Ordinary state-based peridynamic homogenization of periodic micro-structured materials

Abstract In this work, an ordinary state-based peridynamic homogenization method is presented, in which periodic boundary condition is enforced by coupling the displacement of periodic point pairs. Effective material properties are obtained from the peridynamic displacement gradient tensor. The governing equation of peridynamics is in integro-differential form instead of more common spatial differential form, which grants it unique advantage in performing homogenization analysis involving defects. Recently, with the rapid advancement in additive manufacturing technology, micro-structured materials have attracted significant attention. Microscopic defects occurring during manufacturing process can have a noticeable impact on the overall material behavior especially on the fracture strength of the material. The current study provides a new approach to obtain the effective properties of periodic micro-structured materials with defects.