Failure stress of a disordered three-dimensional spring network

This paper concentrates on the failure stress of a disordered three-dimensional spring network. In particular, we investigate the effects of several fracture criteria and of the connectivity at the nodes in the network. A node 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 network configuration with the lowest energy was calculated after each increment of force. Subsequently, the mechanical properties of the relaxed network structures were investigated using various fracture criteria. The largest threshold value of displacement was set to the commonly used criterion for 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 fracture criteria the stress calculations were repeated with different connectivity thresholds. From this investigation it is concluded that it is not sufficient to examine only the fracture strain. In particular, the connectivity, i.e., the connectivity threshold C-0, which controls the spring entanglement between the nodes, has a substantial effect on the crack morphology. Larger C-0's result in smaller fragments caused by crack branching.