Discrete solid element model applied to plasticity and dynamic crack propagation in continuous medium

In this work, the discrete solid element model (DSEM) applied to plasticity and dynamic crack propagation problems in the continuous medium is developed and implemented. First, the Drucker's postulate and the consistency condition are used to establish the plastic flow rule in the DSEM. The plastic scale factor which characterizes the plastic displacement increment of spherical elements is derived by the classical plastic mechanics. The elastoplastic contact constitutive equations of the strain-hardening material are established, which can be used for elasticity, unloading and loading. Second, to accurately simulate the mechanical behavior of continuity, the spring stiffness of spherical elements on the boundary of the DSEM is strictly deduced using the principle of conservation of energy, and the relationship between the spring stiffness and the continuous constitutive parameters is established. Third, the bilinear contact softening model is adopted to simulate the crack propagation in the continuous medium. The criteria for the crack propagation based on the fracture energy of the material are developed. The numerical examples are presented to show the capability and effectiveness of the DSEM in simulating the dynamic buckling and crack propagation problems. The obtained results are in agreement with experimental and numerical results published by other researchers.