Nonlinear effects in composite cylinders: relations and dependence on inhomogeneities

The extension of a cylinder subjected to torsion was investigated by Poynting (1909) and the nonlinear phenomenon has since been called the Poynting effect. Under combined axial and torsional loading, the twist is also dependent on the axial loading as shown by Wang and Wu (2014a), who named this the axial force–twist effect. This paper investigates the relations between these effects in a bilayered cylindrical composite within the framework of second-order elasticity. The results show that: (1) either effect can be positive or negative, (2) there can only be three states, e.g., under tension–torsion either both effects are negative, or both positive, or if they differ in sign the Poynting effect must be positive and the axial force–twist effect must be negative, (3) certain logical relations between the effects exist, e.g., if under tension–torsion loading the Poynting effect is negative, the axial force–twist effect must be negative, (4) there exists a reduced elastic-geometric parameter between each effect and the associated applied loading, and (5) both effects are strong functions of the elastic and geometric inhomogeneities. These findings are significant for applications in regenerative medicine such as the design of replacement tissues.