Lattice Theory for the Existence and Stability of Tensile Cracks

We obtained the most general analytical solution to date for crack propagation in a hexagonal lattice under tensile loading. For non-central forces, we found expressions for surface wave speeds that differ from prior literature. We compiled together 160,000 solutions to form a complete catalog of cracks that demonstrates how a material's elastic and dissipative properties dictate the extent to which surface wave speeds limit crack speeds and when cracks are stable or begin branching or wiggling. Our results are consistent with the qualitative features of fracture in many materials.