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Materials 2010, 3(1), 296-317; doi:10.3390/ma3010296

On Micro-Macro Transition in Non-Linear Mechanics

Lab. M´ecanique des Solides, Ecole polytechnique UMR 7649, 91128 Palaiseau Cedex France
Received: 31 October 2009 / Revised: 10 December 2009 / Accepted: 14 December 2009 / Published: 8 January 2010
(This article belongs to the Special Issue Composite Materials)
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This paper is devoted to the description of the general relationships between microscopic and macroscopic mechanical quantities in non-linear mechanics. From a thermodynamical viewpoint, it is only necessary to know the two macroscopic potentials (macroscopic free energy and macroscopic potential of dissipation) to describe the state of the body and its quasistatic evolution. These global potentials are the averages of the local ones. We point out some particular cases of non-linearities, especially the case of damaged materials.
Keywords: homogeneization; damage; elastoplasticity; concentration tensor homogeneization; damage; elastoplasticity; concentration tensor
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Stolz, C. On Micro-Macro Transition in Non-Linear Mechanics. Materials 2010, 3, 296-317.

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