Peridynamic models that aim to incorporate a given stress-strain constitutive relationship from classical local continuum theory typically start with a nonlocal analog to the local deformation gradient as input to the given local stress-strain constitutive relationship. With a formulated nonlocal analogous deformation gradient, force density functions can then be derived in terms of stress tensor using the concept of energy conjugate. It should be noted that the formulation of this nonlocal analogous deformation gradient plays a significant role in the performance of related correspondence model. Issues such as material instability and penetration are well known in the model formulated based on the nodal average deformation gradient.