An irregular lattice spring model: uniform elasticity, grid refinement and isotropic crack propagation

Abstract

Abstract The Born lattice spring model (LSM) is implemented on an irregular network. This irregular LSM is directly mapped to linear elasticity theory such that the model can capture an elastically uniform system where the direction of resultant fracture propagation is no longer influenced by a regular lattice structure. Furthermore, this allows the density of nodes to be varied throughout the simulation while maintaining the correct elastic mapping. For the first time, the LSM can be refined around areas of interest such as heterogeneities or crack tips, while capturing the spatial cooperative effects of isotropic fracture propagation in heterogeneous materials.