Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Omar Anza Hafsa

Université de Nîmes, Laboratoire MIPA, Site des Carmes, Place Gabriel Péri, 30021 Nîmes, France

omar.anza-hafsa@unimes.fr

Keywords

  • Calculus of variations
  • integral representation
  • relaxation
  • 3d-2d passage
  • Gamma(pi)-convergence
  • determinant type constraints
  • hyperelasticity

Suggested citation

O. Anza Hafsa, J.-P. Mandallena. “Relaxation and 3d-2d Passage Theorems in Hyperelasticity.” Journal of Convex Analysis 19 (2012), No. 3, 759–794.

Copyright Heldermann Verlag 2012