A high-order three-scale approach for predicting thermo-mechanical properties of porous materials with interior surface radiation

Abstract A high-order three-scale approach developed in this work to analyze thermo-mechanical properties of porous materials with interior surface radiation is systematically studied. The microstructures of the porous structures are described by periodical layout of local cells on the microscopic domain and mesoscopic domain, and surface radiation effect at microscale and mesoscale is also investigated. At first, the three-scale formulas based on reiterated homogenization and high-order asymptotic expansion are established, and the local cell solutions in microscale and mesoscale are also defined. Then, two kinds of homogenized parameters are evaluated by upscaling methods, and the homogenized equations are derived on the whole structure. Further, heat flux and strain fields are constructed as the three-scale asymptotic solutions by assembling the higher-order unit cell solutions and homogenized solutions. The significant features of the proposed approach are an asymptotic high-order homogenization that does not require higher order continuity of the macroscale solutions and a new high-order three-scale formula derived for analyzing the coupled problems. Finally, some representative examples are proposed to verify the presented methods. They show that the three-scale asymptotic expansions introduced in this paper are efficient and valid for predicting the thermo-mechanical properties of the porous materials with multiple spatial scales.

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