Analytic insights on isotropic energy forms based on experiments of finite torsion

In finite torsion of cylinder a huge number of non-linear complex effects occur: contraction of the radius, elongation of the cylinder, arising of axial force, and the onset of instability are fascinating effects induced by the fully non-linear context. However, there is no trace in the literature of an exhaustive and complete work which fully investigates each case of torsion from a theoretical and experimental standpoint. Different cases of torsion are accounted for in the framework of non-linear elasticity: free torsion and restrained torsion. For these cases of torsion, experiments are very rare in the literature for soft materials as they require extremely sophisticated devices for the measurement of displacement fields and forces. Moreover, the case of pure torsion, which leads to a fundamental universal relation of solid mechanics, was never investigated in terms of the reliability of its fundamental assumptions. We present a new set of experiments on the free torsion and restrained torsion of polyurethanes and silicon rubbers. Along with the torsion tests, uniaxial tests of the rubber are presented. Based on the experiments and universal relation of pure torsion, we experimentally proof the relevance of the second invariant of deformation. We point out that the relevance of the second deformation invariant decreases as the deformation increases. Characterization of the materials, by means of the best fit procedure of the experiments, shows how much the simultaneous fitting of multiple states of stress can reduce the quality of the fitting. Among the energy forms here considered, both incompressible and compressible, we show that only the compressible energy law can grasp the experimental Poynting elongation of the rubbers. In addition to the above, we propose a new formulation in non-linear elasticity to predict the onset of instability in the case of restrained torsion.