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Bifurcation in the traction problem for a transversely isotropic material

Published online by Cambridge University Press:  24 October 2008

A. Danescu
A. Danescu
Affiliation:
Institute of Mathematics, Str. Academiei No. 14, 70109-Bucharest, Romania
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Summary

The traction problem for a transversely isotropic incompressible elastic material is considered, and it is shown that when only pure homogeneous deformations are considered, the problem can be formulated as a two-dimensional ℤ2-equivariant bifurcation problem in which the bifurcation parameter is the dead-load. Using imperfect bifurcation theory, conditions for bifurcation phenomena are given and, considering a general non-linear form for the stored energy function, the recognition problem is solved in the simplest cases. The last section treats transversely isotropic non-linear perturbations for a Mooney–Rivlin material and a neo-Hookean material and the corresponding bifurcations.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 2 , September 1991 , pp. 385 - 394
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

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