Phase-Field Modeling and Peridynamics for Defect Dynamics, and an Augmented Phase-Field Model with Viscous Stresses

TL;DR

This paper compares peridynamics and phase-field models for interface motion in elastic solids, identifies limitations of standard phase-field models, and proposes an augmented model with viscous stresses to accurately simulate both subsonic and supersonic interface dynamics.

Contribution

It introduces an augmented phase-field model incorporating viscous stresses and improved energy landscape modeling to accurately simulate interface motion, including supersonic regimes.

Findings

Peridynamics aligns with classical results on interface kinetics.

Standard phase-field models cannot qualitatively model supersonic motion.

The augmented model accurately captures both subsonic and supersonic interface dynamics.

Abstract

This work begins by applying peridynamics and phase-field modeling to predict 1-d interface motion with inertia in an elastic solid with a non-monotone stress-strain response. In classical nonlinear elasticity, it is known that subsonic interfaces require a kinetic law, in addition to momentum balance, to obtain unique solutions; in contrast, for supersonic interfaces, momentum balance alone is sufficient to provide unique solutions. This work finds that peridynamics agrees with this classical result, in that different choices of regularization parameters provide different kinetics for subsonic motion but the same kinetics for supersonic motion. In contrast, conventional phase-field models coupled to elastodynamics are unable to model, even qualitatively, the supersonic motion of interfaces. This work identifies the shortcomings in the physics of standard phase-field models to be: (1) the absence of higher-order stress to balance unphysical stress singularities, and (2) the ability of the model to access unphysical regions of the energy landscape. Based on these observations, this work proposes an augmented phase-field model to introduce the missing physics. The augmented model adds: (1) a viscous stress to the momentum balance, in addition to the dissipative phase-field evolution, to regularize singularities; and (2) an augmented driving force that models the physical mechanism that keeps the system out of unphysical regions of the energy landscape. When coupled to elastodynamics, the augmented model correctly describes both subsonic and supersonic interface motion. The augmented model has essentially the same computational expense as conventional phase-field models and requires only minor modifications of numerical methods, and is therefore proposed as a replacement to the conventional phase-field models.