Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

On nonuniqueness in the traction boundary-value problem for a compressible elastic solid


Author: R. W. Ogden
Journal: Quart. Appl. Math. 42 (1984), 337-344
MSC: Primary 73G10
DOI: https://doi.org/10.1090/qam/757172
MathSciNet review: 757172
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Abstract: For a compressible isotropic elastic solid local and global non-uniqueness of the homogeneous deformation resulting from prescribed dead-load boundary tractions is examined. In particular, for the plane-strain problem with equibiaxial in-plane tension, equations governing the paths of deformation branching from the bifurcation point on a deformation path corresponding to in-plane pure dilatation are derived. Explicit calculations are given for a specific strain-energy function and the stability of the branches is discussed. Some general results are then given for an arbitrary form of strain-energy function.


References [Enhancements On Off] (What's this?)

  • [1] R. W. Ogden, Local and global bifurcation phenomena in plane strain finite elasticity, (to appear).
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  • [4] J. M. Ball and D. G. Schaeffer, Bifurcation and stability of homogeneous equilibrium configurations of an elastic body under dead-load tractions, Math. Proc. Cambridge Philos. Soc. 94 (1983), no. 2, 315–339. MR 715037, https://doi.org/10.1017/S030500410006117X
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  • [6] -, Non-linear Elastic Deformations, Ellis Horwood, 1984

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DOI: https://doi.org/10.1090/qam/757172
Article copyright: © Copyright 1984 American Mathematical Society

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