On the possibly multifractal properties of dissipated energy in brittle materials

The paper reports an analytical study on the properties of fracture networks in brittle materials. Micro-deformation gradients are considered random fields and/or scaling fields. Under dynamic crack propagation conditions the possibly fractal properties of the (macro) crack pattern are governed by the interplay of fluctuations and spatial correlations. For "slow" crack propagation they are governed by the kinematic fields in the vicinity of crack or notch tips. The spatial distribution of dissipated energy, due to fracture, is evaluated. It is shown that there is a strong possibility that the dissipated energy is multifractal. Here, its properties are characterized in a fashion similar to the so-called p-model where p herein denotes normalized dissipated energy. For the three cases analyzed - uniaxial tension, pure shear, and dilatation - the dissipated energy under pure shear shows the strongest disorder, the one under dilatation the weakest, and the tension case is always between these two.