Small strain elasto-plastic multiphase-field model

A small strain plasticity model, based on the principles of continuum mechanics, is incorporated into a phase-field model for heterogeneous microstructures in polycrystalline and multiphase material systems (Nestler et al., Phys Rev 71:1-6, 2005). Thereby, the displacement field is computed by solving the local momentum balance dynamically (Spatschek et al., Phys Rev 75:1-14, 2007) using the finite difference method on a staggered grid. The elastic contribution is expressed as the linear approximation according to the Cauchy stress tensor. In order to calculate the plastic strain, the Prandtl-Reuss model is implemented consisting of an associated flow rule in combination with the von Mises yield criterion and a linear isotropic hardening approximation. Simulations are performed illustrating the evolution of the stress and plastic strain using a radial return mapping algorithm for single phase system and two phase microstructures. As an example for interface evolution coupling with elasto-plastic effects, we present crack propagation simulations in ductile material.