  We propose a minimal nonlinear model of brittle crack propagation by
considering only the motion of the crack-tip atom. The model captures many
essential features of steady-state crack velocity and is in excellent
quantitative agreement with many-body dynamical simulations. The model exhibits
lattice-trapping. For loads just above this, the crack velocity rises sharply,
reaching a limiting value well below that predicted by elastic continuum
theory. We trace the origin of the low limiting velocity to the anharmonicity
of the potential well experienced by the crack-tip atom.
