Stefan Müller

Macroscopically stress free states in elastic crystals and quasiconvex hulls

The first part of the talk gave a short review of the research projects of the Leipzig team on microstructure and phase transformations with an emphasis on existing and potential future collaborations within the network. These topics are:

• Variational models of microstructure
• Influence of surface energy on microstructure
• Mathematical tools to describe microstructure
• Numerical computation

The second part of the talk discussed the passage from microscopic energy wells to macroscopically stress free deformations (more precisely zero energy deformations). If the former are given by a set $K$ in $3 \times 3$ matrices the latter are given by the so-called quasiconvex hull $K^{qc}$ of $K$. Recent results on the computation of $K^{qc}$ for the case of two wells were presented (joint work with Georg Dolzmann, Bernd Kirchheim and Vladimir Sverák).