Poynting and axial force–twist effects in nonlinear elastic mono- and bi-layered cylinders: Torsion, axial and combined loadings

The Poynting effect, in which a cylinder elongates or contracts axially under torsion, is an important nonlinear phenomenon in soft materials. In this paper, analytical solutions are obtained for homogeneous and bi-layered cylinders under torsion, axial and combined loadings, employing second-order elasticity and Lagrangian equilibrium equations. Explicit parameters for judging the sign of the Poynting effect are given. It is found that the effect in a soft composite may be significantly amplified over that in homogeneous materials and that it is strongly influenced by the interface position and by the material configuration in the composite. A coupled axial force–twist effect under combined loading, i.e., the twist of a torsionally loaded cylinder can be affected by the axial loading, is also found. Comparison of the predictions with the torque-tension-twist data for cardiac papillary muscles shows reasonable agreement. The solutions also provide the basis for a mechanistic method of determining third-order elastic constants.