The phenomenon of the size-dependence of concrete tensile strength fracture energy is discussed. The scaling of the nominal quantities can be consistently interpreted by means of a multifractal model, the influence microstructural disorder being predominant at the smallest scales. At…
The phenomenon of the size-dependence of concrete tensile strength fracture energy is discussed. The scaling of the nominal quantities can be consistently interpreted by means of a multifractal model, the influence microstructural disorder being predominant at the smallest scales. At the larger scales, the fields homogeneization comes into play, allowing for mean-field definition of asymptotic properties. Two Multifractal Scaling Laws (MFSL) are proposed, respectively for tensile strength and fracture energy. By means of best-fitting of the experimental data, the full range the scaling is described and the asymptotic values of au and Qp, valid real-sized structures, can be determined. 1 Theoretical and experimental evidence of multifractality phenomenon of fracture Criticality is very evident in the phenomenon of fracture of disordered materials: at the critical point a transition occurs in the evolutive behavior of microcracks. Whilst, before the critical strain fw virtually no microcrack can propagate to the structural scale, thus resulting macroscopic integrity of the body, beyond Eu the correlation length of the 1773 increases tending to infinite and microcracks suddenly coalesce, yielding the catastrophic fracture of the body. the basis of this evidence, the mechanical quantities involved in the ..., ................. v.11..11..11. ..... ·JLJLVJLJL, respectively the fracture energy gF and the tensile strength can be treated as critical parameters. Hence, in the asymptotic limit of critical point, they behave as self-similar functions of the independent variables. As it has been widely demonstrated, self-similarity appears to be fundamental character of critical phenomena, either from the Physics or Topology point of view (Wilson, 1971).