On the Consideration of the Geometric and Physical Fractality in Solid Mechanics. I: Theoretical Results

The aim of the present paper is to investigate the influence which the behaviour of solids and structures has on the possible fractality of their geometry or of their material behaviour. To this end certain methods are proposed for the theoretical investigation of this influence, based on the consideration of the fractal as attractor of a deterministic or a random iterated function system. First the mechanical notions and the mechanical laws are extended to fractal geometries. Then certain calculation methods are proposed and their results are investigated.