Three-dimensional elastic–plastic lattice-spring model based on sapphire crystal structure and its application to impact characterisation studies

A thirteen-node octahedral three-dimensional lattice-spring model based on the sapphire crystal structure is established by applying the parameter mapping theory, and the finite element stiffness matrix is mapped into the linear spring stiffness coefficients of the lattice-spring model according to the parameter mapping method, so that the selection of the spring stiffness coefficients has a strict mathematical derivation. The elastic–plastic potential function that unifies the elastic–plastic characteristics of the material and the fracture energy is established. The lattice-spring model is tested by three algorithms, including longitudinal wave velocity, three-dimensional crack extension path under dynamic indentation, and impact compression deformation and lattice size sensitivity test, and the test results show that the established three-dimensional lattice-spring model has a high computational accuracy. The correctness of the calculation of the lattice-spring model is verified by comparing the calculation of the evolution process of spherical impact damage on the edge of sapphire under different crystal directions with the experiment.