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Second-Order Two-Scale Analysis Method for the Quasi-Periodic Structure of Composite Materials under Condition of Coupled Thermo-Elasticity

The second-order two-scale asymptotic expansions of the increment of temperature and the displacement for the quasi-periodic structure of composite materials under coupled thermo-elasticity condition are derived formally in this paper. The characteristic of the asymptotic model is the coupling between macroscopic scale and microscopic scale. Numerical examples including different coefficients are presented illustrating the efficiency and stability of the computational strategy. They show that the expansions to the second terms are necessary to obtain the thermal and mechanical behavior precisely, and the local and global oscillation of the increment of temperature and displacement are dependent on the microscopic and macroscopic part of the coefficients respectively.