A novel algorithm for rate independent small strain crystal plasticity based on the infeasible primal-dual interior point method

Single crystal plasticity plays a major role in the analysis of material anisotropy and texture evolution, treats each crystalline grain individually. The polycrystalline material response is obtained upon considering a structure consisting of various individual grains, often also considering interface effects at the grain boundaries. On the individual grain level, single crystal plasticity can be treated in the mathematical framework of multi-surface plasticity, leading to a constrained optimization problem wherein multiple constraints are defined as yield criteria on the different slip systems. In this work, we present a new algorithm for the solution of the constrained optimization problem based on the Infeasible Primal Dual Interior Point method (IPDIPM). The main motivation herein is the handling of the ill-posed problem without the use of simple perturbation technique, see e.g. Miehe and Schroder [2001]. The proposed algorithm, involving slack variables, is developed for the framework of small strain single crystal plasticity. The use of slack variables therein stabilizes the conventional method and allows for a temporary violation of the constraint condition during the optimization. Moreover, all slip systems are considered simultaneously, omitting an iterative active set search. Several numerical examples are simulated to show the performance of the developed algorithm.