Coupled poro-elastic behavior of hyper-elastic membranes

Abstract: This study investigates the coupled deformation and flow behavior through thin, hyper-elastic, porous membranes subjected to pressure loading. Using bulge test experiments, optical deformation measurements, and flow rate characterization, we analyze the structural and fluid dynamic responses of membranes with varying material stiffness and porosity patterns. A two-parameter Gent model captures the hyper-elastic deformation, while local stretch analyses reveal the evolution of pore sizes across the membrane. We find that membrane stretch is primarily governed by material stiffness and applied pressure, independent of porosity. A gradient of increasing pore size toward the membrane center emerges due to higher local stretch, while the total open pore area remains approximately constant across radial layers of the membrane. Flow rate scaling is characterized using a discharge coefficient that accounts for pore area expansion and pressure losses. While the initial scaling compares well in most cases, it breaks down for scenarios with significantly different pore Reynolds numbers, driven by large variations in initial porosity. To address this, we introduce a Reynolds-dependent correction term that unifies discharge coefficient predictions across diverse porosity and flow velocity conditions. These findings enhance the understanding of poro-elastic systems and provide robust scaling relationships for designing thin, flexible, porous structures in applications such as bio-inspired aerodynamic systems and adaptive flow regulation devices.