Elasto-Plasticity

Abstract

The previous concepts of differential geometry, in particular aspects related to incompatibility, shall be applied to the kinematics of firstand second-order (nonlinear) elasto-plasticity. Thereby it shall be noted that the intermediate configuration of first- and second-order elasto-plasticity is incompatible, see Fig. 8.1. Then two cases may be considered: firstly the incompatibility of the intermediate configuration is measured based on the nonintegrability of plastic tensorial quantities; secondly the situation is reversed: the incompatibility of the intermediate configuration is measured based on the non-integrability of elastic tensorial quantities. Thereby distinction can be made between straightforward measures in terms of the non-integrable plastic or elastic distortions (and double-distortions) and more involved measures in terms of the non-integrable plastic or elastic (strain) metrics (and doublemetrics). The former leads to various dislocation density tensors, whereas the latter results in various incompatibility density tensors.

Comprehensive accounts on first- and second-order elasto-plasticity in Euclidean space are provided for the sake of reference at the end of the chapter in two extended supplements.