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

TL;DR

This paper derives linearized elasticity models from nonlinear multiwell energies with weak coercivity using Gamma-convergence, with applications to nematic elastomers.

Contribution

It extends the derivation of linearized models to energies with weaker coercivity conditions and applies the results to nematic elastomer modeling.

Findings

Linearized models obtained via Gamma-convergence for weak coercivity energies.

Applicable to nematic elastomer energy modeling.

Provides a mathematical framework for multiwell energies with p bounds.

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.