From nonlinear to linearized elasticity via Gamma-convergence: the case of multiwell energies satisfying weak coercivity conditions

Abstract

Linearized elasticity models are derived, via Gamma-convergence, from suitably rescaled nonlinear energies when the corresponding energy densities have a multiwell structure and satisfy a weak coercivity condition, in the sense that the typical quadratic bound from below is replaced by a weaker p bound, 1<p <2, away from the wells. This study is motivated by, and our results are applied to, energies arising in the modeling of nematic elastomers.