Realization methods of computational homogenization for thermal conductivity coefficient of composites

The computational homogenization method has been proved to be a valid method which can be used to predict the equivalent thermal conductivity coefficient of periodical-structure composites. Due to the unconventional load item form of the control equations, there is no corresponding load forms in general finite element software, and it is difficult to solve directly. An analogy method of constitutive relationships and field variables was presented, and it proves that the homogenization equations of equivalent thermal conductivity coefficient and equivalent elastic modulus are equivalent in this analogy. By utilizing the thermal strain method for homogenization equations of solving equivalent elastic modulus, a novel computational solving approach for equivalent thermal conductivity coefficient of homogenization equations was proposed. The equivalent thermal conductivity coefficient of unidirectional fiber reinforced composites and metallic honeycomb panel were calculated by using ABAQUS as platform, the calculation results agree well with reference results. This method provides a simple way for the computational homogenization of equivalent thermal conductivity coefficient of composites in common finite element software.