A computational homogenization framework for non-ordinary state-based peridynamics

Abstract Peridynamic theory has been shown to possess the capabilities of describing phenomena that theories based on partial differential equations are not capable describing. These include nonlocal interactions and presence singularities in system responses. To exploit offered by peridynamics homogenization heterogenous media, a computational peridynamic correspondence model (non-ordinary state-based peridynamics) is proposed. set development rigorous mathematical framework ensure consistency with nature theory, vector calculus was used analysis theory. The proposed two-scale micro–macro-homogenization strategy which constitutive relation at macroscale derived from explicit solution volume constraint problem microscale. justify coupling between two scales, analogues stress strain average theorems as well Hill–Mandel macrohomogeneity condition were derived. Validation achieved via numerical Representative Volume Elements (RVE) composite materials comparing results those obtained means established methodologies.