A continuum mixture model for transient heat conduction in multi-phase composites

The difference between transient thermal responses of each constituent in composites is one of the important factors to cause significant nonuniform deformation, high stress gradient and failure of composites. While direct numerical simulations for transient heat conduction in multi-phase composites are highly costly and even formidable, classical homogenization methods are focused on predicting the effective conductivities and the macroscopic thermal responses of a whole representative volume element, leaving the prediction of this difference at the macroscopic level to be a challenging issue during structural analysis of composite materials. In order to solve this issue, we propose a continuum mixture model for the transient heat conduction in multi-phase composites through dynamic homogenization methods. The derived governing equations retain the identity of each constituent behaviour and relate them to the overall response of each constituent. All the coefficients in the equations can be directly determined by the constituent phases and geometric parameters through explicit relations. The precision of the model is verified by comparison with direct numerical simulations. The results indicate that the model not only captures the disparate thermal responses of each constituent at the macroscopic level, but also accurately predicates the macro-average responses. The methodology can be generalized to other non-equilibrium thermodynamic phenomena such as diffusion and other kinds of conduction in multi-phase systems.