Buckling of residually stressed cylindrical tubes under compression

• Published in: International journal of solids and structures Vol. 321; p. 113578
• Main Authors: Zhang, Tao, Dorfmann, Luis, Liu, Yang
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2025
• Subjects: Bifurcation analysis; Buckling of tubes; Nonlinear elasticity; Residual stress; Stroh formalism; Nonlinear elasticity; Buckling of tubes; Bifurcation analysis; Residual stress; Stroh formalism
• ISSN: 0020-7683; 1879-2146
• DOI: 10.1016/j.ijsolstr.2025.113578

We evaluate the loss of stability of axially compressed, slender and thick-walled tubes subject to a residual stress distribution. The nonlinear theory of elasticity, when used to analyze the underlying deformation, shows that the residual stress induces preferred directions in the reference configuration. The incremental theory, given in Stroh form, is used to derive an exact bifurcation condition. The critical stretch and the associated critical buckling mode are identified for axisymmetric and asymmetric increments in the deformation. Mode transitions are illustrated as the tube slenderness varies. For slender tubes, Euler buckling is energetically favorable, and the effect of residual stress is negligible. However, for short and thick-walled tubes where barreling mode is dominant, the residual stress significantly affects the buckling behavior and may eliminate barreling instability. We show that, depending on its magnitude and direction, residual stress can either accelerate or delay instability. Phase diagrams for various modes are obtained and provide insight into pattern selection across different tube geometries. •The buckling instability of axially compressed tubes with residual stress is investigated.•Exact bifurcation condition is derived using the Stroh formalism and the surface impedance matrix method.•The influence of residual stress on the onset of instability is analyzed in detail.•Phase diagrams are presented to illustrate mode transitions as the tube geometry varies.