Peridynamics review

Abstract

Peridynamics (PD) is a novel continuum mechanics theory established by Stewart Silling in 2000. The roots of PD can be traced back to the early works of Gabrio Piola according to dell’Isola et al. PD has been attractive to researchers as it is a non-local formulation in an integral form, unlike the local differential form of classical continuum mechanics. Although the method is still in its infancy, the literature on PD is fairly rich and extensive. The prolific growth in PD applications has led to a tremendous number of contributions in various disciplines. This manuscript aims to provide a concise description of the PD theory together with a review of its major applications and related studies in different fields to date. Moreover, we succinctly highlight some lines of research that are yet to be investigated.

Mixed peridynamic formulations for compressible and incompressible finite deformations

“…Silling [28] and Silling [29]) and in recent years the area of applications rapidly increased. For a review on Peridynamics the reader is referred to Javili et al [17].…”

Peridynamic Model for a Mindlin Plate Resting on a Winkler Elastic Foundation

“…Peridynamics has been successfully used to analyse different material systems and geometrical configurations [6][7][8][9][10][11][12][13][14]. An extensive literature survey on peridynamics is given in Madenci and Oterkus [15] and Javili et al [16]. Aforementioned benefits of peridynamics have attracted interest in solving solid mechanics problems particularly those involving damage and fracture.…”

Peridynamics formulation for beam structures to predict damage in offshore structures

“…PD theory is based on integro-differential equations which are valid in both continuous and discontinuous models. Therefore, it is suitable to predict damages on structures such as crack propagation and multiple crack growths (Javili et al,2018). PD can also be either combined with finite element analysis (FEA) (Kilic and Madenci, 2010b, Liu and Hong, 2012, Bie et al, 2018 or implemented in FEA framework (Macek and Silling, 2007, Han et al,2016, Diyaroglu et al,2017b, Yang et al, 2018.…”