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This paper discusses the similarity of meshless discretizations ofPeridynamics and Smooth-Particle-Hydrodynamics (SPH), if Peridynamics isapplied to classical material models based on the deformation gradient. We showthat the discretized equations of both methods coincide if nodal integration isused. This equivalence implies that Peridynamics reduces to an old meshlessmethod 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 aresult of the demonstrated equivalence to SPH, enhanced implementations ofPeridynamics should employ more accurate integration schemes.

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