Dynamic propagation of mode III cracks in a Lattice Boltzmann method for solids

Abstract

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 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.

On dynamic crack propagation in a lattice Boltzmann method for elastodynamics in 2D

“…Eventually, it can be concluded, that dynamic crack propagation is indeed possible with a method based on an LBM. While this was already undertaken in a previous work [6], the approach presented there has now been extended to in‐plane crack opening modes I and II. This extension also includes arbitrary directions of growth and thus allows for curved cracks.…”

“…The approach to handle the modelling of crack propagation was published in Müller et al. [6], see also Müller et al. [7].…”

“…In Müller et al. [6], an algorithm is described, that checks the links between lattice points in the vicinity of the crack tip. Only a very small number of points need to be checked. …”

“…The approach to handle the modelling of crack propagation was published in Müller et al [6], see also Müller et al [7]. This algorithm is used here without significant changes.…”

“…This is also favourable for the simulation of cracks. An LBM for solids has already been applied to crack propagation [6,7], where the proof-of-concept was given for mode III cracks, albeit in rather reduced mechanical and numerical setting. The same algorithm is used now with modifications due to the different boundary conditions.…”