Polygonal Fracture Network Formation in a Lattice Model

We model the development of polygonal fracture patterns in two and three dimensions using a lattice Boltzmann model capable of simulating a variety of material rheologies. We model the development of polygonal networks developed under tensile loads in elastic materials and polygonal networks developed under compressive loads in elasto-plastic materials. The lattice Boltzmann model operates using nearest-neighbour rules that are shown to recover the Navier equations of elasticity and the Navier-Stokes equations of viscous flow. Fractures initiate and propagate by the conversion of elastic nodes to open boundaries (tensile failure) or viscous nodes (elasto-plastic failure) based on tensile and shear stress failure criteria. We compare the spatial and temporal characteristics of fracture networks generated by the two modes of failure to each other and to time lapse imagery of a mud desiccation network and a seismic cube containing polygonal faults. Similarity of fracture networks is measured using spatial and time series forecasting methods. Our results indicate that polygonal faulting is caused by shear failure and not tensile failure as has been put forward in previous models.