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.

系统地研究了这项工作中开发的一种高阶三尺度方法，用于分析具有内表面辐射的多孔材料的热机械性能。通过局部区域在微观域和介观域上的周期性布置来描述多孔结构的微观结构，并且还研究了微观尺度和介观尺度的表面辐射效应。首先，建立了基于均质化和高阶渐近展开的三尺度公式，并定义了微观尺度和中尺度尺度的局部细胞解。然后，通过放大方法评估两种均质化参数，并在整个结构上导出均质化方程。进一步，通过组合高阶晶胞溶液和均质溶液，将热通量和应变场构造为三尺度渐近解。所提出的方法的显着特征是不需要宏观解的更高阶连续性的渐进高阶同质化，以及用于分析耦合问题的新的高阶三阶公式。最后，提出了一些代表性的例子来验证所提出的方法。他们表明，本文介绍的三尺度渐近扩展对于预测具有多个空间尺度的多孔材料的热机械性质是有效且有效的。所提出的方法的显着特征是不需要宏观解的更高阶连续性的渐进高阶同质化，以及用于分析耦合问题的新的高阶三阶公式。最后，提出了一些代表性的例子来验证所提出的方法。他们表明，本文介绍的三尺度渐近扩展对于预测具有多个空间尺度的多孔材料的热机械性质是有效且有效的。所提出的方法的显着特征是不需要宏观解的更高阶连续性的渐进高阶同质化，以及用于分析耦合问题的新的高阶三阶公式。最后，提出了一些代表性的例子来验证所提出的方法。他们表明，本文介绍的三尺度渐近扩展对于预测具有多个空间尺度的多孔材料的热机械性质是有效且有效的。