The energy functional of linear elasticity is obtained as Γ-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 ∇v 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 Γ-convergence under weak coerciveness conditions. Ann. Inst. H. Poincaré Anal. Non Linéaire 29 (2012), no. 5, pp. 715–735DOI 10.1016/J.ANIHPC.2012.04.001