Center for                           Nonlinear Analysis CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact 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, 2018Time: 11:30 amLocation: Wean Hall 5421Submitted by:  Ian TiceNote: Note special time and location.