On the fractal nature of problems in mechanics

This paper investigates the influence of fractal geometry and fractal material behaviour in solid and structural mechanics. For that, certain methods are proposed for the theoretical and numerical investigation of this influence based on the consideration of the fractal as the “fixed point” of a given iterated function system or as the fractal graph of a fractal interpolation function which interpolates a given set of data. First the definitions of the mechanical quantities and the mechanical laws are extended to fractal sets by using some results from the theory of Besov spaces. Then an attempt is made to extend certain calculation methods to the case of fractal interfaces and to the case of fractal nonmonotone interface laws. Finally the results of these methods are investigated.