Nonconvex potentials and microstructures in finite-strain plasticity
Carsten Carstensen, Klaus Hackl, and Alexander Mielke
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Submission date: 05. Nov. 2000
published in: Proceedings of the Royal Society of London / A, 458 (2002) 2018, p. 299-317
DOI number (of the published article): 10.1098/rspa.2001.0864
Keywords and phrases: finite elastoplasticity, incremental formulation, variational problem, continuum mechanics, quasiconvexity, relaxation
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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.