Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.
MiS Preprint
53/2002
Liquid-like behaviour of shape memory alloys
Georg Dolzmann and Bernd Kirchheim
Abstract
In this note, we prove that the identity matrix is an inner point of the quasiconvex hull $K^{qc}$ of a compact set $K\subset\{X\in\mathbb{M}^{3\times 3}:\,\det X=1\}$ whenever $K^{qc}$ contains a three-well configuration. This is in particular the case for the cubic to tetragonal and the cubic to orthorhombic phase transformations, and answers a question discussed in [S. Müller, Microstructures, phase transitions and geometry, in: Proceedings European Congress of Mathematics, Budapest, 1996, Birkhäuser 1998]
