Soliton instability and fold formation in laterally compressed few-layer graphene

We investigate -- through simulations and analytical calculations -- the consequences of uniaxial lateral compression applied to the upper layer of few-layer graphene. The simulations of compressed graphene show that strains larger than 2.8 \% induce soliton-like deformations that further develop into large, mobile folds. Such folds were indeed experimentally observed in graphene and other solid lubricants two-dimensional materials. Interestingly, in the soliton-fold regime the shear stress decreases with the strain s, initially as $s^{-2/3}$ and rapidly going to zero. Such instability is consistent with the recently observed negative dynamic compressibility of two-dimensional materials. We also predict that the curvatures of the soliton-folds are given by $r_c = \delta\sqrt{\beta/2\alpha},$ where $1\le \delta \le2,$ and $\beta$ and $\alpha$ are respectively related to the layer bending modulus and to the exfoliation energy of the material. This finding might allow experimental estimates of the $\beta/\alpha$ ratio of two-dimensional materials from fold morphology.