  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.
