Mechanical behaviour of short membranous liquid-filled cylinders under axial loadings

Abstract The mechanical behaviour of membranous liquid-filled cylinders is important in many industrial and biomedical applications, such as in modelling the incudostapedial joint in the middle ear. Although membranous liquid-filled containers with various geometries have been investigated under different loading conditions, no study on the mechanical behaviour of membranous circular tubes under tension-compression testing has been published. In this work, we use the theory of large deformations of elastic membranes to develop an analytical model for a liquid-filled circular tube under an axial load, neglecting the effect of gravity. We use the Mooney–Rivlin strain-energy function and numerically calculate solutions for short to moderate tube lengths. A finite-element model of the tube is also developed and the simulation results are compared with the solution from the analytical model. The finite-element model is then used for the case of a tube with an elliptical cross-section. We observe a nonlinear behaviour in the force-displacement curve of the tubes when close to the zero-force configuration. Furthermore, the tube can go through instabilities when the force changes sign. The unstable region grows if some liquid is removed from the membranous container, causing the straight walls to become convex, and also if the tube length is increased. The tube becomes stiffer and the nonlinear behaviour becomes less significant when the tube cross-section is changed from circular to elliptical. The results may provide insight into experimental observations of the mechanical behaviour of the incudostapedial joint.