Generalized effective fields method in peridynamic micromechanics of random structure composites

We consider a static problem for statistically homogeneous matrix linear bond-based peridynamic composite materials (CMs). For the media subjected to remote homogeneous volumetric boundary loading, one proved that the effective behavior of this media is governed by conventional effective constitutive equation as in the local elasticity theory. It was made by the most exploitation of the popular tools and concepts used in conventional elasticity of composite materials (CMs) with their adaptation to peridynamics. This is extraction from the material properties a constituent of the matrix properties. Effective moduli are expressed through the introduced new notion of the average local polarization tensor. 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 peridynamic counterparts. In particular, in the generalized effective field method (EFM) 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 micromechanics of peridynamic CMs. Comparative numerical analyses of these methods are performed for 1D case. (C) 2020 Elsevier Ltd. All rights reserved.