Coupled poro-elastic behavior of hyper-elastic membranes

Abstract

This study investigates the coupled deformation and flow behavior of 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 accurately captures the hyper-elastic deformation, and local stretch analysis reveals non-uniform stretch distributions across the membrane. We find that membrane deformation is primarily governed by material stiffness and pressure, independent of porosity. Pore diameter scales linearly with local stretch, leading to a radial gradient of increasing pore size toward the membrane center. Flow rate scaling is characterized using a discharge coefficient, which accounts for both pore area expansion and pressure losses. Together, these results establish a unified framework that links structural deformation and flow performance in flexible porous membranes, providing robust scaling laws for the design of adaptive, bio-inspired flow-regulating systems.