Calibrated localization relationships for elastic response of polycrystalline aggregates

In recent years, our research group has formulated a new framework called materials knowledge systems (MKS) for establishing highly accurate reduced-order (surrogate) models for localization (opposite of homogenization) linkages in hierarchical materials systems. These new computationally efficient linkages are designed to capture accurately the microscale spatial distribution of a response field of interest in the representative volume element (RVE) of a material, when subjected to an imposed macroscale loading condition. In prior work, the viability and computational advantages of the MKS approach were demonstrated in a number of case studies involving multiphase composites, where the local material state in each spatial bin of the RVE was permitted to be any one of a limited number of material phases (i.e. restricted to a set of discrete local states of the material). In this paper, we present a major extension to the MKS framework that allows a computationally efficient treatment of a significantly more complex local state of the material, i.e. crystal lattice orientation. This extension of the MKS framework is formulated by the use of suitable Fourier representation of the influence functions. This paper describes this new formulation and the associated calibration protocols, and demonstrates its viability with case studies comprising low and moderate contrast cubic and hexagonal polycrystals.