Scalable algorithms for solving elasto-plastic problems

Abstract

In the thesis we propose an algorithm for the efficient parallel implementation of elastoplastic problems with hardening based on the so-called TFETI (Total Finite Element Tearing and Interconnecting) domain decomposition method. We consider three different associated elasto-plastic models: the von Mises model with isotropic hardening, the von Mises model with kinematic hardening and the Drucker-Prager perfectly plastic model. Such models are discretized by the implicit Euler method in time and the consequent one time step elasto-plastic problem by the finite element method in space. The latter results in a system of nonlinear equations for equality constraints or system of nonlinear inequations with a strongly semismooth and strongly monotone operator. The semismooth Newton method is applied to solve this nonlinear system. Corresponding linearized problems arising in the Newton iterations are solved in parallel or sequentially by the above mentioned TFETI domain decomposition method. The proposed TFETI based algorithm was implemented in Matlab parallel environment and its performance is illustrated on 2D and 3D elasto-plastic benchmarks. Numerical results for different time discretizations and mesh levels are presented and discussed and a local quadratic convergence of the semismooth Newton method is observed. We also demonstrate parallel and numerical scalability of the proposed algorithms for solving elasto-plasticity.