Relaxed grain cluster (RGC) homogenization scheme

An efficient homogenization scheme for polycrystals is presented. The scheme is based on a generalization of the grain interaction (GIA) model. A volume element consisting of eight (= 2 × 2 × 2) hexahedral grains is considered. The kinematics of the relaxed grain cluster (RGC) scheme is formulated within a finite deformation framework, where the relaxation of the local deformation gradient of each individual grain is described by interface relaxation vectors. In the present model, the relaxation vectors are determined such that the total energy (or work) density of the cluster is minimum. A penalty term is added into the energy minimization landscape, which accounts for an energy density associated to the mismatch at the grain boundaries due to relaxations. Effectively, this penalty term mimics the kinematical condition of deformation compatibility at the grain boundaries. Furthermore, simulations have been performed for a polycrystalline sample. The overall behavior of the sample undergoing uniaxial tension and simple shear, is studied for various microstructural configurations. The prediction of the RGC scheme is compared with predictions using other averaging schemes, as well as the result of finite element (FE) simulation.