Study of the Correlations between Different Effective Fractal Dimensions Used for Fracture Parameters Descriptions

The analysis of the effective fractal dimensions corresponding to the fracture parameters points out the existence of at least: a) 8 different effective mechanical fractal dimensions, b) 8 diferent effective topographical fractal dimensions, as well as of: c) 4 different effective lacunarity measures L, corresponding to the mass-radius method and to the methods described by the works. The accomplished study pointed out the existence of a unique deterministic relation between such effective fractal dimensions, the relation: w G D D D + = σ connecting the fractal dimensions corresponding to the fracture energy G, to the stress σ and to the stress-crack opening displacement w, respectively. It was found also the presence of some correlations of medium intensity between the topographical fractal dimensions, as well as of the ordering: power spectral islands lakes counting box divider D D D D D < < < < − . Some similar ordering relations have been obtained for certain effective lacunarities. The accomplished work points out the necessity of some detailed theoretical and of numerical analysis studies of the correlations between the different effective fractal dimensions in order to improve the accuracy of the fractal descriptions of the physical parameters and of the fracture parameters, particularly.