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We propose an algorithm for the efficient parallel implementation ofelastoplastic problems with hardening based on the so-called TFETI (TotalFinite Element Tearing and Interconnecting) domain decomposition method. Weconsider an associated elastoplastic model with the von Mises plastic criterionand the linear isotropic hardening law. Such a model is discretized by theimplicit Euler method in time and the consequent one time step elastoplasticproblem by the finite element method in space. The latter results in a systemof nonlinear equations with a strongly semismooth and strongly monotoneoperator. The semismooth Newton method is applied to solve this nonlinearsystem. Corresponding linearized problems arising in the Newton iterations aresolved in parallel by the above mentioned TFETI domain decomposition method.The proposed TFETI based algorithm was implemented in Matlab parallelenvironment and its performance was illustrated on a 3D elastoplasticbenchmark. Numerical results for different time discretizations and mesh levelsare presented and discussed and a local quadratic convergence of the semismoothNewton method is observed.

A TFETI Domain Decomposition Solver for Elastoplastic Problems