Journal of Convex Analysis 19 (2012), No. 3, 759--794
Copyright Heldermann Verlag 2012
Relaxation and 3d-2d Passage Theorems in Hyperelasticity
Omar Anza Hafsa
Université de Nîmes, Laboratoire MIPA, Site des Carmes, Place Gabriel Péri, 30021 Nîmes, France
omar.anza-hafsa@unimes.fr
Jean-Philippe Mandallena
Université de Nîmes, Laboratoire MIPA, Site des Carmes, Place Gabriel Péri, 30021 Nîmes, France
jean-philippe.mandallena@unimes.fr
We give an overview of relaxation and 3d-2d passage theorems in hyperelasticity in the framework of the multidimensional calculus of variations. We give several improvements of the proofs and we introduce the concept of p-ample integrand in showing its interest with respect to determinant type constraints. Some open questions are addressed.
Keywords: Calculus of variations, integral representation, relaxation, 3d-2d passage, Gamma(pi)-convergence, determinant type constraints, hyperelasticity.
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