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

2013/08/19 by Virginia Agostiniani, Agostiniani, Virginia, Timothy Blass +3
Mathematics · #49J45 #74B15 #74G65 #76A15 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:49J45 #msc:74B15 #msc:74G65 #msc:76A15

paper · pdf · doi:10.48550/arxiv.1308.3994

arxiv created 2014/03/11 · arxiv updated 2014/03/12

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.

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