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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 106
PROCEEDINGS OF THE TWELFTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
Edited by:
Paper 86

Variational Methods to Model Porous Materials with Non-Associated Flow Rules

L. Cheng1, Y. Jia1, W. Shen1, A. Oueslati1, D. Kondo2 and G. de Saxcé1

1Laboratoire de Mécanique de Lille, University Lille 1, France
2Institut Jean Le Rond d'Alembert, University Pierre and Marie Curie, Paris, France

Full Bibliographic Reference for this paper
, "Variational Methods to Model Porous Materials with Non-Associated Flow Rules", in , (Editors), "Proceedings of the Twelfth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 86, 2014. doi:10.4203/ccp.106.86
Keywords: homogenization, limit analysis, porous materials, von Mises model, non associated Drucker-Prager model, bipotential..

Summary
In Gurson's footstep, many works were devoted to the kinematical approach of limit analysis coupled with the hollow sphere model to propose macrostress yield criteria of the ductile porous materials. Recently, the authors proposed a stress variational homogeneization based on the dual statical approach, starting from Hill's variational principle for the associated plasticity. Relaxing the stress equilibrium condition on the void boundary, we deduce for a matrix having von Mises matrix a first criterion depending not only on the first and second invariant of the macroscopic stress tensor but also on the sign of the third invariant of the stress deviator and the triaxiality. Two more accurate criteria are also proposed, the first one depending on the third invariant, and the second one based on a fully statically admissible trial stress field. Also we extended the previous model to the non associated case with the aid of a variational method based on the bipotential approach which permits the generalization the classical limit analysis to the non-associated ductile porous media.

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