ABSTRACT
On the other hand, incomplete similarity, or similarity of the second kind, is governed by renormalisation groups and by scale-interaction between strength and toughness. It is in fact impossible to measure constant material properties, unless we depart from integer dimensions of material ligament at peak load and of fracture surface at final rupture. In physical reality, they may be considered as multifractals, of dimension 1.5 and 2.5, respectively, at small scales, and dimension 2.0 at large scales. This means that, at large scales, the disorder is not visible, the size of the heterogeneities being limited, whereas, at small scales, a self-similar distribution of Griffith cracks and a Brownian crack formation prevail. Keywords: Complete and incomplete similarity, dimensional analysis, disordered materials, fractals and multifractals, renormalisation group theory, scaling laws.
