A Second-Order Two-Scale Algorithm for Thermo-Mechanical Coupling Problems in Quasi-Periodic Porous Materials

Abstract

This work develops a second-order two-scale (SOTS) model based on homogenization method to predict thermo-mechanical coupling performance of porous materials with quasi-periodic structures. For the kinds of porous materials, the corresponding material coefficients are dependent on the macroscopic variable and the radiation effect at microscale is considered in this paper. The quasi-periodic properties of the thermo-mechanical coupling models which consider mutual interaction between temperature and displacement fields are proposed at first. Then, the two-scale formulas for the thermo-mechanical coupling problems with radiation boundary conditions are derived successively, and the finite element algorithms based on the SOTS model are brought forward in detail. Finally, by some typical examples, the effectiveness and validity of the proposed algorithms are confirmed. The computational results demonstrate that the SOTS method is efficient and valid to predict the thermo-mechanical coupling properties, and can acquire the microscale information of the porous materials accurately.

Asymptotic computation for transient heat conduction performance of periodic porous materials in curvilinear coordinates by the second‐order two‐scale method

“…In practical computation, it has been validated that the SOTS solutions are much better than the first-order solutions and homogenization solutions. After that, the SOTS analysis method has been developed and extended to study the linear elasticity and thermoelastic problems for quasi-periodic structures [18][19][20], the integrated heat transfer problems with conduction, convection and radiation in periodic or porous materials [21][22][23][24], and the dynamic thermoelastic problems of periodic composite or random particulate composites [25][26][27][28][29][30].As is known that in practical applications, various structures made of porous materials are designed and created to satisfy the industrial demand in many particular situations, such as the curved thermal protection layer in the thermal protection system of the spacecraft, hollow cylinder, ball, and the honeycomb structure, most of which are not periodically arranged along the Cartesian axis. However, the SOTS asymptotic expansion is based on the periodicity of the composite structures.…”