A review on connection between meshfree peridynamics and meshfree methods

Abstract

Peridynamics is an integro-differential nonlocal reformulation of the classical theory of continuum mechanics, which has attracted great interest and been widely applied for solving engineering science problems recently. The most common and widely used discretization method for peridynamic models is the node-based meshfree approach. It appears that more exposition of connection between meshfree peridynamics and classes of meshless methods are needed. In the light of the matter, this paper presents a review on connection between meshfree methods and meshfree peridynamic method. This review is focused on how meshfree discretization of peridynamic model can be related to the existing and well-known meshfree formulations. The connection emphasizes how the formulations and discretizations share some features (including limitations), thus allowing one to recast possible equivalence and generalization upon which improvements and enhancements among the methods may be further developed.