A Review of Peridynamics and its Applications; Part1: The Models based on Peridynamics

Peridynamics is a nonlocal version of the continuum mechanics, in which partial differential equations are replaced by integro-differential ones. Due to not using spatial derivatives of the field variables, it can be applied to problems with discontinuities. In the primary studies, peridynamics has been used to simulate crack propagation in brittle materials. With proving the capabilities of peridynamics, the idea of using this theory to simulate crack propagation in quasi-brittle materials and plastic behavior has been proposed. To this end, formulations and models based on peridynamics have been developed. Meanwhile, the high computational cost of peridynamic methods is the main disadvantage of this theory. With the development of peridynamic methods and introduction of hybrid methods based on peridynamics and local theories, the computational cost of peridynamic methods has been reduced to a large extent. This paper introduces peridynamics and the models based on it. To this end, we first review peridynamics, its formulations, and the methods based on it. Then we discuss the modeling of quasi-brittle materials, simulation of plastic behavior and employing the differential operators in this theory.