On the similarity of meshless discretizations of Peridynamics and Smooth-Particle Hydrodynamics

• The similarity between Peridynamics and Smooth-Particle Hydrodynamics is studied.
• A widely used meshfree discretization of Peridynamics is equivalent to SPH.
• Discretized Peridynamics can suffer from the same instabilities as SPH.

This paper discusses the similarity of meshless discretizations of Peridynamics and Smooth-Particle-Hydrodynamics (SPH), if Peridynamics is applied to classical material models based on the deformation gradient. We show that the discretized equations of both methods coincide if nodal integration is used. This equivalence implies that Peridynamics reduces to an old meshless method and all instability problems of collocation-type particle methods apply. These instabilities arise as a consequence of the nodal integration scheme, which causes rank-deficiency and leads to spurious zero-energy modes. As a result of the demonstrated equivalence to SPH, enhanced implementations of Peridynamics should employ more accurate integration schemes.