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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium

Carolin Kreisbeck
Mathematical Sciences, Carnegie Mellon University
Title: Analytical aspects of relaxation for single-slip models in finite crystal plasticity

Abstract: (Joint work with Sergio Conti and Georg Dolzmann) Modern mathematical approaches to plasticity result in non-convex variational problems for which the standard methods of the calculus of variations are not applicable. In this contribution we consider geometrically nonlinear crystal elasto-plasticity in two dimensions with one active slip system. In order to derive information about macroscopic material behavior the relaxation of the corresponding incremental problem is studied. We focus on the question if realistic systems with an elastic energy leading to large penalization of small elastic strains can be well-approximated by models based on the assumption of rigid elasticity. The interesting finding is that there are qualitatively different answers depending on whether hardening is included or not. In presence of hardening we obtain a positive result, which is mathematically backed up by Gamma-convergence, while the material shows very soft macroscopic behavior in case of no hardening. The latter is due the vanishing relaxation for a large class of applied loads.

Date: Thursday, December 2, 2010
Time: 1:30 pm
Location: Wean Hall 8220
Submitted by:  David Kinderlehrer