THE GEOMETRY OF PREFRACTAL RENORMALISATION: APPLICATION TO CRACK SURFACE ENERGIES

Abstract

Natural fractal objects, unlike their mathematical counterparts, tend to exhibit power law scaling over a limited range of scales. In this paper a prefractal theoretical framework is constructed for natural fractal objects and illustrated through the application to natural crack surfaces. The prefractal model is linked with both traditional and current fractal methods for determining the energy of fracture. It is shown how the prefractal model gives the same size effect law as incorporated by existing recent fractal theories, but with the advantage of retaining the correct physical dimensions. The prefractal theory developed within the paper has general application to a range of other scientific and engineering problems.