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

摘要: Novel properties of the present cohesive crack models provide a better insight and an effective tool to explain multiscale nature fracture process associated transitions from macro- meso- nanolevels material response deformation fracture. These features any real appear be inherent defense mechanisms provided by nature. New parameters introduced into theory described here are: quantum a0 dimension D fractal used represent surface, or equivalently — exponent α = (2−D)/2, where varies between 1 (smooth crack) 2 (very rough crack). As degree fractality increases, characteristic length is shown rapidly grow levels around three orders magnitude higher than those predicted for classic case. Such effect helpful in explaining unusual size-sensitivity testing materials with cementitious bonding such as concrete certain types ceramics, cracks are commonly observed. It turns out that while effects due quantization model tend disappear longer cracks, influence geometry remains significant, even becomes more pronounced long cracks. In limit vanishing and/or reduced quantized crack, presented here, reduces well-known Dugdale-Barenblatt linear elastic mechanics theories. Therefore, basic concepts mechanics, all incorporated theory.