Peridynamic Micromechanics of Composites: A Review

A static peridynamic (proposed by Silling, see J. Mech. Phys. Solids 2000; 48:175–209) composite materials (CMs) of both the random and periodic structures are considered. In the framework of the second background of micromechanics (also called computational analytical micromechanics, CAM), one proved that local micromechanics (LM) and peridynamic micromechanics (PM) are formally similar to each other for CM of both random and periodic structures. It allows straightforward generalization of LM methods to their PM counterparts. It turns out that a plurality of micromechanics phenomena [e.g. statistically homogeneous and inhomogeneous media, inhomogeneous loading (inhomogeneous body force is included), nonlinear and nonlocal constitutive laws of phases, and coupled physical phenomena] can be analyzed by one universal tool (called CAM), which is sufficiently flexible and based on physically clear hypotheses that can be modified and improved if necessary (up to abandonment of these hypotheses) in the framework of a unique scheme for analyses of a wide class of mentioned problems. The schemes of these approaches are considered in the current paper.