  We analyze a piece-wise linear elastic model for the propagation of a crack
in a stripe geometry under mode III conditions, in the absence of dissipation.
The model is continuous in the propagation direction and discrete in the
perpendicular direction. The velocity of the crack is a function of the value
of the applied strain. We find analytically the value of the propagation
velocity close to the Griffith threshold, and close to the strain of uniform
breakdown. Contrary to the case of perfectly harmonic behavior up to the
fracture point, in the piece-wise linear elastic model the crack velocity is
lower than the sound velocity, reaching this limiting value at the strain of
uniform breakdown. We complement the analytical results with numerical
simulations and find excellent agreement.
