Peridynamics: Past, Present and Future

In order to determine the deformation response of materials and structures subjected to external loading conditions, classical continuum mechanics (CCM) was introduced by disregarding the atomistic structure. CCM has been successfully applied to numerous challenging problems. However, its governing equation faced a difficulty when there is any discontinuity in the structure such as a crack, since spatial partial derivatives in its governing equation are not defined for such a condition. To overcome this problem, a new continuum mechanics approach, Peridynamics (PD), was recently introduced with the intention that PD equations remain always valid whether there is any discontinuity in the structure or not. This character of PD makes this new approach a powerful tool for predicting crack initiation and propagation. Moreover, PD can be considered as the continuum version of molecular dynamics. Therefore, PD can be a suitable candidate for multi-scale analysis of materials. Furthermore, PD formulation can also be extended to other fields such as thermal diffusion, moisture diffusion, etc., so that it can be used as a single platform for multiphysics analysis of materials and structures with damage prediction capability. Hence, in this study, a brief information about peridynamics will be provided by covering past developments, presenting current progress, and highlighting potential future research directions.