Nonlinear wave propagation and shock wave formation in quasi-brittle materials

Fracture of quasi-brittle materials such as concrete, rocks by impact, ceramics and calculi is known to occur due to the formation and development of microcracks. Microcracks reduce the macroscopic value of Young’s modulus of the material and hence reduce the wave speed when the dynamic problem is considered. By applying the continuum model for microcracking, nonlinear wave propagation is analyzed numerically for an infinite plate made of granite. The plate is subjected to an impact compressive stress at one surface. Another surface of the plate is assumed to be stress free. It is shown that the process forming the shock wave progresses near the stress-free surface by the occurrence of microcracks according to the tensile strain caused by the wave reflection.