Peridynamic Differential Operator
This chapter describes the peridynamic differential operator (PDDO) introduced by Madenci et al. (2016, 2017). The PDDO employs the concept of PD interactions, and it is based on the orthogonality property of the PD functions. It restores the nonlocal interactions at a point by considering its association with the other points within an arbitrary domain of interaction. The PD differentiation recovers the local differentiation as this interaction domain approaches zero. It converts the local form of differentiation to its nonlocal PD form. It is simply a bridge between differentiation and integration. Therefore, the PDDO enables numerical differentiation through integration.