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

Anne-Laure Bessoud (1) , Françoise Krasucki (2) , Gérard Michaille (2, 3)

1 LMGC - Laboratoire de Mécanique et Génie Civil
2 I3M - Institut de Mathématiques et de Modélisation de Montpellier
3 UNIMES - Université de Nîmes

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.

Mots clés: Variational convergences; Gamma-convergence.; Young measures; Gamma-convergence; Micro structures

Domaines: Equations aux dérivées partielles [math.AP]; Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]

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, 2010, 27 (2), pp.447-469. ⟨10.1016/j.anihpc.2010.01.007⟩. ⟨hal-00790256⟩