Modeling nonlinear elastic solid with correlated lattice bond cell for dynamic fracture simulation

The correlated lattice bond cell is a kind of lattice model developed for modeling nonlinear elastic solid. Unlike the usual lattice model, the present one is composed of unit cells, which can adopt any geometry with any number of bonds. The unit cells are compiled together via the particles along their boundaries to form a discrete system. The energy of unit cell is characterized by the modified Stillinger–Weber (SW) potential, in which the initial value of each bond angle in the reference configuration, not the ‘ideal’ tetrahedral angle, is taken as the reference value of this bond angle in the current configuration. This makes the modified SW potential applicable to other materials than silicon. Because the modified SW potential can simultaneously account for the bond stretch and rotation effect, the present lattice model can represent variable Poisson ratios. The bond parameters are calibrated as the function of material constants (Young’s modulus, Poisson ratio), the volume and the total bond number of a unit cell based on the ideal unit cell conception. Enriched with a more elaborate fracture mechanism than the two-body potential through the modified SW potential, the present lattice model can capture most characters of dynamic fracture, providing an efficient nonlinear elasticity modeling method for dynamic fracture simulation. For the present method can directly simulate the dynamic fracture initiation, arrest, propagation and branching in the finite deformation cases without any separate criterion, its perspective should be inspiring.