Fractal cracks
An attempt is made to take into account the irregular structure of the surface of a real crack in describing the fracture process. The crack surface is modelled using a fractal set of fractional dimension. Using the self-similarity of the fractal, a hierarchical process of the transfer of elastic energy generated during the motion of the crack tip from one scale to another is suggested. Analysis of this process makes it possible to obtain asymptotic expressions for describing the behaviour of the cracks and displacements near the crack tip. The propagation of a fractal crack in a brittle material is analysed from the positions of the Griffith's criterion.
scientific article; zbMATH DE number 500935