A relaxation process for bifunctionals of displacement-Young measure state variables: A model of multi-material with micro-structured strong interface

Bessoud, Anne Laure ; Krasucki, Françoise ; Michaille, Gérard

Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010), p. 447-469 / Harvested from Numdam

Résumé

The gradient displacement field of a micro-structured strong interface of a three-dimensional multi-material is regarded as a gradient-Young measure so that the stored strain energy of the material is defined as a bifunctional of displacement-Young measure state variables. We propose a new model by computing a suitable variational limit of this bifunctional when the thickness and the stiffness of the strong material are of order ε and $ \frac{1}{\epsilon }$ respectively. The stored strain energy functional associated with the model in pure displacements living in a Sobolev space is obtained as the marginal map of the limit bifunctional. We also obtain a new asymptotic formulation in terms of Young measure state variable when considering the other marginal map.

Détail

Publié le : 2010-01-01

MR 2595187 | Zbl 1184.49020

DOI : https://doi.org/10.1016/j.anihpc.2010.01.007
Classification:  49J45,  74N15,  35B40

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