Linear elasticity obtained from finite elasticity by -convergence under weak coerciveness conditions

  • Antonio DeSimone

    SISSA, via Bonomea 265, 34136 Trieste, Italy
  • Virginia Agostiniani

    SISSA, via Bonomea 265, 34136 Trieste, Italy
  • Gianni Dal Maso

    SISSA, via Bonomea 265, 34136 Trieste, Italy

Abstract

The energy functional of linear elasticity is obtained as -limit of suitable rescalings of the energies of finite elasticity. The quadratic control from below of the energy density for large values of the deformation gradient is replaced here by the weaker condition , for some . Energies of this type are commonly used in the study of a large class of compressible rubber-like materials.

Cite this article

Antonio DeSimone, Virginia Agostiniani, Gianni Dal Maso, Linear elasticity obtained from finite elasticity by -convergence under weak coerciveness conditions. Ann. Inst. H. Poincaré Anal. Non Linéaire 29 (2012), no. 5, pp. 715–735

DOI 10.1016/J.ANIHPC.2012.04.001