Thermo-elastic properties of random particulate nano-materials for various models of interphase

A mathematical model based on the method of conditional moments combined with a notion of the energy-equivalent inhomogeneity is adopted here in the investigation of the effective thermo-elastic properties of random nanomaterials. In the proposed model the inhomogeneities and their interphases with the matrix are replaced by energy-equivalent inhomogeneities with mechanical and thermal properties modified so as to incorporate the interphase effects. The effective coefficient of thermal expansion is subsequently determined by the method of conditional moments. Closed-form expression for the effective coefficient of thermal expansion of a composite consisting of a matrix and randomly distributed spherical inhomogeneities is derived for the Gurtin-Murdoch and spring layer model of interphases. Two numerical examples are presented to illustrate the quality of the approach.