Deformation analysis of an incompressible composite cylindrical tube subjected to end axial loads and internal constraint

In this paper, the problem of axially symmetric deformation is examined for a composite cylindrical tube under equal axial loads acting on its two ends, where the tube is composed of two different incompressible neo-Hookean materials. Significantly, the implicit analytical solutions describing the deformation of the tube are proposed. Numerical simulations are given to further illustrate the qualitative properties of the solutions and some meaningful conclusions are obtained. In the tension case, with the increasing axial loads or with the decreasing ratio of shear moduli of the outer and the inner materials, it is proved that the tube will shrink more along the radial direction and will extend more along the axial direction. Under either tension or compression, the deformation along the axial direction is obvious near the two ends of the tube, while in the rest, the change is relatively small. Similarly, for a large domain of the middle part, the axial elongation is almost constant; however, the variation is very fast near the two ends. In addition, the absolute value of the axial displacement increases gradually from the central cross-section of the tube and achieves the maximum at the two endpoints.