Are crumpled sheets marginally stable?

Recently, elastically coupled bistable elements were proposed as a model for the mechanics of crumpled sheets. We study a disordered network of bistable springs and demonstrate that this model displays features associated with marginality and criticality under quasistatic drive. The bistable potential has two basins of attraction, with a short and long state, separated by an “unstable” regime where the second derivative of the energy is negative. Interestingly, a small fraction of the bonds are in the unstable regime. We show that these unstable bonds have interesting properties and play a pivotal role in initiating instabilities. We characterize the response at the single bond level and show that the distance to instability has a quasi-gap. That is, the distribution of distances to an instability is power-law, such that bonds can be arbitrarily close to undergoing an instability. Furthermore, the local effective stiffnesses are also power-law distributed, implying that the local susceptibility to a deformation has diverging moments. We also measure the distribution of avalanches and find that they grow sub-extensively with the system size. Our work provides insight into the occurrence of marginality and could have relevance to glasses and packings.