Article Dans Une Revue Annales de l'Institut Henri Poincaré (C), Analyse non linéaire (Nonlinear Analysis) Année : 2010

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

Résumé

The gradient displacement field of a micro-structured strong inter-face 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 1/ε 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.

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hal-00790256 , version 1 (02-03-2015)

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Anne-Laure Bessoud, Françoise Krasucki, Gérard Michaille. A relaxation process for bifunctionals of displacement-Young measure state variables: A model of multi-material with micro-structured strong interface. Annales de l'Institut Henri Poincaré (C), Analyse non linéaire (Nonlinear Analysis), 2010, 27 (2), pp.447-469. ⟨10.1016/j.anihpc.2010.01.007⟩. ⟨hal-00790256⟩
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