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
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
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.
- R. W. Ogden, Nearly isochoric elastic deformations: application to rubberlike solids, J. Mech. Phys. Solids 26 (1978), no. 1, 37–57. MR 505905, DOI https://doi.org/10.1016/0022-5096%2878%2990012-1
- P. J. Flory, Thermodynamic relations for high elastic materials, Trans. Faraday Soc. 57 (1961), 829–838. MR 128117
R. W. Ogden, Volume changes associated with the deformation of rubberlike solids, J. Mech. Phys. Solids 24, 323–338 (1976)
R. W. Ogden, On the anisotropy of compressibility of rubberlike solids, to be published.
- R. W. Ogden, On plane deformations of incompressible isotropic elastic solids, Math. Proc. Cambridge Philos. Soc. 83 (1978), no. 1, 127–136. MR 468480, DOI https://doi.org/10.1017/S0305004100054360
- R. W. Ogden and D. A. Isherwood, Solution of some finite plane-strain problems for compressible elastic solids, Quart. J. Mech. Appl. Math. 31 (1978), no. 2, 219–249. MR 489206, DOI https://doi.org/10.1093/qjmam/31.2.219
R. W. Penn, Volume changes accompanying the extension of rubber, Trans. Soc. Rheol. 14, 509–517 (1970)
R. W. Ogden, Nearly isochoric elastic deformations: application to rubberlike solids, J. Mech. Phys. Solids 26, 37–57 (1978)
P. J. Flory, Thermodynamic relations for high elastic materials, Trans. Faraday Soc. 57, 829–838 (1961)
R. W. Ogden, Volume changes associated with the deformation of rubberlike solids, J. Mech. Phys. Solids 24, 323–338 (1976)
R. W. Ogden, On the anisotropy of compressibility of rubberlike solids, to be published.
R. W. Ogden, On plane deformations of incompressible isotropic elastic solids, Math. Proc. Cambridge Phil. Soc. 83, 127–136, (1978)
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)
R. W. Penn, Volume changes accompanying the extension of rubber, Trans. Soc. Rheol. 14, 509–517 (1970)
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
73G10
Retrieve articles in all journals
with MSC:
73G10
Additional Information
Article copyright:
© Copyright 1979
American Mathematical Society
