Simulations of crack development in brittle materials under dynamic loading using the numerical manifold method

Crack development in brittle materials under dynamic loading is widely involved in engineering, in which crack initiation, propagation and coalescence are typical phenomena. The numerical manifold method (NMM) is a unified continuous-discontinuous numerical method employing two cover systems, namely, mathematical covers and physical covers, which encounters no difficulty in the numerical representation of continua and complex discontinuities within one framework. In the present work, NMM is developed for the simulation of crack initiation, propagation and coalescence problems in brittle materials under dynamic loading based on the tensile strength criterion and the Mohr-Coulomb strength criterion for tensile and shear cracking, respectively. Four typical examples including the splitting of a rock bar, the Kalthoff-Winkler experiment, the cracking in tensile loaded pre-notched rectangular plates and the double-hole blasting of rectangular plates are simulated. The numerically derived crack development results are compared with corresponding theoretical or experimental results. The mesh size sensitivity is discussed for the first two examples; the dynamic cracking mechanism in the rock bar example is investigated along with the stress wave propagation analysis; the influence of the initial crack and hole locations on the crack path in the tensile loaded pre-notched example as well as the effect of the guiding notch in the double-hole blasting example are studied. Results indicate that the crack initiation, propagation and coalescence in brittle materials under dynamic loading are quite satisfactorily reproduced by NMM.