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

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• Qualitative behavior of solutions for thermodynamically consistent Stefan problems with surface tension
• Self-similar solutions with compactly supported profile of some nonlinear Schr{ö}dinger equations
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