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A two-scale thermo-mechanical model for porous solids is derived and is implemented into a multi-scale multiphysics analysis method. The model is derived based on the mathematical homogenization method and can account for the scale effect of unit cells, which is our particular interest in this paper, on macroscopic thermal behavior and, by extension, on macroscopic deformation due to thermal expansion/contraction. The scale effect is thought to be the result of microscopic heat transfer, the amount of which depends on the micro-scale pore size of porous solids. We first formulate a two-scale model by applying the method of asymptotic expansions for homogenization and, by using a simple numerical model, verify the validity and relevancy of the proposed two-scale model by comparing it with a corresponding single-scale direct analysis with detailed numerical models.

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