We examine nonlinear interface propagation using peridynamics and phase-field modeling. In classical elas-ticity and strain-gradient models, interface dynamics has been shown to require closure through kinetic relations in the subsonic dissipative regime, while kinetic relations are not required in the supersonic inertial regime. We find that peridynamics agrees with this classical result, in that different choices of model parameters provide different kinetics in the dissipative regime but the same kinetics in the inertial regime.  In contrast, standard phase-field models are unable to model, even qualitatively, the inertial regime; interfaces cannot move super-sonically in phase-field models. The key physical distinction between phase-field models on the one hand, and peridynamics, strain gradient models, and classical elasticity on the other hand, is that the latter models are based solely on the momentum equation whereas the former model introduces an entirely new phase-field variable and an associated equation for its evolution. Based on this observation, we propose a phase-field model that aims to constrain, in some regimes, the phase-field evolution to the strain evolution, and find that this constrained model works well in both the dissipative and inertial regimes. Our approach to constraining the evolutions is based on a nucleation-like mechanism, suggesting that perhaps the fast motion of interfaces in the inertial regime can be interpreted as a nucleation-like phenomenon.  More broadly, our approach suggests features that are important for non-equilibrium phase-field models in settings such as dynamic fracture.

Comparing Phase-Field Modeling and Peridynamics in the Inertial and Dissipative Regimes

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