ABSTRACT
Multifractals are the generalization of self-similar fractals, which describe the local features of non-uniform fractals with self-similarity. A multifractal was originally introduced by Mandelbrot in the discussion of turbulence and extended by Mandelbrot to many other contexts. In this chapter, the authors discuss a few of the basic ideas of multifractals, illustrating them with simple examples. Later, they will discuss experimental evidence for multifractal behavior, especially multifractal fracture. Mixed mechanisms are actually combinations of these two ideal mechanisms, as reflected in the character of the fracture surface. Examples are cleavage facets distributed over a generally ductile fracture surface. In order to fully understand the correlation (ordering) between the energetics of various fracture mechanisms and the complicated geometries of material damage, Williford has given a quantitative description by a multifractal fracture model based on the brittle/ductile partition of fracture..
