Coupled poro-elastic behavior of hyper-elastic membranes

TL;DR

The paper addresses the coupled deformation and flow in thin poro-elastic membranes under pressure. It combines bulge tests, optical local-stretch measurements, and pore-size tracking to derive scaling laws, showing that porosity minimally affects deformation while a two-parameter Gent constitutive law captures the nonlinear biaxial response. Local stretch drives nonuniform pore growth, with pore diameter scaling linearly with local stretch and a membrane-average diameter ratio that scales with deformation. Flow behavior is linked to a discharge coefficient Cd, which encapsulates evolving pore geometry and inertial–viscous effects, enabling a unified, predictive framework for the design of adaptive, bio-inspired porous 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.

Figures (9)

• Figure 1: Porosity definition for the radial six-spoke pattern and examples of patterns with 1, 3, 5, and 9 layers of pores leading to initial solidities of $\epsilon_0 = 0.9987, 0.985, 0.962$, and $0.886$. A radial three-spoke pattern is used for the $m = 1$ layer porosity membranes and six-spoke patterns for membranes with $m = 3, 5$ and $9$ layers.
• Figure 2: (a) Top view on the experimental apparatus showing expanding pores for a five-layer pore pattern. (b) Bulge test stand with direct measurements of pressure difference $\Delta p$, flow rate $Q$, and sample height $w_0$. Machine vision cameras in stereo configuration track the shape and local stretch of the samples.
• Figure 3: (a) Dimensions of the expanding membrane and the relation between the internal and external pressure with the membrane tension, (b) Schematic of expanding pores for a five-layer porosity pattern.
• Figure 4: (a) Normalized membrane center-line deformation $w_0 / D$ as a function of the pressure difference $\Delta p$ acting on the membrane, (b) Normalized membrane center-line deformation as a function of the Cauchy number $\hat{\textit{Ca}\xspace}$ based on linear membrane theory, (c) Normalized membrane center-line deformation as a function of the Cauchy number Ca from the Gent model, and (d) Average membrane stretch $\bar{\lambda}$ as a function of average membrane stress $\bar{\sigma}$, shown for different solidities $\epsilon_0$ and materials $G$.
• Figure 5: Local stretch $\lambda_{i,j}$ definition for each radial position of pores.