Finite torsion of transversely isotropic compressible hyperelastic circular cylinders

Abstract

The paper develops an analytical formulation able to study the finite torsion problem for circular cylinders made of transversely isotropic compressible material. To this end, a three-dimensional displacement field is introduced a priori to take into account the large twisting of a cylindrical body, including both a variation of length in the longitudinal direction and a radial constant contraction. A transversely isotropic hyperelastic material is obtained by combining the stored energy function that characterizes the Mooney–Rivlin model for compressible and isotropic constituents with the standard reinforcing model as far as the anisotropic part is concerned. The nonlinear analyses are carried out analytically in both Lagrangian and Eulerian frameworks aiming at the evaluation of the corresponding stress components, which are respectively included in the Piola–Kirchhoff and Cauchy tensors, once the kinematic unknowns are computed. The problems of free torsion and restrained torsion are considered to investigate the mechanical behavior of the hyperelastic bodies in terms of twisting moment and axial response (force or longitudinal displacement, depending on the boundary conditions). Finally, the influence of the transverse isotropy on the stresses is discussed.