Calculus of Variations and Geometric Measure Theory

V. Agostiniani - G. Dal Maso - A. DeSimone

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

created by virginia on 29 Jun 2011
modified by dalmaso on 18 Nov 2015


Published Paper

Inserted: 29 jun 2011
Last Updated: 18 nov 2015

Journal: Ann. Inst. H. Poincare Anal. Non Lineaire
Volume: 29
Pages: 715-735
Year: 2012


The energy functional of linear elasticity is obtained as $\Gamma$-limit of suitable rescalings of the energies of finite elasticity. The quadratic control from below of the energy density $W(\nabla v)$ for large values of the deformation gradient $\nabla v$ is replaced here by the weaker condition $W(\nabla v)\geq
\nabla v
^p$, for some $p>1$. Energies of this type are commonly used in the study of a large class of compressible rubber-like materials.

Keywords: Gamma-convergence, nonlinear elasticity, linearized elasticity, rigidity estimates