Homogenization of a Fully Coupled Thermoelasticity Problem for a Highly Heterogeneous Medium With a Priori Known Phase Transformations

Abstract

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 due to phase transformations. After transforming the moving geometry to an $\epsilon$-periodic, fixed reference domain, we establish the well-posedness of the model and derive a number of $\epsilon$-independent a priori estimates. Via a two-scale convergence argument, we then show that the $\epsilon$-dependent solutions converge to solutions of a corresponding upscaled model with distributed time-dependent microstructures.

25 pages, 1 figure

References in corpus (1)

• Homogenization of a Double Porosity Model In Deformable Media

Cited by in corpus (2)

• Existence of weak solutions for a pseudo-parabolic system coupling chemical reactions, diffusion and momentum equations
• Corrector Estimates for the Homogenization of a Two-Scale Thermoelasticity Problem With a Priori Known Phase Transformations