Failure stress of a disordered three-dimensional spring network - art. no.064202

This paper concentrates on the failure stress of a disordered three-dimensi onal spring network. In particular, we investigate the effects of several f racture criteria and of the connectivity at the nodes in the network. A nod e cannot be connected with another node if its relative distance is larger than a certain cutoff radius or a so-called connectivity threshold. In our modeling approach, the spring networks were loaded in compression and the n etwork configuration with the lowest energy was calculated after each incre ment of force. Subsequently, the mechanical properties of the relaxed netwo rk structures were investigated using various fracture criteria. The larges t threshold value of displacement was set to the commonly used criterion fo r brittle fracture, i.e., a fraction criterion of 1%, but also lower values (0.75%, 0.50%, and 0.25%) were examined. In addition, for each of these fr acture criteria the stress calculations were repeated with different connec tivity thresholds. From this investigation it is concluded that it is not s ufficient to examine only the fracture strain. In particular, the connectiv ity, i.e., the connectivity threshold C-0, which controls the spring entang lement between the nodes, has a substantial effect on the crack morphology. Larger C-0's result in smaller fragments caused by crack branching.