Remarks on the Instability of an Incompressible and Isotropic Hyperelastic, Thick-Walled Cylindrical Tube |
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Authors: | Feixia Pan Millard F Beatty |
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Institution: | (1) Department of Engineering Mechanics, University of Nebraska–Lincoln, Lincoln, NE, 68588-0347, U.S.A |
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Abstract: | The problem of instability of a hyperelastic, thick-walled cylindrical tube was first studied by Wilkes 1] in 1955. The solution
was formulated within the framework of the theory of small deformations superimposed on large homogeneous deformations for
the general class of incompressible, isotropic materials; and results for axially symmetrical buckling were obtained for the
neo-Hookean material. The solution involves a certain quadratic equation whose characteristic roots depend on the material
response functions. For the neo-Hookean material these roots always are positive. In fact, here we show for the more general
Mooney–Rivlin material that these roots always are positive, provided the empirical inequalities hold. In a recent study 2]
of this problem for a class of internally constrained compressible materials, it is observed that these characteristic roots
may be real-valued, pure imaginary, or complex-valued. The similarity of the analytical structure of the two problems, however,
is most striking; and this similarity leads one to question possible complex-valued solutions for the incompressible case.
Some remarks on this issue will be presented and some new results will be reported, including additional results for both
the neo-Hookean and Mooney–Rivlin materials.
This revised version was published online in August 2006 with corrections to the Cover Date. |
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Keywords: | stability nonlinear elasticity Mooney-Rivlin material incompressible material thick-walled tube |
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