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ON NON-UNIQUENESS IN THE TRACTION BOUNDARY-VALUE PROBLEM FOR A COMPRESSIBLE ELASTIC SOLID
R. W. OGDEN
Quarterly of Applied Mathematics
Vol. 42, No. 3 (October 1984), pp. 337-344
Published by: Brown University
Stable URL: http://www.jstor.org/stable/43637268
Page Count: 8
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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.
Quarterly of Applied Mathematics © 1984 Brown University