Rubber band recoil

When an initially stretched rubber band is suddenly released at one end, an axial-stress front propagating at the celerity of sound separates a free and a stretched domain of the elastic material. As soon as it reaches the clamped end, the front rebounds and a compression front propagates backward. When the length of the compressed area exceeds Euler critical length, a dynamic buckling instability develops. The rebound is analysed using Saint-Venant's theory of impacts and we use a dynamical extension of the Euler-Bernoulli beam equation to obtain a relation between the buckled wavelength, the initial stretching and the rubber band thickness. The influence of an external fluid medium is also considered: owing to added mass and viscosity, the instability growth rate decreases. With a high viscosity, the axial-stress front spreads owing to viscous frictional forces during the release phase. As a result, the selected wavelength increases significantly.