A statistically homogeneous random matrix medium with the bond-based peridynamic properties of constituents is considered. For the media subjected to remote homogeneous volumetric boundary loading, one proved that the effective behavior of this media is governing by conventional effective constitutive equation which is the same as for the local elasticity theory. The average is performed over the surface of the extended inclusion phase rather than over an entire space. Any spatial derivatives of displacement fields are not required. The basic hypotheses of locally elastic micromechanics are generalized to their peri-static counterparts. In particular, in the generalized method of effective field proposed, the effective field is evaluated from self-consistent estimations by the use of closing of a corresponding integral equation in the framework of the quasi-crystalline approximation. In so doing, the classical effective field hypothesis is relaxed, and the hypothesis of the ellipsoidal symmetry of the random structure of CMs is not used. One demonstrates some similarity and difference with respect to other methods (the dilute approximation and Mori-Tanaka approach) proposed before in peridynamic micromechanics of CMs. Comparative numerical analyses of these methods are performed for 1D case.

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