Self-similarity in concrete fracture: size-scale effects and transition between different collapse mechanisms

Abstract

Since the pioneering paper by Mandelbrot (Nature, 308:721-722, 1984) on the fractal character of the fracture surfaces in metals, the fractal aspects in the deformation and failure of materials have been investigated by several Researchers (see the reviews by Bouchaud (J Phys Condens Matter, 9:4319-4344) and Carpinteri et al. (Appl Mech Rev, 59:283-305, 2006)) and the attempts to apply fractals to fracture have grown exponentially. Aim of this paper is 2-fold: on one hand, it summarizes in a detailed yet concise fashion the major results of the fractal approach to the scaling of mechanical properties in solid mechanics; on the other hand, it reports some recent results concerning the size effect in the failure of reinforced concrete (RC) beams. These recent findings clearly show that the picture of the size-scale effects is much more complex when interaction among different collapse mechanisms occurs. The consequences on the size-scale effects are discussed in detail.

Determination of Young’s modulus, fracture energy and tensile strength of refractories by inverse estimation of a wedge splitting procedure

“…It is commonly recognized that the nominal tensile strength increases with decreasing structural size in the quasi-brittle materials especially in the presence of notches or cracks [36][37][38]. Several general laws comprising the structural sizes and characteristic length (or brittleness number) were developed to describe the size effect on the nominal tensile strength in the last decades [39][40][41][42]. Especially, a formula of the ratio NT/ ft dependent of the brittleness number was given in the case of wedge splitting test according to Tschegg, and this ratio decreased with increasing brittleness number [26].…”

A review on experimental research using scale models for buildings: Application and methodologies

“…Fractal geometry is already proven to play a role in geometrical scale change [45,46,72]. However, this field is nowadays relatively useful for architects because of its deep mathematical content.…”