Gradient Polyconvexity in Evolutionary Models of Shape-Memory Alloys

0519027 - ÚTIA 2021 RIV US eng J - Journal Article
Kružík, Martin - Pelech, P. - Schloemerkemper, A.
Gradient Polyconvexity in Evolutionary Models of Shape-Memory Alloys.
Journal of Optimization Theory and Applications. Roč. 184, č. 1 (2020), s. 5-20. ISSN 0022-3239. E-ISSN 1573-2878
R&D Projects: GA ČR GA17-04301S; GA ČR GA18-03834S; GA ČR(CZ) GF16-34894L
Institutional support: RVO:67985556
Keywords : Gradient polyconvexity * Invertibility of deformations * Shape-memory alloys
OECD category: Pure mathematics
Impact factor: 2.249, year: 2020
Method of publishing: Limited access
http://library.utia.cas.cz/separaty/2020/MTR/kruzik-0519027.pdf https://link.springer.com/article/10.1007/s10957-019-01489-9

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.
Permanent Link: http://hdl.handle.net/11104/0304160