Bifurcation analysis of elastic residually-stressed circular cylindrical tubes

Abstract The theory of superimposed incremental elastic deformations is applied to a de-formed con_guration of a residually-stressed circular cylindrical tube. The tube issubject to internal or external pressure and an axial load that maintain its circular cylindrical shape, and then bifurcations from this shape are analyzed. Detailed 1 Highlighted Revision governing equations and boundary conditions are provided for axisymmetric, pris- matic 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 reects the magnitude of the residual stress. Numerical computa-tions 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 signi_cant e_ect compared with the corresponding results without residual stress.