Author
Jean-Claude Michel
Other affiliations: Centre national de la recherche scientifique
Bio: Jean-Claude Michel is an academic researcher from Aix-Marseille University. The author has contributed to research in topics: Transformation (function) & Finite element method. The author has an hindex of 19, co-authored 37 publications receiving 2944 citations. Previous affiliations of Jean-Claude Michel include Centre national de la recherche scientifique.
Papers
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TL;DR: In this paper, two different families of numerical methods are considered to solve the problem of a homogeneous linear reference material undergoing a nonhomogeneous periodic eigenstrain, and the relative merits of the two methods are compared and several examples are discussed.
1,028 citations
TL;DR: In this paper, two modified fast Fourier transform methods were proposed to handle composites with high contrast (typically above 104) or infinite contrast (those containing voids or rigid inclusions or highly non-linear materials).
Abstract: A numerical method making use of fast Fourier transforms has been proposed in Moulinec and Suquet (1994, 1998) to investigate the effective properties of linear and non-linear composites. This method is based on an iterative scheme the rate of convergence of which is proportional to the contrast between the phases. Composites with high contrast (typically above 104) or infinite contrast (those containing voids or rigid inclusions or highly non-linear materials) cannot be handled by the method. This paper presents two modified schemes. The first one is an accelerated scheme for composites with high contrast which extends to elasticity a scheme initially proposed in Eyre and Milton (1999). Its rate of convergence varies as the square root of the contrast. The second scheme, adequate for composites with infinite contrast, is based on an augmented Lagrangian method. The resulting saddle-point problem involves three steps. The first step consists of solving a linear elastic problem, using the fast Fourier transform method. In the second step, a non-linear problem is solved at each individual point in the volume element. The third step consists of updating the Lagrange multiplier. Applications of this scheme to rigidly reinforced and to voided composites are shown. Copyright © 2001 John Wiley & Sons, Ltd.
398 citations
TL;DR: In this article, a decomposition of the microscopic anelastic strain field on a finite set of transformation fields is proposed to describe the overall behavior of composites with nonlinear dissipative phases.
342 citations
206 citations
TL;DR: In this article, a reduced model for the effective behavior of nonlinear composites, such as metal-matrix composite materials, has been recently proposed by the authors, which extends and improves on the Transformation Field Analysis of Dvorak by considering nonuniform transformation strains, also called plastic modes.
190 citations
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TL;DR: In this paper, a review of continuum-based variational formulations for describing the elastic-plastic deformation of anisotropic heterogeneous crystalline matter is presented and compared with experiments.
1,573 citations
TL;DR: In this article, a gradient-enhanced computational homogenization procedure is proposed for the modeling of microstructural size effects, within a general non-linear framework, where the macroscopic deformation gradient tensor and its gradient are imposed on a micro-structural representative volume element (RVE).
Abstract: A gradient-enhanced computational homogenization procedure, that allows for the modelling of microstructural size effects, is proposed within a general non-linear framework. In this approach the macroscopic deformation gradient tensor and its gradient are imposed on a microstructural representative volume element (RVE). This enables us to incorporate the microstructural size and to account for non-uniform macroscopic deformation fields within the microstructural cell. Every microstructural constituent is modelled as a classical continuum and the RVE problem is formulated in terms of standard equilibrium and boundary conditions. From the solution of the microstructural boundary value problem, the macroscopic stress tensor and the higher-order stress tensor are derived based on an extension of the Hill-Mandel condition. This automatically delivers the microstructurally based constitutive response of the higher-order macro continuum and deals with the microstructural size in a natural way. Several examples illustrate the approach, particularly the microstructural size effects.
752 citations
TL;DR: In this paper, the extended finite element method (X-FEM) is used to solve multiscale analysis of complex geometries, where the mesh does not need to conform to the physical surfaces, it needs to be fine enough to capture the geometry of these surfaces.
663 citations
TL;DR: In this paper, a second-order computational homogenization approach is applied for the multi-scale analysis of simple shear of a constrained heterogeneous strip, where a pronounced boundary size effect appears.
594 citations