Homogenization of a fully coupled thermoelasticity problem for a highly heterogeneous medium with a priori known phase transformations
Michael Eden, Adrian Muntean · Mathematical Methods in the Applied Sciences · 2017
We investigate a linear, fully coupled thermoelasticity problem for a highly heterogeneous, two‐phase medium. The medium in question consists of a connected matrix with disconnected, initially periodically distributed inclusions separated by a sharp interface undergoing an a priori known interface movement because of phase transformations. After transforming the moving geometry to an ϵ‐periodic, fixed reference domain, we establish the well‐posedness of the model and derive a number of ϵ‐independent a priori estimates. Via a two‐scale convergence argument, we then show that the ϵ‐dependent solutions converge to solutions of a corresponding upscaled model with distributed time‐dependent microstructures. Copyright © 2017 John Wiley & Sons, Ltd.