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) no. 2, pp. 447-469

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 $\frac{1}{ϵ}$ 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.

Classification : 49J45, 74N15, 35B40
Keywords: Micro structures, Young measures, Variational convergences, Γ-convergence

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