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MiS Preprint

Liquid-like behaviour of shape memory alloys

Georg Dolzmann and Bernd Kirchheim


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]

Jul 4, 2002
Jul 4, 2002
MSC Codes:
quasiconvex hulls, phase transformations

Related publications

2003 Repository Open Access
Georg Dolzmann and Bernd Kirchheim

Liquid-like behavior of shape memory alloys

In: Comptes rendus mathematique, 336 (2003) 5, pp. 441-446