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Contribution à l'étude théorique de la localisation plastique dans les poreux

Abstract : This work presents a study in theoretical mechanics, in the classical framework of homogenization of heterogeneous media. It addresses a notoriously problematical situation of non-linear behavior and infinite contrast between two phases, one of which is a plastic solid phase and the other one, the porosity of the medium. Its aim is to investigate how plastic strain localization manifests itself at the level of the overall effective behavior of the medium in presence of pores, and in particular in the non-trivial limit of small porosity. This question, important to the understanding of ductile damage, is examined both numerically and theoretically, in the restricted situation of bi-dimensional systems, and using a deformation theory approach of plasticity. The numerical investigations consist of quasi-exact computations of the strain and stress fields in the voided medium, by means of a Fast Fourier Transform method, and using a particular Green function. The theoretical approach makes use of exact solutions, which can be obtained in particular cases of a periodic void lattice, as well as of a recent "second-order" nonlinear homogenization approach. The virtues of the latter are evaluated in two steps, first by studying the underlying linear anisotropic homogenization step (an essential ingredient), then by studying the nonlinear step itself. The nature and significance of the singularities of the theory which appear in the limit of small porosity, confirmed by numerical computations, are partly elucidated. Finally, original observations are presented as to the relation between plastic deformation patterns in an ideal disordered medium, and some features of the macroscopic strain/stress curve.
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Submitted on : Sunday, March 4, 2007 - 12:49:40 AM
Last modification on : Wednesday, November 17, 2021 - 12:28:05 PM
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  • HAL Id : tel-00134643, version 1


François Willot. Contribution à l'étude théorique de la localisation plastique dans les poreux. Physique mathématique [math-ph]. Ecole Polytechnique X, 2007. Français. ⟨tel-00134643⟩



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