Peridynamics for axisymmetric analysis

This study uses Peridynamics (PD) to predict the crack propagation in cylindrical domains subjected to axisymmetric loading. The weak form of the PD equation of motion is solved for elastic and isotropic materials. The internal force vector appearing in the PD equations of motion is derived directly by applying the PD differential operator to the Navier’s displacement equilibrium equations under axisymmetric assumptions. The solution of resulting system of equations is achieved through an implicit solver until crack initiation, and it continues with an explicit time integration algorithm during crack growth. The accuracy of this approach is demonstrated by considering a cylindrical body in the absence of a crack. The crack initiation and propagation are simulated in a cylindrical body by considering an internal ring crack based on the maximum principal stress and the visibility criteria.