Development of a Lattice Boltzmann Method for the Simulation of Dynamic Crack Propagation in Brittle Materials

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The goal of this project is to develop a numerical method for the simulation of crack propagation in brittle (i.e. linear elastic) materials, which also considers the inertia of the surrounding material. For this purpose a so-called Lattice Boltzmann Method (LBM) will be used. Typically, the LBM is used to simulate fluid flows. The idea of the LBM is to model the macroscopic behavior of a continuum by computing the evolution of distribution functions, which represent the behavior of the fluid on a microscopic level. The distribution functions are defined at discrete lattice points and are transported along a predefined spatial lattice to the neighbor lattice points in one discrete time step. In the subsequent collision step, distribution functions are recomputed in dependence of all other distribution functions at the considered lattice point, material parameters and lattice quantities.In order to simulate structural problems with the LBM, it is necessary to extend an already existing LBM for simplified deformation assumptions of a solid (i.e. antiplane shear deformation). This means that the existing method needs to be modified in order to be able to model plane strain and plane stress problems. Subsequently, stationary (i.e. non-moving) cracks will be implemented by modeling the boundary conditions at the crack correctly. This is not a trivial task since it is intended that the method sets few limitations on possible crack patterns. Eventually, crack growth based on a criterion of fracture mechanics will also be implemented in the LBM. To this end, a suited approach will be chosen from the literature and adapted to the LBM. At this point the developed LBM will be able to realistically model dynamic crack growth in brittle materials. This implies that features of dynamic fracture such as characteristic upper limits of the crack speed and dynamic crack branching can be observed in simulations.The method described above will be implemented in a software that allows the simulation of various user-defined dynamic linear elastic problems as well as problems of dynamic crack growth in linear elastic materials. The inherent explicit and parallelizable character of the LBM will be exploited in order to significantly decrease the runtime compared to other methods. Furthermore, the software will include interfaces for user-defined extensions and will provide the framework for a future extension to three-dimensions.