On fractal cracks in micropolar elastic solids

In this paper we review the fracture mechanics of smooth cracks in micropolar (Cosserat) elastic solids. Griffith's fracture theory, is generalized for cracks in micropolar solids and shown to have two possible forms. The effect of fractality, of fracture surfaces on the powers of stress and couple-stress singularity is studied. We obtain the orders of stress and couple-stress singularities at the tip of a fractal crack in a micropolar solid using dimensional analysis and an asymptotic method that we call "method of crack-effect zone." It is shown that orders of stress and couple-stress singularities are equal to the order of stress singularity, at the tip of the same fractal crack in a classical solid.