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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium

Patrick Dondl
University of Freiburg
Title: Energy estimates, relaxation, and existence for strain gradient plasticity with cross hardening

Abstract: We will consider a model for single-crystal elasto-plasticity, where a non-convexity arises through the imposition of a hard 'single-plane' side condition on the plastic deformation. This well-posed variational model arises as the relaxation of a more fundamental 'single-slip' model in which at most one slip system can be activated at each spatial point. The relaxation procedure is motivated by the desire for efficient, oscillation-free simulation of single-crystal plasticity, but it is not immediately obvious how to implement the hard side-condition (that at most one slip-plane may be activated at each point) numerically.

Our approach to the implementation problem is to regularise the side-condition by introducing a large, but finite, integral cross-hardening penalty into the plastic energy. The regularised model is then amenable to finite-element methods, and, with the aid of div-curl arguments, one can show that it $\Gamma$-converges to the single-plane model.

Date: Tuesday, April 17, 2018
Time: 11:30 am
Location: Wean Hall 5421
Submitted by:  Ian Tice
Note: Note special time and location.