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Publication 57

From Nonlinear to Linearized Elasticity via Convergence: The Case of Multiwell Energies Satisfying Weak Coercivity Conditions

Authors:

Virginia Agostiniani
Mathematical Institute
University of Oxford
24-29 St. Giles'
Oxford, OX1 3LB, UK

Timothy Blass
Department of Mathematical Sciences, Carnegie Mellon University

Konstantinos Koumatos
Mathematical Institute
University of Oxford
24-29 St. Giles'
Oxford, OX1 3LB, UK

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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multiwellBlass.pdf

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