Finite Elastoplasticity Lie Groups and Geodesics on SL(d)

Abstract

The notions of nonlinear plasticity with finite deformations is interpreted in the sense of Lie groups. In particular, the plastic tensor P=F p −1 is considered as element of the Lie group SL(d). Moreover, the plastic dissipation defines a left-invariant Finsler metric on the tangent bundle of this Lie group. In the case of single crystal plasticity this metric is given interms of the different slip systems and is piecewise affine on each tangent space. For von Mises plasticity the metric is a left-invariant Riemannian metric. A main goal is to study the associated distance metric and the geodesic curves.