It is important to study failures of rocks under dynamic loads for expounding mechanisms of geological disasters and for predicting and preventing these disasters on theoretical and practical aspects. Owing to advantages of numerical simulation

numerical methods applicable to modeling dynamic fracturing processes must be especially emphasized. Based on the combined Lagrangian-discrete element method

a continuum-discontinuum method considering the dynamic constitutive model was presented

in which the Zhu-Wang-Tang constitutive model was used to replace the generalized Hooke law. The continuum-discontinuum method considering the dynamic constitutive model was validated through modeling uniaxially compressive experiments of sandstone rock specimens for different loading velocities. Evolution of the number of crack segments with the longitudinal strain of the rock specimen was investigated

and evolution of the minimum principal stresses of nodes at the longitudinal symmetric line was also monitored. Deformation-fracturing processes of granite specimens for different loading velocities were modeled

and fracturing mechanisms of rock specimens were revealed. The following results were found. Shear bands include en echelon shear cracks. The minimum principal stress of the node exhibits a fluctuant decrease

followed by an increase in the oscillation form. The increasing stage corresponds to the strain-softening stage of the rock specimen. A large oscillatory amplitude of the minimum principal stress is found for the separating node

which is due to the fact that large stress waves are induced by node separations and contact between elements. Shear separations of nodes occur due to concentrations of the minimum principal stresses at the shear band tip. Motion of the triangle wedge of the rock specimen leads to tensile separations of nodes whose stress states are similar to those of the compact tension experiment.