A trust region algorithm for finite-strain plasticity with strongly coupled hardening

Abstract

As extensions to our Lagrangian finite-strain plasticity framework based on the approximate exponential integrator, we introduce two new algorithms: (i) a fixed-radius trust region root finder for the nonlinear system involving the elastic right Cauchy Green tensor and plastic multiplier (ii) a partitioned approach for the hardening variables, which are determined in a staggered form using the strongly-coupled concept typically adopted for multiphysics problems. This allows the use of intricate hyperelastic laws combined with recent yield functions, which otherwise would involve a laborious treatment, and the use of corresponding work-hardening. Work-hardening would introduce significant nonlinearities in the constitutive system if used in a fully-coupled form. For the partitioned approach, a dynamic relaxation algorithm is adopted. This allows the efficient solution of the two nonlinear equations without significant drifting. Results show that robustness and efficiency are significantly improved. Herein, algorithms are described in detail. Significant testing is performed with imposed strains up to 100 for a carbon steel. This contributes to the robustness of equilibrium iterations. Drifting is also assessed as a function of number of steps in the dynamic relaxation algorithm. Numerical experimentation is performed in the 3D tension test for an anisotropic yield function.