Surface node method for the peridynamic simulation of elastodynamic problems with Neumann boundary conditions

Peridynamics is a nonlocal theory that can effectively handle discontinuities, including crack initiation and propagation. However, near the boundaries, the incomplete nonlocal regions are the cause of the peridynamic surface effect, resulting in unphysical stiffness variation. Additionally, imposing local boundary conditions in a peridynamic (nonlocal) model is often necessary. To address these issues, the surface node method has been proposed for improving accuracy near the boundaries of the body. Although this method has been verified for a variety of problems, it has not been applied for elastodynamic problems involving Neumann boundary conditions. In this work we show a numerical example of this case, comparing the results with the corresponding peridynamic analytical solution. The numerical results exhibit no stiffness variations near the boundaries throughout the entire simulation timespan. Therefore, we conclude that the surface node method allows to effectively solve elastodyn...