Fracturing of marginally stable structures: fiber networks and topological metamaterials*

We present simulation results on fracture mechanics of two lattice models on the verge of mechanical instability. For both models, we show that the fracture and failure mechanism is distinctive from traditional brittle solids: stress does not concentrate on crack tips. In the first model which is a randomly diluted triangular lattice under isostaticity, we observed that nonlinear alignments of fiber chains lead to a steady state in which new load-bearing fiber chains emerge to replace those lost to fracture. We show that the stress concentration is dissipated and eventually prevented when the rigidity of the model decreases to zero. In the second model which is a kagome lattice with topologically protected states of self stress on devised domain walls, we show that stress concentrates on domain walls instead of cracks, leading to delayed catastrophic failure. Suitable boundary conditions for experiments will also be discussed.