Nonlinearity tunes crack dynamics in soft materials

TL;DR

This study uses a fracture phase field model to explore how nonlinearity influences crack behaviors in soft materials, revealing how strain-stiffening and strain-softening affect crack stability, speed, and oscillations.

Contribution

It introduces a phase diagram approach to classify crack dynamics in nonlinear soft materials, highlighting the universal role of wave speed in crack oscillations and transitions.

Findings

Crack morphologies can be reproduced in a 2D pre-strained model.

Strain-softening limits cracks to sub-Rayleigh speeds.

Strain-stiffening enables supershear fracture.

Abstract

Cracks in soft materials exhibit diverse dynamic patterns, involving straight, oscillation, branching, and supershear fracture. Here, we successfully reproduce these crack morphologies in a two-dimensional pre-strained fracture scenario and establish crack stability phase diagrams for three distinct nonlinear materials using a fracture phase field model. The contrasting phase diagrams highlight the crucial role of nonlinearity in regulating crack dynamics. In strain-softening materials, crack branching prevails, limiting the cracks to sub-Rayleigh states. Yet strain-stiffening stabilizes crack propagation, allowing for the presence of supershear fracture. Of particular interest is the large-strain linear elastic materials, where crack oscillation is readily triggered. The onset speed of such instability scales linearly with the characteristic wave speed near the crack tip, supporting the notion that such crack oscillations are a universal instability closely tied to the wave speed. The oscillation wavelength is shown to be a bilinear function of the nonlinear scale and crack driving force, with a minimum length scale associated with the dissipative zone. Moreover, our findings suggest that the increase in characteristic wave speed due to strain-stiffening can account for the observed transition of cracks from sub-Rayleigh to supershear regimes.