An analytical solution for multiple inclusions subject to a general applied thermal field

Abstract

In this study, we present a general numerical solution to the thermoelastic problem of interacting elliptical inhomogeneities in an infinite matrix material. Our solution provides a framework to study microstructural responses to the external mechanical, thermal, electric, and magnetic fields simultaneously. The proposed semi-analytical method, which enables us to reduce the computational cost and calculate the interactions between many inclusions, is based on conformal mapping, series expansion of the corresponding complex potentials and boundary conditions. The temperature, stress, strain, and displacement functions are derived explicitly in the matrix material and inclusions. The thermal loadings tested in this study include temperature variations and a uniform heat flow. The model is validated against multiple analytical calculations and benchmark numerical problems. The method is ready to apply for simulations with many inclusions.