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.
R. W. Ogden, Local and global bifurcation phenomena in plane strain finite elasticity, (to appear).
R. S. Rivlin, Stability of pure homogeneous deformations of an elastic cube under dead loading, Quart. Appl. Math. 32, 265–271 (1974)
K. N. Sawyers, Stability of an elastic cube under dead loading: two equal forces, Int. J. Non-Linear Mech. 11, 11–23,(1976)
- 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, DOI https://doi.org/10.1017/S030500410006117X
- R. W. Ogden, Inequalities associated with the inversion of elastic stress-deformation relations and their implications, Math. Proc. Cambridge Philos. Soc. 81 (1977), no. 2, 313–324. MR 431884, DOI https://doi.org/10.1017/S030500410005338X
---, Non-linear Elastic Deformations, Ellis Horwood, 1984
R. W. Ogden, Local and global bifurcation phenomena in plane strain finite elasticity, (to appear).
R. S. Rivlin, Stability of pure homogeneous deformations of an elastic cube under dead loading, Quart. Appl. Math. 32, 265–271 (1974)
K. N. Sawyers, Stability of an elastic cube under dead loading: two equal forces, Int. J. Non-Linear Mech. 11, 11–23,(1976)
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, 315–339, (1983)
R. W. Ogden, Inequalities associated with the inversion of elastic stress-deformation relations and their implications, Math. Proc. Cambridge Philos. Soc. 81, 313–324, (1977)
---, Non-linear Elastic Deformations, Ellis Horwood, 1984
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Article copyright:
© Copyright 1984
American Mathematical Society
