Effects of a prestress on a reinforced, nonlinearly elastic and compressible tube subjected to combined deformations

Abstract

We consider a nonlinearly elastic and prestressed tube subjected to a combined torsion and circular and axial shearing. The hollow cylinder’s inner and outer surfaces are allowed to rotate by the torsion and the circular shear, and to displace in the longitudinal direction by the axial shear but not move radially. The analysis is carried out for a class of Blatz–Ko response augmented with unidirectional reinforcing that is characterized by a single additional constitutive parameter for strength of reinforcement. The form of solution sought leads to a system of nonlinear equations which are solved numerically. For different transverse isotropic materials, we show the effects of the prestress on the local volume change, the circumferential stretch ratio and the stress distributions.