On the thermo-elasto-statics of composites with coated randomly distributed inclusions

We consider a linearly elastic composite medium with stress free strains, which consists of a homogeneous matrix containing a homogeneous and statistically uniform random set of coated ellipsoidal inclusions having all the same form, orientation and mechanical properties. We are using the main hypothesis of many micromechanical methods, according to which each inclusion is located inside a homogeneous so-called e€ective ®eld. It is shown, in the framework of the e€ective ®eld hypothesis, that from a solution of the pure elastic problem (with zero stress free strains) for the composite the relations for e€ective thermal expansions, stored energy and average thermoelastic strains inside the components can be found. This way one obtains the generalization of the classical formulae by Rosen and Hashin (1970. Int. J. Eng. Sci. 8, 157±173), which are exact for two-component composites. The proposed theory is applied to the example of composites reinforced with particles with thin inhomogeneous (along inclusion surface) coatings. For a single coated inclusion the micromechanical approach is based on the Green function technique as well as on the interfacial Hill operators