On thermodynamic restrictions in peridynamics

This note examines restrictions imposed by the second law of thermodynamics on peridynamics in both the bond-based and the state-based formulations. Our study was carried out in the framework of thermomechanics with internal variables. In bond-based peridynamics, there are two possible thermomechanical interpretations of the dissipation function. One interpretation only admits a thermodynamic orthogonality of Ziegler, while the other admits powerless forces within a representation theory of Edelen. The latter interpretation is admissible in state-based peridynamics. Since the dissipation function of peridynamics is set up in velocity space, a link to statistical mechanics of irreversible phenomena does not appear possible.