Instability analysis in pressurized three-layered fiber-reinforced anisotropic rubber tubes in torsion

Instability analysis of the large deformation of three-layered fiber-reinforced anisotropic rubber tubes subjected to an inner pressure combined with torsion and axial stretch is examined within the framework of finite elasticity. Based on a fiber-reinforced incompressible hyper-elastic material model, the relation between the principal stretch and the inner pressure, torsion and axial stretch is obtained. It is shown that there exists a critical thickness for the tubes. For a thin-walled tube which is thinner than the critical thickness, the tube under-goes a uniform stable inflation when the inner pressure is small. However, the tube may under-go a strikingly non-uniform deformation when the inner pressure is larger than a certain critical value. One portion of the tube may become highly distended as a bubble and it is proved that this deformation is unstable. While a thick-walled tube which is thicker than the critical thickness, always under-goes a uniform inflation. The critical thickness of the tube to take unstable deformation is given based on the deformation curve and its slope. Furthermore, the effect of axial stretch, torsion and the distribution angle or the strength of the fiber on the deformation and the stress of the tube are discussed.