A relaxation process for bifunctionals of displacement-Young measure state variables: A model of multi-material with micro-structured strong interface
Annales de l'I.H.P. Analyse non linéaire, Volume 27 (2010) no. 2, p. 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.

DOI : https://doi.org/10.1016/j.anihpc.2010.01.007
Classification:  49J45,  74N15,  35B40
Keywords: Micro structures, Young measures, Variational convergences, Γ-convergence
@article{AIHPC_2010__27_2_447_0,
author = {Bessoud, Anne Laure and Krasucki, Fran\c coise and Michaille, G\'erard},
title = {A relaxation process for bifunctionals of displacement-Young measure state variables: A model of multi-material with micro-structured strong interface},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {27},
number = {2},
year = {2010},
pages = {447-469},
doi = {10.1016/j.anihpc.2010.01.007},
zbl = {1184.49020},
mrnumber = {2595187},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2010__27_2_447_0}
}

Bessoud, Anne Laure; Krasucki, Françoise; Michaille, Gérard. A relaxation process for bifunctionals of displacement-Young measure state variables: A model of multi-material with micro-structured strong interface. Annales de l'I.H.P. Analyse non linéaire, Volume 27 (2010) no. 2, pp. 447-469. doi : 10.1016/j.anihpc.2010.01.007. http://www.numdam.org/item/AIHPC_2010__27_2_447_0/

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