  Cracks in brittle materials produce two types of generic surface structures:
facets at low velocities and micro-branches at higher ones. Here we observe a
transition from faceting to micro-branching in polyacrylamide gels that is
characterized by nonlinear dynamic localization of crack fronts. To better
understand this process we derive a first-principles nonlinear equation of
motion for crack fronts in the context of scalar elasticity. Its solution shows
that nonlinear focusing coupled to rate-dependence of dissipation governs the
transition to micro-branching.
