Transformations and equation reductions in finite elasticity I: Plane strain deformations

Mathematics and Mechanics of Solids

Volumn 1, Issue 2, 1996, Pages 155-175

  Hill, James M ^a   Arrigo, Daniel J ^a  

^a UNIVERSITY OF WOLLONGONG   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

CYLINDRICAL POLAR COORDINATES; HELMHOLTZ EQUATION; INCOMPRESSIBILITY; MONGE-AMPERE EQUATION; PLANE STRAIN DEFORMATION; PLANE STRESS THEORY; SECOND ORDER PROBLEM; STRAIN ENERGY FUNCTIONS;

DEFORMATION; ELASTICITY; FUNCTIONS; INTEGRAL EQUATIONS; LINEARIZATION; MATHEMATICAL TRANSFORMATIONS; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; STRAIN; STRESSES;

MECHANICS;

EID: 0030173943     PISSN: 10812865     EISSN: None     Source Type: Journal    
DOI: 10.1177/108128659600100201     Document Type: Article

References (10)

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2. Varga, O. H.: Stress-Strain Behaviour of Elastic Materials. Interscience, New York, 1966.
3. Dickie, R. A. and Smith, T. L.: Viscoelastic properties of rubber vulcanizates under large deformations in equal biaxial tension, pure shear and simple tension. Transactions of the Society of Rheology, 15, 91-110 (1971).
4. Ogden, R. W. : Large deformation isotropic elasticity - on the correlation of theory and experiment for incompressible rubberlike solids. Proceedings Royal Society London A, 326, 565-584 (1972).
5. Rivlin, R. S. and Saunders, D. W.: Large elastic deformation of isotropic materials, Part VII. Experiments on the deformation of rubber. Philosophical Transactions of the Royal Society of London A, 243, 251-288 (1951).
6. Holden, J. T.: A class of exact solutions for finite plane strain deformations of a particular elastic material. Applied Science Research, 19, 171-181 (1968).
7. Hill, J. M.: Partial solutions of finite elasticity. I. Plane deformations. Journal of Applied Mathematics and Physics (ZAMP), 24, 401-408 (1973).
8. Ames, W. F.: Nonlinear Partial Differential Equations in Engineering, Vol I. Academic Press, New York, 1965.
9. Adkins, J. E.: A reciprocal property of the finite plane strain equations. Journal of the Mechanics and Physics of Solids, 6, 267-275 (1958).
10. Shield, R. T.: Inverse deformation results in finite elasticity. Journal of Applied Mathematics and Physics (ZAMP), 18, 490-500 (1967).