FRACTAL AND MULTIFRACTAL CHARACTERISTICS OF STOCHASTIC BRITTLE-FRACTURE

The spatiotemporal development of stochastic fracture process in brittle materials is studied on the basis of the fractal approaches. The fractal tree is proposed to be an analogue of the discretization scheme for the region under study. The scale-invariant load redistribution procedure is used for the fulfillment of the equilibrium law. It is analogous to the random multiplicative cascade and reflects the real process of stress redistribution under the generation and propagation of the macroscopic discontinuities as a result of the damage accumulation. This process could be characterized by the fractal dimension of the fracture's morphology and by the multifractal load distribution near the macroscopic defect. The effect of the type of material's stochasticity on the fractal dimension and multifractal spectrum is studied for three characteristic cases. The influence of initial macroscopic defect (V-shape notch) on the damage accumulation and crack propagation is analyzed.