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Gradient Polyconvexity in Evolutionary Models of Shape-Memory Alloys

Author

Listed:
  • Martin Kružík

    (Institute of Information Theory and Automation
    Czech Technical University)

  • Petr Pelech

    (Charles University)

  • Anja Schlömerkemper

    (University of Würzburg)

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.

Suggested Citation

  • Martin Kružík & Petr Pelech & Anja Schlömerkemper, 2020. "Gradient Polyconvexity in Evolutionary Models of Shape-Memory Alloys," Journal of Optimization Theory and Applications, Springer, vol. 184(1), pages 5-20, January.
    • Handle: RePEc:spr:joptap:v:184:y:2020:i:1:d:10.1007_s10957-019-01489-9
    DOI: 10.1007/s10957-019-01489-9
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