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 focused on systematic account of the proposed basic concepts, as well as on the most important result of fractal solid mechanics. Special attention is paid to the thermodynamic tbeory of elasticity of multifractals wbich is effective for modeling various types of behavior patterns of deformed materials with multifractal microstructure. The fractal concepts in fracture mechanics are considered. It is shown, that the nature of fractal geometry of fracture of a solid is associated with fundamental phenomenon of transverse strains of salid (Poisson's effect). This is manifested by the self-similarity of self-affinity of heterogeneous stresses in irreversibly deformed solids. Sorne of the most useful analytical and computer models are discussed. The result of theoretical predictions are compared with experimental data. It is shown that the proposed approach is very effective for adequate description of various behavior patterns and sorne other phenomena in deformed solids.