The effect of finite element model and formulation on simulations in large deformation polycrystal plasticity

Abstract

Second, a stabilized mixed finite element method is presented for crystal plasticity at large strains. This is compared to a standard mixed finite element formulation. The stabilized implementation takes advantage of a mesh dependent stabilization term to bypass the requirements of the Ladyzenskaya-Babuska-Brezzi condition. This allows for the use of P1/P1 elements (linear interpolation for displacement and pressure). In contrast, the standard mixed finite element formulation is restricted to P2/P1 elements (quadratic interpolation for displacement and linear interpolation in pressure). Results using stabilized P1/P1 elements are compared with standard P1/P1 elements as well as standard P2/P1 elements as a control case, for a polycrystal. The pressure field is shown to fluctuate through out the polycrystal when considering the standard model using P1/P1 elements vs. the control case. The pressure field for the stabilized P1/P1 elements accurately matches the general control case.The study presented here examines the effect of finite element model and formulation on simulations in crystal plasticity. First, a grain representation study is examined. Simulation results from finite element models with voxel, or stair stepped grain boundaries, are compared with results using smooth grain boundaries. Both models are generated from the same periodic grain geometry. Comparable mesh sizes are implemented for each type of geometric model. A mesh convergence study for both topologies is examined. Both topologies undergo large strain deformation and the macroscale behavior is compared, as well as the model efficiencies. Texture, stress and slip are examined for a more localized comparison.