Peridynamic micromechanics of periodic structure composites subjected to body force with compact support

A static peridynamic (proposed by Silling, see J. Mech. Phys. Solids 2000; 48:175–209) composite materials (CMs) of the periodic structures are analyzed. A body force with compact support is applied to a thermoelastically mismatched CM at constant temperature. Within the framework of computational analytical micromechanics (CAM)—a branch of micromechanics referred to as the second background—it has been established that local micromechanics (LM) and peridynamic micromechanics (PM) exhibit formal equivalence for CMs with random and periodic structures. This equivalence facilitates a seamless extension of LM methodologies to their PM analogs. Specifically, key LM concepts, such as the decomposition of real fields into load and residual components, as well as isolating matrix-specific properties from material properties of phases, have been successfully generalized to PM. The concept of the representative volume element (RVE), pivotal in LM, has also been adapted and extended to PM. For inhomogeneous body forces with compact support, CAM is employed to estimate the effective behavior of CMs, leading to the creation of innovative compressed data sets. These data sets are developed using a fundamentally new RVE concept that does not depend on the constitutive laws of the individual phases or the form of the predicted effective (surrogate) operator. The data sets incorporating this novel RVE concept serve as a critical foundation for integration into existing machine learning (ML) and neural network (NN) approaches for predicting nonlocal surrogate operators for both locally elastic and peridynamic CMs. The new RVE concept systematically eliminates size scale inaccuracies, boundary layer effects, and edge effects, ensuring robust and reliable predictions for periodic CMs.