Shape memory alloys as gradient-polyconvex materials

2018/07/25 by Kružík, Martin, Pelech, Petr, Schlömerkemper, Anja
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1807.09855

Abstract

We show existence of an energetic solution to a model of shape memory alloys in which the elastic energy is described by means of a gradient-polyconvex functional. This allows us to show existence of a solution based on weak continuity of nonlinear minors of deformation gradients in Sobolev spaces. Resulting deformations are orientation-preserving and injective everywhere in a domain representing the specimen.

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