This study presents the use of weak form of Bond-Associated Nonordinary State-Based Peridynamics (BA NOSB PD) for modeling inelastic material response within the MOOSE framework. The BA NOSB model provides a bond specific definition of the deformation gradient which accurately represents the state of the bond in the current configuration. This definition enables the implementation of material models of classical continuum mechanics within the PD framework. The predictions from this approach are free of any numerical oscillations. Also, the essential and natural boundary conditions are directly imposed. Numerical results concern the creep behavior of nuclear fuel pellet under thermal loading conditions.