Inversion and perversion in twist incompatible isotropic tubes

Abstract Tubular and rod-like structures in nature can experience twist due to non-torque loadings such as inflation and extension. Interestingly, the twist can change its direction and even vanish along the loading path. These counter-intuitive phenomena are referred to as inversion and perversion, respectively, and stem from the anisotropic structure of the tubes. In this work we show that a similar response can be achieved with bi-layer tubes comprising two isotropic layers that are twisted in different directions and adhered together. We refer to these tubes as geometrically incompatible. By employing the Gent model, we find that the inversion and perversion effects stem from the changes in the torsional stiffness of the layers as a result of inflation or extension. We derive relations for the torsional stiffness in terms of the geometry, the stiffness, the lock-up stretch which accounts for the strain-stiffening effect, and the deformation. We illustrate that different thickness and stiffness ratios between the layers lead to a variety of induced twist responses. To better understand the influence of the geometric and the material properties of the layers on the overall twist response, we map the combinations of thickness and stiffness ratios that lead to inversion and perversion and demonstrate the richness of these phenomena. The findings and insights from this work are of value to a wide range of applications, including the design of soft rotational robots, artificial muscles, and soft torsional actuators.