Experiments on the finite torsion of nearly incompressible rubber-like materials: Nonlinear effects, analytic modeling and rubber characterization

We present experiments and analytic modeling of different states of finite torsion of soft cylinders. The problems of free torsion and restrained torsion are investigated. In free torsion, the cylinder is twisted and left free to elongate, thus exhibiting the Poynting elongation. In restrained torsion, the elongation of the cylinder is inhibited, so a reactive axial force arises (Poynting force). The nonlinear Poynting effects, elongation and force, are observed and quantified with a specifically designed device able to simulate both cases of torsion. Punctual laser devices, digital image correlation monitoring, and load cells are used to measure the contraction of the cylinder diameter, Poynting elongation, Poynting force, and twisting moment. The experiments are performed on three rubber-like materials: a silicone rubber and two polyurethanes. Uniaxial tension and compression have been performed along with the torsion tests. The tests show that the investigated materials are nearly incompressible, allowing to model the restrained torsion tests with the theory of simple torsion of incompressible materials. The results of restrained torsion tests reveal that a universal relation established for incompressible materials independent of the second invariant of deformation is violated. Hence, the material characterization is carried out for energy laws of the form $W(I_1,I_2)$ and a compressible Mooney–Rivlin law. The experimental behavior of the universal relation indicates that the energy dependence on the second invariant of deformation decreases as the deformation increases. We show that simultaneous fitting of uniaxial and torsion tests relevantly reduces the quality of the best-fit procedure. The present work points out the importance of the compressibility of the material for an accurate prediction of the Poynting elongation, which is not grasped well by the incompressible laws.