On fractals and size effects

Following an extensive and critical review of fractals and size effects models, this paper seeks to generalize Baˇzant’s size effect law to fractal cohesive cracks. This is achieved through a Newtonian approach in which the cohesive and far field stress intensity factors of fractal cracks (derived by Yavari) are set equal. It will be shown that the fractal size effect law is a generalization of the one of Baˇzant (derived in Euclidian space). In light of the derived equation, the multi-fractal model of Carpinteri and the size effect law of Baˇzant are revisited. Finally, the paper will conclude with some general considerations pertaining to the so-called “New Kind of Science” developed by Wolfram, and its applicability to fracture mechanics.