Gradient polyconvexity and modeling of shape memory alloys [report]

Martin Horák, Martin Kružík, Petr Pelech, Anja Schlömerkemper, Technische Informationsbibliothek (TIB)
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
more » ... here in the domain representing the specimen. Theoretical results are supported by three-dimensional computational examples. This work is an extended version of [36].
doi:10.34657/8607 fatcat:bbgvlses4rhuvny4xn2cdpdrum