Swelling-driven soft elastic catapults

The paper outlines and analyzes the conditions for optimizing a catapult mechanism that emerges in a soft rod, initially completely adhered to a rigid lubricated substrate, as a result of oil absorption. Oil diffusion causes differential swelling across the rod thickness, inducing rod bending that is counteracted by adhesion to the substrate. The effect culminates in a gradual detachment of the rod from the substrate, followed by a rapid shooting phase when one end detaches. To elucidate this intricate phenomenon, we employ a modified Euler elastica model that incorporates two additional parameters: the spontaneous stretching lambda, that quantifies the relative elongation of the material with respect to its dry, unstressed configuration, and the spontaneous curvature, c(0), that captures the rod tendency to deflect due to diffusion-induced non-uniform stretching through the thickness. The interrelated parameters lambda and c(0), which evolve over time as they are influenced by the diffusion process are then calculated numerically with a FEM code that combines the finite elasticity model with the Flory-Rehner diffusion model. Finally, we present a comprehensive optimization study of the catapult based on its geometric and material properties, providing insights for the design and control of this novel mechanism.