A note on finite elastic deformations of fiber-reinforced non-linearly elastic tubes

Abstract

A fibre-reinforced non-linearly elastic tube subject to a finite radially symmetric deformation given by the combination of axial stretch, radial deformation and torsion is analysed. The deformation is supported by axial load, internal pressure and end moment. The materials at hand are neo-Hookean models augmented with a function that accounts for the existence of a unidirectional reinforcement. This function endows the material with its anisotropic character and is referred to as a reinforcing model. The nature of the considered anisotropy has a particular influence on the shear response of the material, in contrast to previous analyses in which the reinforcing model was taken to depend only on the stretch in the fibre direction. Furthermore, the ellipticity analysis of the deformations at hand has been carried out. It is shown that most of the deformations are non-elliptic, which opens the possibility to discontinuous solutions.