Dynamic Crack Propagation in a Lattice Boltzmann Method for Solid Mechanics

In recent years, Lattice Boltzmann methods (LBMs) have been adapted and developed to simulate the behavior of solids. They have already been applied to fractures as well. However, until now, our previous work has been restricted to stationary cracks.

In this work, we regard the reduced 2D case of anti‐plane shear deformation with mode III crack opening. The wave equation is the governing equation for this problem, which is solved via an LBM.

The main contribution of this work is the introduction of an algorithm to handle crack growth in an LBM for solids. The underlying scheme is based on geometric assumptions, which is well suited for the regular lattice used by the LBM. A fracture criterion based on the stress intensity factor is implemented and illustrated by a numerical example.