Shooting rubber bands: dynamic buckling in unconstrained elastic ribbons
Oratis, Alexandros Thomas
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Most of us are familiar with stretching and shooting rubber bands. However, it is not immediately obvious to state which side of the rubber band will hit a predetermined target first. When a rubber band is stretched and suddenly released an axial stress wave propagates towards the end it is divides the rubber band into a stretched and relaxed area. As the wave reaches the end it reflects and causes a compression wave that propagates backwards causing dynamic buckling if the length of the compressed area is larger than the Euler critical length. If the elastic became unconstrained in a similar manner to shooting rubber bands, it is unknown whether buckling would occur and how it would affect the trajectory of the elastic. Using high speed photography we find dynamic buckling occurs when shooting rubber bands. Using a Neo-Hookean model for the rubber band we find that the wavelength is proportional to the thickness and the square root of the inverse stretch ratio. Moreover, we analyze the trajectory of the rubber band when shot by developing a model of the front and back speeds using the propagation of stress waves in rubber. We conclude that the both front and back speeds are proportional to a fraction of the speed of sound in the material based on the amount of stretching. Using the front and back speed scaling we show that our analysis is valid only for short time scales since at larger time scales the effects of the rubber band curvature and the rotation applied when launched tend to dominate.