Scale Effects in Infinitesimal and Finite Thermoelasticity of Random Composites

A method for homogenization of linear or non-linear (finite strain) thermoelastic random composites is presented. With the help of variational principles, the method leads to hierarchies of scale-dependent bounds on constitutive responses, which are illustrated in several cases through computational mechanics. This, in turn, provides estimates of the minimal size of the Representative Volume Element (RVE). The effects of mismatch between the composite's phases as well as the temperature difference on the minimal size of the RVE are also considered. The results of linear and non-linear thermoelasticity theories are compared.