Inflation-Induced Twist in Geometrically Incompatible Isotropic Tubes

Abstract

The fundamental twist motion in tubes is commonly generated by torque. However, twist can also be indirectly induced by mechanical loadings (inflation/extension), growth and remodeling processes, and environmental conditions. This unusual coupling commonly originates from material anisotropy. In this study, we propose a configuration of isotropic bilayer tubes that twists upon inflation. This mechanism is based on twist incompatibility: two tubes are axially twisted in opposing directions and glued to form a bilayer tube. The residual stress that develops gives rise to deformation-induced anisotropy, which enables twist under inflation. To demonstrate the induced-twist response, we employ the neo-Hookean and the Gent models. We derive closed-form expressions for the twist angle as a function of the pressure in neo-Hookean bilayer tubes and show that a terminal angle exists in the limiting pressure. Numerical studies of bilayer Gent tubes are carried out and reveal that the lock-up effect governs the terminal twist angle. Interestingly, we find that in bilayer Gent tubes, the twist direction and handedness can be reversed upon inflation. These counter-intuitive effects, known as inversion and perversion, respectively, stem from the load-dependent variations in the ratio between the torsional stiffness of the two layers. We provide criteria that allow to program the induced twist response of bilayer tubes through the design of the properties of the two layers. This approach may be of value in the design of soft robots, artificial muscles, and soft actuators.