Closed form solutions for large deformation of cylinders under combined extension-torsion

Abstract

In this paper, the mechanical response of an incompressible isotropic nonlinear elastic solid circular cylinder is investigated under combined extension and torsion. Since the deformation tensor in extension-torsion is non-diagonal, implementing stretch based energy functions are complex. Hence, in this study, an analytical solution is proposed for both invariant- and stretch-based models. Moreover, finite element analysis of extension-torsion of hyperelastic materials is carried out using both UHYPER and VUMAT user-defined subroutine in ABAQUS to verify the presented analytical methods. Both stretch and invariant-based exponential forms of strain energy function are employed, and its corresponded material parameters are calibrated for silicon-rubber. The finite element results for stress distribution show a good agreement with analytical findings which confirms the validity and accuracy of the proposed method. Results show that the both invariant- and stretch-based exp-exp models are less conservative for a relatively small stretch and twist while for large stretches they yield higher stresses than the other models and the rate of stress variation increases significantly, especially for a stretch-based exp-exp model. For both Invariant- and stretch-based exp-exp models, an alteration axial stretch is identified where the torsion induced axial force alters from tensile to compressive. For stretches smaller than this alteration point, the cylinder always elongates while for the larger stretches, the cylinder tends to shorten for small twists and then elongates on further twisting. Also, as the axial stretch increases the alteration point appears in larger twists.