Eigenstrain based reduced order homogenization for polycrystalline materials

In this manuscript, an eigenstrain based reduced order homogenization method is developed for polycrystalline materials. A two-scale asymptotic analysis is used to decompose the original equations of polycrystal plasticity into micro- and macroscale problems. Eigenstrain based representation of the inelastic response field is employed to approximate the microscale boundary value problem using an approximation basis of much smaller order. The reduced order model takes into account the grain-to-grain interactions through influence functions that are numerically computed over the polycrystalline microstructure. The proposed approach is also endowed with a hierarchical model improvement capability that allows accurate representation of stress and deformation state within subgrains. The proposed approach was implemented and its performance was assessed against crystal plasticity finite element simulations. Numerical studies point to the capability to efficiently compute the mechanical response of the polycrystal RVEs with good accuracy and the ability to capture stress risers near grain boundaries.