Gradient Polyconvexity in Evolutionary Models of Shape-Memory Alloys

Martin Kružík (), Petr Pelech () and Anja Schlömerkemper ()
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Martin Kružík: Institute of Information Theory and Automation
Petr Pelech: Charles University
Anja Schlömerkemper: University of Würzburg

Journal of Optimization Theory and Applications, 2020, vol. 184, issue 1, No 2, 5-20

Abstract: Abstract We show the 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 the existence of a solution based on weak continuity of nonlinear minors of deformation gradients in Sobolev spaces. Admissible deformations do not necessarily have integrable second derivatives. Under suitable assumptions, our model allows for solutions which are orientation preserving and globally injective everywhere in the domain representing the specimen.

Keywords: Gradient polyconvexity; Invertibility of deformations; Orientation-preserving mappings; Shape-memory alloys; 49J45; 35B05 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-019-01489-9

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