  A class of peridynamic material models known as constitutive correspondence
models provide a bridge between classical continuum mechanics and peridynamics.
These models are useful because they allow well-established local constitutive
theories to be used within the nonlocal framework of peridynamics. A recent
finite deformation correspondence theory (Foster and Xu, 2018) was developed
and reported to improve stability properties of the original correspondence
model (Silling et al., 2007). This paper presents a stability analysis that
indicates the reported advantages of the new theory were overestimated.
Homogeneous deformations are analyzed and shown to exibit unstable material
behavior at the continuum level. Additionally, the effects of a particle
discretization on the stability of the model are reported. Numerical examples
demonstrate the large errors induced by the unstable behavior. Stabilization
strategies and practical applications of the new finite deformation model are
discussed.
