New mathematical models pertinent to material fracture at meso- and nanoscales

In the limit of vanishing fracture quantum and/or reduced degree of fractality the quantized cohesive model of a fractal crack, as presented here, reduces to the well-known classic models of Dugdale-Barenblatt or to the linear elastic fracture mechanics or the quantized fracture mechanics theories. Therefore, the basic concepts of linear elastic fracture mechanics, quantized fracture mechanics and fractal geometry are all incorporated into the present theory.