Abstract
Residual stresses in an unloaded configuration of an elastic material have a significant influence on the response of the material from that configuration, but the effect of residual stress on the stability of the material, whether loaded or unloaded, has only been addressed to a limited extent. In this paper we consider the level of residual stress that can be supported in a thick-walled circular cylindrical tube of non-linearly elastic material without loss of stability when subjected to fixed axial stretch and either internal or external pressure. In particular, we consider the tube to have radial and circumferential residual stresses, with a simple form of elastic constitutive law that accommodates the residual stress, and incremental deformations restricted to the cross section of the tube. Results are described for a tube subject to a level of (internal or external) pressure characterized by the internal azimuthal stretch. Subject to restrictions imposed by the strong ellipticity condition, the emergence of bifurcated solutions is detailed for their dependence on the level of residual stress and mode number.
Highlights
Residual stresses have a significant effect on the mechanical behaviour of materials in which they are supported, as has been reported in a number of recent works, for example Merodio et al [1] and Merodio and Ogden [2] where the influence of the response of circular cylindrical tubes subject to residual stress under various loading conditions was analysed
In biological tissues residual stresses are developed during growth and remodelling and have an important influence on the mechanical response of the tissue in normal physiological conditions
In the present paper we examine the effect of axial load, internal and external pressure and residual stress on the stability of a circular cylindrical tube of incompressible elastic material based on the linear theory of elastic increments superimposed on the circular cylindrical configuration, with attention restricted to increments confined to the radial–circumferential plane
Summary
Residual stresses have a significant effect on the mechanical behaviour of materials in which they are supported, as has been reported in a number of recent works, for example Merodio et al [1] and Merodio and Ogden [2] where the influence of the response of circular cylindrical tubes subject to residual stress under various loading conditions was analysed. Residual stresses can have damaging consequences when generated in components during the manufacturing process, for example. In biological tissues residual stresses are developed during growth and remodelling and have an important influence on the mechanical response of the tissue in normal (or abnormal) physiological conditions. Understanding the influence of residual stresses from a theoretical point of view has important practical consequences
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