MiS Preprint Repository

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

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.

Nov 22, 2003
Nov 22, 2003
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