College
College of Engineering
Mentor Information
Sonya Tiomkin
Description
Flexible membrane wings appear throughout both natural and engineered flyers — parachutes, sails, birds, and bats — and are known to confer favorable aerodynamic characteristics through deformation in response to the surrounding flow. To date, flexibility and porosity have largely been studied in isolation, yet in a poroelastic membrane the two are coupled: as the membrane extends under load, its pores stretch with the surface. This study takes the first step toward analyzing that coupling by characterizing how the effective elasticity of the membrane depends on its porosity under uniform static pressure. Circular clamped membranes were simulated across a range of pressure loads and initial pore distributions. The resulting mid-plane deflection profiles were inverted through large-deflection membrane theory (using Hencky’s model) to recover the effective Young modulus; a procedure which was validated for the impermeable membrane for which the modulus is known. The results establish a quantitative relationship between porosity and effective elastic response, providing a model that connects membrane deformation to porosity under static uniform load.
Theoretical model for a poroelastic membrane under uniform load
Flexible membrane wings appear throughout both natural and engineered flyers — parachutes, sails, birds, and bats — and are known to confer favorable aerodynamic characteristics through deformation in response to the surrounding flow. To date, flexibility and porosity have largely been studied in isolation, yet in a poroelastic membrane the two are coupled: as the membrane extends under load, its pores stretch with the surface. This study takes the first step toward analyzing that coupling by characterizing how the effective elasticity of the membrane depends on its porosity under uniform static pressure. Circular clamped membranes were simulated across a range of pressure loads and initial pore distributions. The resulting mid-plane deflection profiles were inverted through large-deflection membrane theory (using Hencky’s model) to recover the effective Young modulus; a procedure which was validated for the impermeable membrane for which the modulus is known. The results establish a quantitative relationship between porosity and effective elastic response, providing a model that connects membrane deformation to porosity under static uniform load.
