Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Nearly isochoric elastic deformations: volume changes in plane strain

Author: R. W. Ogden
Journal: Quart. Appl. Math. 36 (1979), 337-345
MSC: Primary 73G10
DOI: https://doi.org/10.1090/qam/520119
MathSciNet review: 520119
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Abstract: Plane deformations of nearly incompressible elastic solids are examined with a view to calculating the volume changes accompanying an arbitrary (plane) deformation. The dilatation is shown to be determined from a knowledge of the deformation appropriate to the corresponding incompressible material under the same boundary conditions. This work parallels that given in a previous paper for three-dimensional deformations and relies on the decomposition of the deformation gradient into its dilatational and isochoric parts.

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

  • [1] R. W. Ogden, Nearly isochoric elastic deformations: application to rubberlike solids, J. Mech. Phys. Solids 26, 37-57 (1978) MR 505905
  • [2] P. J. Flory, Thermodynamic relations for high elastic materials, Trans. Faraday Soc. 57, 829-838 (1961) MR 0128117
  • [3] R. W. Ogden, Volume changes associated with the deformation of rubberlike solids, J. Mech. Phys. Solids 24, 323-338 (1976)
  • [4] R. W. Ogden, On the anisotropy of compressibility of rubberlike solids, to be published.
  • [5] R. W. Ogden, On plane deformations of incompressible isotropic elastic solids, Math. Proc. Cambridge Phil. Soc. 83, 127-136, (1978) MR 0468480
  • [6] R. W. Ogden and D. A. Isherwood, Solution of some plane-strain problems for compressible elastic solids, Quart. J. Mech. Appl. Math. 31, 219-249 (1978) MR 0489206
  • [7] R. W. Penn, Volume changes accompanying the extension of rubber, Trans. Soc. Rheol. 14, 509-517 (1970)

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DOI: https://doi.org/10.1090/qam/520119
Article copyright: © Copyright 1979 American Mathematical Society

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