Journal of Elasticity

, Volume 105, Issue 1–2, pp 313–330 | Cite as

On the Stability of Incompressible Elastic Cylinders in Uniaxial Extension

  • Jeyabal Sivaloganathan
  • Scott J. Spector


Consider a cylinder (not necessarily of circular cross-section) that is composed of a hyperelastic material and which is stretched parallel to its axis of symmetry. Suppose that the elastic material that constitutes the cylinder is homogeneous, transversely isotropic, and incompressible and that the deformed length of the cylinder is prescribed, the ends of the cylinder are free of shear, and the sides are left completely free. In this paper it is shown that mild additional constitutive hypotheses on the stored-energy function imply that the unique absolute minimizer of the elastic energy for this problem is a homogeneous, isoaxial deformation. This extends recent results that show the same result is valid in 2-dimensions. Prior work on this problem had been restricted to a local analysis: in particular, it was previously known that homogeneous deformations are strict (weak) relative minimizers of the elastic energy as long as the underlying linearized equations are strongly elliptic and provided that the load/displacement curve in this class of deformations does not possess a maximum.


Uniaxial tension Incompressible Homogeneous absolute minimizer 

Mathematics Subject Classification (2000)

74B20 35J50 49K20 74G65 


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of BathBathUK
  2. 2.Department of MathematicsSouthern Illinois UniversityCarbondaleUSA

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