A review of lattice type model in fracture mechanics: theory, applications, and perspectives

The lattice model is a discrete model that is typically used to simulate the fracture process of brittle materials. This review summarizes the main achievements during the development history of the state-of-the-art lattice model during the past 80 years from the theory and application viewpoints. It is found that the classical lattice spring model (LSM) can only simulate a fixed Poisson's ratio. This problem has been partially or fully solved in developed versions of novel lattice models by using (1) extra nodal DOFs, (2) extra shear springs, (3) extra nonlocal energy parameters, and (4) higher dimensional normal springs. The lattice model has already been successively applied in simulations of fracture processes of different materials and under different loads. However, the applications in fracture analyses of metals, dynamic load-induced fracture, and real large-scale structures, are not sufficient. Innovative areas of future research in reference to the use of the lattice model in engineering practice include constitutive relations, failure criteria, anisotropic material modeling and efficient computing techniques to expand its use and range of applications.