References of "Nguyen, Van Dung"
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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 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 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)

Detailed reference viewed: 6 (6 ULg)