MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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]

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