Nonlinearity tunes crack dynamics in soft materials

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. The intriguing crack oscillations are verified to be a universal instability closely tied to the local wave speed, as manifested by its onset speed scaling linearly with the characteristic shear wave speed. The wavelength of such instability 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 local wave speed near the crack tip can account for the transition of cracks from sub-Rayleigh to supershear regimes in homogeneous materials.