Mean-field homogenization of multi-phase thermo-elastic composites: a general framework and its validation

This paper deals with mean-field Eshelby-based homogenization techniques for multi-phase composites and focuses on three subjects which in our opinion deserved more attention than they did in the existing literature. Firstly, for two-phase composites, that is when in a given representative volume element all the inclusions have the same material properties, aspect ratio and orientation, an interpolative double inclusion model gives perhaps the best predictions to date for a wide range of volume fractions and stiffness contrasts. Secondly, for multi-phase composites (including two-phase composites with non-aligned inclusions as a special case), direct homogenization schemes might lead to a non-symmetric overall stiffness tensor, while a two-step homogenization procedure gives physically acceptable results. Thirdly, a general procedure allows to formulate the thermo-elastic version of any homogenization model defined by its isothermal strain concentration tensors. For all three subjects, the theory is presented in detail and validated against experimental data or finite element results for numerous composite systems.