The peridynamic differential operator is a mathematical tool used in the field of peridynamics, a non-local continuum mechanics theory that describes the behavior of material over large distances. The operator plays a crucial role in formulating the equations of motion in peridynamics, which accounts for interactions between material points at a distance without relying on local spatial derivatives. The peridynamic differential operator is used to define the peridynamic state-based force function, which determines the forces acting between material points based on their positions and states. It is a key component in predicting the deformation and failure of material structures in various applications, such as modeling damage and fracture in solids, granular materials, and biological tissues. Overall, the peridynamic differential operator is essential for solving problems in peridynamics and offers a unique perspective on the behavior of materials under extreme conditions or complex environments. Through its use, researchers can gain insights into phenomena that may not be captured by traditional continuum mechanics models.