Analysis Seminar - 26/2/2014

Wednesday, 26 February 2014, 2:00 p.m.

Lecturer: Carolin Kreisbeck, Universitӓt Regensburg

Title: "Relaxation of models in finite plasticity with two active slip systems".

Local: Room 1.5, Edifício VII
Faculdade de Ciências e Tecnologia, Quinta da Torre, Caparica

Abstract: 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 investigate the macroscopic material response of a variational model in geometrically nonlinear elasto-plasticity with two active slip systems, rigid elasticity, and linear selfhardening. In particular, an explicit formula for the relaxation of the underlying energy density is given. One observes that the relaxation mechanism is identical to the one derived in the regime with only one active slip system. Due to the presence of a second slip system, however, the effective material behavior is softer and the relaxed energy is finite for all volume preserving deformations. In contrast to two-slip models without hardening, where laminates of infinite order are needed to carry out the relaxation process, the essential step here is the construction of a suitable first-order laminate. This allows to predict the microstructure that realizes the effective energy in the system, which could be experimentally verified. Finally, we show that the assumption of elastically rigid material behavior is justified, since models with rigid elasticity can be obtained as Γ-limits of models with finite elastic energy for diverging moduli of elasticity.

This is joint work with Sergio Conti and Georg Dolzmann.