From fractal media to continuum mechanics

摘要: This paper presents an overview of modeling fractal media by continuum mechanics using the method dimensional regularization. The basis this is to express balance laws for in terms fractional integrals and, then, convert them integer-order conventional (Euclidean) space. Following account method, we develop (continuity, linear and angular momenta, energy, second law) discuss wave equations several settings (1d 3d motions, Timoshenko beam, elastodynamics under finite strains). We then extremum variational principles, fracture mechanics, turbulent flow media. In all cases, derived depend explicitly on dimensions reduce forms continuous with Euclidean geometries upon setting integers. also point out relations potential extensions regularization other models microscopically heterogeneous physical systems.