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

Nonconvex potentials and microstructures in finite-strain plasticity

Carsten Carstensen, Klaus Hackl and Alexander Mielke


A mathematical model for a finite-strain elastoplastic evolution problem is proposed in which one time-step of an implicit time-discretisation leads to generally non-convex minimisation problems. The elimination of all internal variables enables a mathematical and numerical analysis of a reduced problem within the general framework of calculus of variations and nonlinear partial differential equations. The results for a single slip-system and von Mises plasticity illustrate that finite-strain elastoplasticity generates reduced problems with non-quasiconvex energy densities and so allows for non-attainment of energy minimisers and microstructures.

finite elastoplasticity, incremental formulation, variational problem, continuum mechanics, quasiconvexity, relaxation

Related publications

2002 Repository Open Access
Carsten Carstensen, Klaus Hackl and Alexander Mielke

Non-convex potentials and microstructures in finite-strain plasticity

In: Proceedings of the Royal Society of London / A, 458 (2002) 2018, pp. 299-317