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MiS Preprint
72/2000

Nonconvex potentials and microstructures in finite-strain plasticity

Carsten Carstensen, Klaus Hackl and Alexander Mielke

Abstract

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.

Received:
Nov 5, 2000
Published:
Nov 5, 2000
Keywords:
finite elastoplasticity, incremental formulation, variational problem, continuum mechanics, quasiconvexity, relaxation

Related publications

inJournal
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