Critical analyses of RVE concepts in local and peridynamic micromechanics of composites

Abstract: A static peridynamic (proposed by Silling, see J. Mech. Phys. Solids 2000; 48:175--209) composite materials (CMs) of 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 for the straightforward generalization of LM methods to their PM counterparts. The representative volume element (RVE) playing a central role in the LM is generalized to PM. For the inhomogeneous body force with compact support, CAM is developed for the estimation of the effective behavior of CM which is used as a new compressed dataset. The preparation of these datasets is selected by the use of a fundamentally new RVE concept that directly depends on neither constitutive laws of phases nor the form of the predicted effective (surrogate) operator. The mentioned datasets with intrinsically incorporated new RVE concept as a necessary ingredient can be implemented into any known ML and neural network (NN) technique used for the prediction of nonlocal surrogate operators. Exploitation of the new RVE concept eliminates any potential incorrectness related to both size scale, boundary layer, and edge effects.