Representation and calibration of elastic localization kernels for a broad class of cubic polycrystals

Abstract

Localization kernels play an important role in the study of hierarchical material systems with well separated length scales. They allow for a computationally efficient communication of critical information between the constituent length scales. They are particularly well suited for capturing how an imposed variable (e.g., stress or strain) at the higher length scale is spatially distributed at the lower length scale (i.e., localization linkages). In recent work, our research group has presented a novel framework called Materials Knowledge Systems (MKS) for the representation and calibration of the localization kernels, and demonstrated the viability of this approach on selected individual material systems. In this work, we present and demonstrate an important extension to the MKS framework that allows representation and calibration of the localization kernels for an entire class of materials (e.g., a selected class of single phase cubic polycrystalline materials).