Thermo-Elastic Localization Relationships for Multi-Phase Composites

In this paper, we present a computationally efficient multi-scale framework for predicting the local fields in the representative volume element of a multiphase material system subjected to thermo-mechanical loading conditions. This framework for localization relationships is a natural extension of our recent work on two-phase composites subjected to purely mechanical loading. In this novel approach, the localization relationships take on a simple structure expressed as a series sum, where each term in the series is a convolution product of local structure and the governing physics expressed in the form of influence coefficients. Another salient feature of this approach is its exploitation of discrete Fourier transforms (DFTs) in calibrating the localization relationships to numerical datasets produced by finite element models. In this paper, we extend and validate this new framework for localization relationships in two important ways: (i) application to thermomechanical loading conditions, and (ii) application to multi-phase composites.