00-30   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Carsten Carstensen, Klaus Hackl, Alexander Mielke:

Nonconvex Potentials and Microstructures in Finite-Strain Plasticity

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.

Keywords: Finite elastoplasticity, incremental formulation, variational problems, continuum mechanics, quasi-convexity, relaxation

Mail an Jens Burmeister
[Thu Feb 19 18:56:35 2009]
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