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Adaptation élastoplastique et homogénéisation périodique

Abstract : This work is devoted to the analysis of the mechanical strength of heterogeneous media submitted to variable loads. Indeed, we propose a numerical method for analyzing, by a direct approach essentially based on the static theorem of Melan, shakedown of 3D, heterogeneously periodic, and elastic-perfectly plastic media. The main objective is to couple the elastic plastic shakedown theory, which allows to study the behavior of media submitted to variable loads, and the periodic homogenization theory, which allows to take into account the influence of the microscopic behavior of heterogeneous media on the macroscopic one. The methodology consists in carrying out the shakedown analysis on a 3D unit cell -considered as a microstructure representative of the heterogeneities- and in expressing the results, thanks to average conditions, in terms of admissible domains of external loads: the macroscopic strains and stresses. Numerically, this leads to couple a finite element software, which allows to take into account the heterogeneities by rigorously expressing the periodicity and average conditions, with a nonlinear constrained optimization software, which allows to express the shakedown problem. The method is applied to classical 3D media and also to thin heterogeneous periodic plates. The resulting numerical tool is completely general: indeed, it allows to study how to avoid failure of heterogeneous media by unlimited plastic dissipation, whatever the considered 3D unit cell.
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Contributor : Hélène Magoariec <>
Submitted on : Friday, October 8, 2004 - 3:04:34 PM
Last modification on : Thursday, January 23, 2020 - 6:22:03 PM
Long-term archiving on: : Monday, September 20, 2010 - 12:07:37 PM


  • HAL Id : tel-00007063, version 2


Hélène Magoariec. Adaptation élastoplastique et homogénéisation périodique. Mécanique []. Université de la Méditerranée - Aix-Marseille II, 2003. Français. ⟨tel-00007063v2⟩



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