  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.
