An Einstein Model of Brittle Crack Propagation
  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. 
Brad Lee Holian (Los Alamos National Laboratory), Raphael Blumenfeld   (Cambridge Hydrodynamics / Los Alamos National Labora...