interpolation that avoids the need of the identical mesh condition on opposite RVE boundaries. [less ▲]

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See detailProjects in Fracture Simulations
Noels, Ludovic ULg; Becker, Gauthier; Wu, Ling ULg et al

Scientific conference (2011, September)

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