Bifurcation analysis of elastic residually-stressed circular cylindrical tubes

The theory of superimposed incremental elastic deformations is applied to a deformed configuration of a residually-stressed circular cylindrical tube. The tube is subject to internal or external pressure and an axial load that maintain its circular cylindrical shape, and then bifurcations from this shape are analysed. Detailed governing equations and boundary conditions are provided for axisymmetric, prismatic and asymmetric bifurcations for a general form of strain–energy function that incorporates radial and circumferential residual stress components. The theory is applied to a simple model strain–energy function with two material parameters and a parameter that reflects the magnitude of the residual stress. Numerical computations are used to illustrate the dependence of the results of the bifurcation analysis on these parameters and the axial and radial underlying deformation. It is shown that in general the presence of residual stress has a significant effect compared with the corresponding results without residual stress.