A semi-analytical model for evaluation of effective thermal conductivity of composites with periodic microstructure

This paper presents a semi-analytical micromechanical model for evaluation of effective thermal conductivity of composite materials with periodic microstructure. The model is based on the equivalent inclusion thermal problem and utilizes Fourier series for representation of periodic functions involved in the material homogenization approach. Two main objectives can be highlighted in the work. The first of them is the derivation of the thermal micromechanical model, which consists in an extension of a formulation originally derived for homogenization of elastic heterogeneous solids. The second objective consists in a detailed investigation on the performance of the model, considering convergence of results and efficiency of strategies employed for the approximate solution of the thermal homogenization problem. Analyses on the complexity of transformation temperature gradient functions are also included in this investigation. The results obtained for two examples of periodic composites with different microstructural architectures are presented and discussed in detail.