Variational estimates for the effective response and field statistics in thermoelastic composites with intra-phase property fluctuations

Abstract

In this work, variational estimates are provided for the macroscopic response, as well as for the first and second moments of the stress and strain fields, in thermoelastic composites with non-uniform distributions of the thermal stress and elastic moduli in the constituent phases. These estimates are obtained in terms of a ‘comparison composite’ with uniform phase properties depending on the first and second moments of a certain combination of the given intra-phase thermal stresses and modulus field distributions. Under certain hypotheses, these estimates can be shown to lead to upper and lower bounds for the free energy of the composite, which reduce to standard results when the intra-phase fluctuations vanish. An illustrative application is given for rigidly reinforced composites with a non-uniform distribution of the thermal stress in the matrix phase.