Theoretical study of buckling-based nonlinear transition near a static bifurcation point

We theoretically investigate the nonlinear behavior of a buckled tip near the bifurcation point under external stress. We present a mechanical model for the buckled tip and derive the governing equation that describes the "buckling-to-flipping" nonlinear transition of the tip motion. Our minimal mechanistic model fully captures the velocity-dependent flipping phenomena, in which the flip position of the tip varies with the speed of the surface motion, as consistently observed in previous experiments. The present study could be applicable for sensitive detection of directional surface motion such as seismic waves.