FRACTAL SOLID MECHANICS

The purpose of present article is to review a new general approach to solid mechanics, named, fractal solid mechanics. The attention is focu sed on systematic account of the proposed basic concepts, as well as o n the most important result of fractal solid mechanics. Special attent ion is paid to the thermodynamic theory of elasticity of multifractals which is effective for modeling various types of behavior patterns of deformed materials with multifractal microstructure. The fractal conc epts in fracture mechanics are considered. It is shown, that the natur e of fractal geometry of fracture of a solid is associated with fundam ental phenomenon of transverse strains of solid (Poisson's effect). Th is is manifested by the self-similarity of self-affinity of heterogene ous stresses in irreversibly deformed solids. Some of the most useful analytical and computer models are discussed. The result of theoretica l predictions are compared with experimental data. It is shown that th e proposed approach is very effective for adequate description of vari ous behavior patterns and some other phenomena in deformed solids.