Abstract：Seals play an important role in modern engineering applications, especially in the oil and gas industry. Compression of a rubber tube where the outer boundary is confined is an important procedure when sealing a packer. Instability leading to a buckling profile may cause the seal to fail. Generally speaking, the rubber tube (or packer) undergoes a relatively large deformation during the whole sealing procedure. In this paper, we study the bifurcations of a hyper-elastic tube with confined outer boundary in the framework of the exact theory of nonlinear elasticity. Due to the restriction, the initial deformed state is no longer homogeneous, the basic state of which is first characterized by solving the equilibrium equation. Then the incremental governing equations and boundary conditions are established for an axial mode and a linear bifurcation analysis is carried out. The bifurcation condition is numerically solved using the determinant method. Then the bifurcation curves are obtained when the geometric parameters are specified. It is found that the critical axial mode number is always finite. In addition, the relation between the critical bifurcation stretch (or stress) and wall thickness of the tube is obtained, from which it is found that a thin-walled tube is more stable compared with a thick-walled one. According to the relation between the axial stretch and stretch on the inner surface, our results may provide insight into designing the gap between the base pipe and the oil pipe in order to avoid instability. On the other hand, we provide the formulae of contact stress in terms of the applied axial stress for both boundaries when a seal is finished, which correct an existing result in literature and also validate the accuracy of results based on the theory of linear elasticity. Finally, the stability analysis for a packer designed by the CNOOC EnerTech-Drilling & Production Company is conducted and the lowest stress to achieve a full seal is given.
2018, Vol. 39 
