Volume-constrained deformation of a thin sheet as a route to harvest elastic energy

Thin sheets exhibit rich morphological structures when subjected to external constraints. These structures store elastic energy that can be released on demand when one of the constraints is suddenly removed. Therefore, when adequately controlled, shape changes in thin bodies can be utilized to harvest elastic energy. In this paper, we propose a mechanical setup that converts the deformation of the thin body into a hydrodynamic pressure that potentially can induce a flow. We consider a closed chamber that is filled with an incompressible fluid and is partitioned symmetrically by a long and thin sheet. Then, we allow the fluid to exchange freely between the two parts of the chamber, such that its total volume is conserved. We characterize the slow, quasistatic, evolution of the sheet under this exchange of fluid, and derive an analytical model that predicts the subsequent pressure drop in the chamber. We show that this evolution is governed by two different branches of solutions. In the limit of a small lateral confinement we obtain approximated solutions for the two branches and characterize the transition between them. Notably, the transition occurs when the pressure drop in the chamber is maximized. Furthermore, we solve our model numerically and show that this maximum pressure behaves nonmonotonically as a function of the lateral compression.