Dynamic inflation of hyperelastic spherical membranes

Abstract

International audienceThe dynamic inflation of hyperelastic spherical membranes of a Mooney–Rivlin material is analyzed in this study. Various inflation regimes are identified through ranges of the material parameters and driving pressure. In particular, the conditions for oscillatory inflation around the static fixed point are examined. It is found that, for a given material, the frequency of oscillation exhibits a maximum at some pressure level, which tends to increase for materials closer to neo-Hookean behavior

Dynamic inflation of non-linear elastic and viscoelastic rubber-like membranes

“…The resolution of the corresponding semi-analytical problem is detailed in Reference [22]. Consider a spherical hyperelastic membrane.…”

Nonlinear Forced Vibration Analysis of Dielectric-Elastomer Based Micro-Beam with Considering Yeoh Hyper-Elastic Model

“…Also they illustrated dependency of frequency on the deformation, stress and aspect ratio. Verron et al (1999) studied dynamic inflation of hyper-elastic spherical membranes with Mooney-Rivlin material. In addition, they examined the conditions for oscillatory inflation around the static fixed point and found that the frequency of oscillation reaches a maximum at some pressure level, which tends to increase for materials with Neo-Hookean material.…”

Some qualitative properties of incompressible hyperelastic spherical membranes under dynamic loads

“…For spherical structures, the problems of radial oscillation of spherical shells composed of incompressible hyperelastic materials were examined [3][4][5][6] , and the formulas that describe the period and the amplitude of periodic oscillation were proposed. The dynamic behaviors of incompressible hyperelastic membranes composed of isotropic MooneyRivlin materials were studied [7] . The dynamic cavitation problems were studied for solid spheres composed of several classes of incompressible hyperelastic materials in the context of nonlinear elastodynamics [8][9][10] , in which the authors proved that a cavity would form in the interior of the sphere as the tensile dead load exceeds a critical value and that the motion of the formed cavity would present a nonlinear periodic oscillation.…”