Case studies in numerical simulation of crack trajectories in brittle materials

Statistical Fracture Mechanics, formalism of few natural ideas is applied to simulation of cracktrajectories in brittle material. The “diffusion approximation” of the crack diffusion model represents cracktrajectories as a one-dimensional Wiener process with advantage of well-developed mathematical formalismand simplicity of creating computer generated realizations (fractal dimension d = 1.5). However, the most ofreported d values are in the range 1.1-1.3. As a result, fractional integration of Wiener processes is applied forlowering d and to generate computer simulated trajectories. Case studies on numerical simulation ofexperimentally observed crack trajectories in sandstone (discs tested in indirect tensile strength test) andconcrete (compact tension specimens tested in the quasi-static splitting tensile test) are presented here