  This work presents concepts and algorithms for the simulation of dynamic
fractures with a Lattice Boltzmann method (LBM) for linear elastic solids. This
LBM has been presented previously and solves the wave equation, which is
interpreted as the governing equation for antiplane shear deformation. Besides
the steady growth of a crack at a prescribed crack velocity, a fracture
criterion based on stress intensity factors (SIF) has been implemented. This is
the first time, that crack propagation with a mechanically relevant criterion
is regarded in the context of LBMs. Numerical results are examined to validate
the proposed method. The concepts of crack propagation introduced here are not
limited to mode III cracks or the simplified deformation assumption of
antiplane shear. By introducing a rather simple processing step into the
existing LBM at the level of individual lattice sites, the overall performance
of the LBM is maintained. Our findings underline the validity of the LBM as a
numerical tool to simulate solids in general as well as dynamic fractures in
particular.
