Buckling-Fracture Transition and the Geometrical Charge of a Crack

We present a unifying approach that describes both surface bending and fracture in the same geometrical framework. An immediate outcome of this view is a prediction for a new mechanical transition: the buckling-fracture transition. Using responsive gel strips that are subjected to nonuniform osmotic stress, we show the existence of the transition: Thin plates do not fracture. Instead, they release energy via buckling, even at strains that can be orders of magnitude larger than the Griffith fracture criterion. The analysis of the system reveals the dependence of the transition on system's parameters and agrees well with experimental results. Finally, we suggest a new description of a mode I crack as a line distribution of Gaussian curvature. It is thus exchangeable with extrinsic generation of curvature via buckling. The work opens the way for the study of mechanical problems within a single nonlinear framework. It suggests that fracture driven by internal stresses can be completely avoided by a proper geometrical design.