Relaxation and 3d-2d Passage Theorems in Hyperelasticity

Omar Anza Hafsa (1) , Jean-Philippe Mandallena (2)

1 M3 - Modélisation Mathématique en Mécanique
2 MIPA - Mathématiques, Informatique, Physique, et Applications / Université de Nîmes

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.

Mots clés: Calculus of variations; integral representation; relaxation; 3d-2d passage; Γ(π)-convergence; determinant type constraints; hyperelasticity

Domaines: Analyse classique [math.CA]

Omar Anza Hafsa, Jean-Philippe Mandallena. Relaxation and 3d-2d Passage Theorems in Hyperelasticity. Journal of Convex Analysis, 2012, 19 (3), pp.759-794. ⟨hal-00797479⟩