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

Algebraic detection of $T_k$-configurations

Carl Friedrich Kreiner, Johannes Zimmer and Isaac Chenchiah


The problem of detecting so-called $T_k$-configurations is addressed here. These configurations are the most prominent examples of sets with nontrivial rank-one convex hulls. Rank-one convex hulls play an important rôle in the calculus of variations and the modelling of effective properties of materials.

An efficient algorithm, based on algebraic methods, is presented. Unlike previous work on the computation of rank-one convex hulls, it is not based on discretization and gives exact results. This algorithm enables, for the first time, large numbers of tests for these configurations. Stochastic experiments in several space dimensions are reported here.

rank-one convex hull, $t_k$-configuration

Related publications

2004 Repository Open Access
Carl Friedrich Kreiner, Johannes Zimmer and Isaac Vikram Chenchiah

Towards the efficient computation of effective properties of microstructured materials

In: Comptes rendus mécanique, 332 (2004) 3, pp. 169-174