Narrow Results

In this paper, we introduce the concept of intrinsic strength which is used to describe the node's intrinsic property. Furthermore, we present a single preferential attachment model for the evolution of weighted networks in which the network growth is coupled with dynamical evolution of weights and intrinsic strength. The model yields a nontrivial time evolution of nodes' properties and generalized power law distributions for the weight, strength and degree, as confirmed in many real networks. The numerical simulation results are in good agreement with the analytical expressions.

Using molecular mechanics (MM) simulations, the failure stress of bicrystalline graphene with different tilt angles is investigated using their free-standing indentation behaviour, in which two types of grain boundaries, including armchair (ac) and zigzag (zz) grain boundaries, and two types of indenter tip, including cylindrical and spherical tips are considered. For reference purposes, the corresponding results under inplane stretching are also examined. It is found that the failure stress of grain boundary (GB) in bicrystalline graphene decreases with the decrease of the GB tilt angle $\theta$, which is similar to that determined in inplane stretching. In indentation, the stress concentration under the indenter tip will decrease the failure stress of graphene; in addition, the out-of-plane deformation of graphene in indentation can partially release the pretension induced by the GB in bicrystalline graphene. For the GB with a small prestress, the effect of the former is larger than that of the latter; but for the GB with a larger prestress, the effect of the latter is larger than that of the former. Consequently, the effect of tilt angle $\theta$ on the GB strength of bicrystalline graphene is lower in indentation than that given by inplane stretching.