In contrast to the classical local and nonlocal theories, the peridynamic equation of motion introduced by Silling (J. Mech. Phys. Solids 2000; 48: 175–209) is free of any spatial derivatives of displacement. The new general integral equations (GIE) connecting the displacement fields in the point being considered and the surrounding points of random structure composite materials (CMs) is proposed. For statistically homogeneous thermoperistatic media subjected to homogeneous volumetric boundary loading, one proved that the effective behaviour of this media is governing by conventional effective constitutive equation which is intrinsic to the local thermoelasticity theory. It was made by the most exploitation of the popular tools and concepts used in conventional thermoelasticity of CMs and adapted to thermoperistatics. A generalization of the Hills equality to peri-static composites is proved. The classical representations of effective elastic moduli through the mechanical influence functions for elastic CMs are generalized to the case of peristatics, and the energetic definition of effective elastic moduli is proposed. The general results establishing the links between the effective properties (effective elastic moduli, effective thermal expansion) and the corresponding mechanical and transformation influence functions are obtained by the use of the decomposition of local fields into load and residual fields. Effective properties of thermoperistatic CM are expressed through the introduced local stress polarization tensor averaged over the extended inclusion phase. This similarity opens a way for straightforward expansion of analytical micromechanics tools for locally elastic CMs to the new area of random structure peri-dynamic CMs. Detailed numerical examples for 1D case are considered.

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