On the validity of the self-consistent scale transition model for inclusions with varying morphologies

Scale transition models based on Eshelby’s solution provide interesting information on the properties and multi-scale mechanical states experienced by materials presenting complex microstructures, such as composite materials, accounting for the constituents’ properties but also microstructural parameters such as the morphology of the heterogeneous inclusions constituting the material. Nevertheless, until now, these approaches cannot reliably account for multiple inclusion morphologies in the same representative elementary volume of the modeled material, as they predict two distinct sets of properties depending of the quantities (strains or stresses) used to formulate the homogenization procedure.The present work aims to investigate the validity of Kröner–Eshelby self-consistent model for thermo-elastic behaviour, in the case when several morphologies do coexist within the same representative elementary volume. A study of the two resulting formulations and their limits leads to suggest a mixed formulation inspired of Vook–Witt’s model, as an understandable but acceptable compromise between the two alternatives. The results of this formulation are also described in the case of a thermo-mechanical load.