Bifurcation in the traction problem for a transversely isotropic material
- 1 September 1991
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 110 (2) , 385-394
- https://doi.org/10.1017/s0305004100070444
Abstract
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.Keywords
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