  We show that the delivery of fracture work to the tip of an advancing planar
crack is strongly reduced by surface phonon emission, leading to forbidden
ranges of crack speed. The emission can be interpreted through dispersion of
the group velocity, and Rayleigh and Love branches contribute as well as other
high frequency branches of the surface wave dispersion relations. We also show
that the energy release rate which enters the Griffith criterion for the crack
advance can be described as the product of the continuum solution with a
function that only depends on the lattice geometry and describes the lattice
influence on the phonon emission. Simulations are performed using a new finite
element model for simulating elasticity and fractures. The model, built to
allow fast and very large three-dimensional simulations, is applied to the
simplified case of two dimensional samples.
