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.
On Thermodynamic Restrictions in Peridynamics
Manuscript received September 18, 2011; final manuscript received March 20, 2012; accepted manuscript posted June 7, 2012; published online October 29, 2012. Editor: Robert M. McMeeking.
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Ostoja-Starzewski, M., Demmie, P. N., and Zubelewicz, A. (October 29, 2012). "On Thermodynamic Restrictions in Peridynamics." ASME. J. Appl. Mech. January 2013; 80(1): 014502. https://doi.org/10.1115/1.4006945
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