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A Theory of Large Elastic Deformation
Abstract
It is postulated that (A) the material is isotropic, (B) the volume change and hysteresis are negligible, and (C) the shear is proportional to the traction in simple shear in a plane previously deformed, if at all, only by uniform dilatation or contraction. It is deduced that the general strain-energy function, W, has the form W=G4 ∑ i=13(λi−1λi)2+H4 ∑ t=13(λi2−1λi2),where the λi's are the principal stretches (1+principal extension), G is the modulus of rigidity, and H is a new elastic constant not found in previous theories. The differences between the principal stresses are σi[minus]σi=λi∂ W/∂λi[minus]λi∂ W/∂λi. Calculated forces agree closely with experimental data on soft rubber from 400 percent elongation to 50 percent compression.
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Cited by
A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials
Arruda, E. M., & Boyce, M. C. (1993) · Journal of the Mechanics and Physics of Solids · doi:10.1016/0022-5096(93)90013-6 · Cited by 3,239
Biological materials: Structure and mechanical properties
Meyers, M. A., Chen, P.-Y., Lin, A. Y.-M., & Seki, Y. (2008) · Progress in Materials Science · doi:10.1016/j.pmatsci.2007.05.002 · Cited by 2,573
Shepherd, R. F., Ilievski, F., Choi, W., Morin, S. A., Stokes, A. A., Mazzeo, A. D., Chen, X., Wang, M., & Whitesides, G. M. (2011) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1116564108 · Cited by 2,111
Theory of the elastic properties of rubber
James, H. M., & Guth, E. (1943) · The Journal of Chemical Physics · doi:10.1063/1.1723785 · Cited by 1,230
Finite element implementation of incompressible, transversely isotropic hyperelasticity
Weiss, J. A., Maker, B. N., & Govindjee, S. (1996) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/0045-7825(96)01035-3 · Cited by 797
Metadata
- Authors
- Mooney, M.
- Venue
- Journal of Applied Physics
- Publisher
- AIP Publishing
- Published
- 1940-09-01
- Volume
- 11
- Issue
- 9
- Pages
- 582-592
- ISSN
- 0021-8979 (ISSN-L)
- 1089-7550
- OpenAlex
- W2006730584
- Cited by
- 3,580
- References
- 0
- FWCI
- 11.38
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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