WIAS Preprint No. 2851, (2021)

Gradient polyconvexity and modeling of shape memory alloys


  • Horák, Martin
  • Kružík, Martin
    ORCID: 0000-0003-1558-5809
  • Pelech, Petr
    ORCID: 0000-0002-2271-7147
  • Schlömerkemper, Anja
    ORCID: 0000-0002-2744-0044

2020 Mathematics Subject Classification

  • 49J45 49J52 74C99 74N10 74N30


  • Gradient polyconvexity, numerical approximations, rate-independent problems, shape memory alloys




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. 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. Theoretical results are supported by three-dimensional computational examples. This work is an extended version of [36].

Appeared in

  • Variational Views in Mechanics, P.M. Mariano, ed., vol. 46 of Advances in Mechanics and Mathematics, Birkhäuser, Cham, 2021, pp. 133--156, DOI 10.1007/978-3-030-90051-9_5 .

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