Continuum Mechanics and Thermodynamics

, Volume 28, Issue 1–2, pp 157–174 | Cite as

Extension, inflation and torsion of a residually stressed circular cylindrical tube

  • José Merodio
  • Ray W. Ogden
Original Article


In this paper, we provide a new example of the solution of a finite deformation boundary-value problem for a residually stressed elastic body. Specifically, we analyse the problem of the combined extension, inflation and torsion of a circular cylindrical tube subject to radial and circumferential residual stresses and governed by a residual-stress dependent nonlinear elastic constitutive law. The problem is first of all formulated for a general elastic strain-energy function, and compact expressions in the form of integrals are obtained for the pressure, axial load and torsional moment required to maintain the given deformation. For two specific simple prototype strain-energy functions that include residual stress, the integrals are evaluated to give explicit closed-form expressions for the pressure, axial load and torsional moment. The dependence of these quantities on a measure of the radial strain is illustrated graphically for different values of the parameters (in dimensionless form) involved, in particular the tube thickness, the amount of torsion and the strength of the residual stress. The results for the two strain-energy functions are compared and also compared with results when there is no residual stress.


Residual stress Finite elasticity Elastic tube deformation 

Mathematics Subject Classification

74B20 74E10 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Continuum Mechanics and Structures, E.T.S. Ingenieros Caminos, Canales y PuertosUniversidad Politécnica de MadridMadridSpain
  2. 2.School of Mathematics and StatisticsUniversity of GlasgowGlasgowUK

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