Homogenization of a fully coupled thermoelasticity problem for a highly heterogeneous medium with a priori known phase transformations |
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Authors: | Michael Eden Adrian Muntean |
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Institution: | 1. Center for Industrial Mathematics, FB 3, University of Bremen, Bremen, Germany;2. Department of Mathematics and Computer Science, University of Karlstad, Karlstad, Sweden |
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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 because of phase transformations. After transforming the moving geometry to an ? ‐periodic, fixed reference domain, we establish the well‐posedness of the model and derive a number of ? ‐independent a priori estimates. Via a two‐scale convergence argument, we then show that the ? ‐dependent solutions converge to solutions of a corresponding upscaled model with distributed time‐dependent microstructures. Copyright © 2017 John Wiley & Sons, Ltd. |
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Keywords: | homogenization two‐phase thermoelasticity two‐scale convergence time‐dependent domains distributed microstructures |
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