Deformation of perforated elastic sheets due to the hydrodynamic loading by a viscous fluid

From spider webs and insect wings, to wire fences and parachutes, Nature and technology present vast examples of porous and perforated flexible structures that deform due to fluid flow. Whereas fluid flow through porous media has been studied extensively, the fluid-structure interactions of a perforated, slender elastic object undergoing large deformations due to the hydrodynamic loading of a surrounding viscous fluid has received much less attention. Here, we use precision desktop experiments to focus on the prototypical problem of a perforated elastic plate moving through a viscous fluid, at low to moderate Reynolds number: 0.1 ≤ Re ≤ 10. We seek to provide a predictive framework for the deformation of perforated plates due to hydrodynamic loading so as to rationalize our experimental findings. For this purpose, we use a reduced theoretical model based on Kirchhoff-Euler beam theory coupled with a description of the fluid loading, at low Reynolds numbers. We quantify the effect of the interplay between elasticity, permeability, and fluid loading on the deformed shape of the structure. We hope that our findings may lead to a better understanding of fluid-structure interactions between porous slender structures and viscous flows, across biological and technological applications.