Multi-scale method for thermo-elasticity properties of composite materials with small periodic configuration

This paper predicts the thermal conductivities, elastic modulus and the thermal expansion coefficients of composite materials with small periodic configuration based on multi-scale method. Aiming at the equations of coupled thermo-elasticity, the microscopic coordinate and the macroscopic coordinate are introduced to describe the heterogeneous microstructure of the cell and the homogeneous macrostructure. The multi-scale expressions of the temperature and the displacement of the structure are established by the perturbation method. The expressions of the effective thermal conductivities, the stiffness and the thermal expansion coefficients of composite materials are also given. Combining with finite element technique, investigators analyses the changes of the effective properties of the composite materials due to the variety of the inclusion volume fraction, the variety of inclusion shape, the variety of inclusions' space length as well as the distributing fashions of the inclusions.