Differential scheme for effective thermoelastic properties of multiphase composite materials with application to damaged composites. Vladimir Vinogradov Abstract The Differential Scheme (DS) is extended to estimate the effective thermoelastic properties of multiphase statistically homogeneous particulate composites. The calculation procedure is shown to be related to the inclusion size distribution of different phases. The consistency of the DS is proved. Rosen-Hashin formula, connecting effective thermal coefficients of arbitrary two-phase composites with the effective stiffness, is obtained as a particular case of the DS for two-phase materials. The method is applied to evaluate stiffness and thermal expansion coefficients of microcracked particulate composites and a composite with debonded inclusions. Asymptotic solutions for some limiting microgeometries (such as a light foam with embedded particles, a composite with high crack density etc.) are considered. Energy based fracture criterion is applied to predict debonding development in a composite.