Gradient Polyconvexity in Evolutionary Models of Shape-Memory Alloys

0519027 - ÚTIA 2021 RIV US eng J - Článek v odborném periodiku
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
Grant CEP: GA ČR GA17-04301S; GA ČR GA18-03834S; GA ČR(CZ) GF16-34894L
Institucionální podpora: RVO:67985556
Klíčová slova: Gradient polyconvexity * Invertibility of deformations * Shape-memory alloys
Obor OECD: Pure mathematics
Impakt faktor: 2.249, rok: 2020
Způsob publikování: Omezený přístup
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.
Trvalý link: http://hdl.handle.net/11104/0304160