Principal stress and strain trajectories in nonlinear elastostatics
Author:
R. W. Ogden
Journal:
Quart. Appl. Math. 44 (1986), 255-264
MSC:
Primary 73C50
DOI:
https://doi.org/10.1090/qam/856179
MathSciNet review:
856179
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: The Maxwell-Lamé equations governing the principal components of Cauchy stress for plane deformations are well known in the context of photo-elasticity, and they form a pair of coupled first-order hyperbolic partial differential equations when the deformation geometry is known. In the present paper this theme is developed for nonlinear isotropic elastic materials by supplementing the (Lagrangean form of the) equilibrium equations by a pair of compatibility equations governing the deformation. The resulting equations form a system of four first-order partial differential equations governing the principal stretches of the plane deformation and the two angles which define the orientation of the Lagrangean and Eulerian principal axes of the deformation. Coordinate curves are chosen to coincide locally with the Lagrangean (Eulerian) principal strain trajectories in the undeformed (deformed) material.
- H. T. Jessop, Photoelasticity, Elastizität und Plastizität, Handbuch der Physik, herausgegeben von S. Flügge, Bd. 6, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1958, pp. 127–228. MR 0093121
A. Franek, J. Kratochvil and L. Travnicek, ZAMM 63, 156–158 (1983)
- 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
R. W. Ogden, Non-linear elastic deformations, Ellis Horwood, 1984
- A. E. Green and W. Zerna, Theoretical elasticity, 2nd ed., Clarendon Press, Oxford, 1968. MR 0245245
- A. E. Green and J. E. Adkins, Large elastic deformations, Clarendon Press, Oxford, 1970. Second edition, revised by A. E. Green. MR 0269158
R. T. Shield, The rotation associated with large strains, SIAM J. Appl. Math. 25, 483–491 (1973)
- A. Franěk, J. Kratochvíl, and L. Trávníček, Inhomogeneous inverse problem in finite elasticity, J. Elasticity 14 (1984), no. 4, 363–372 (English, with German summary). MR 770297, DOI https://doi.org/10.1007/BF00125606
H. J. Jessop, Photoelasticity, in Handbuch der Physik, Vol. VI (Edited by S. Flügge), Springer, 1958
A. Franek, J. Kratochvil and L. Travnicek, ZAMM 63, 156–158 (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)
R. W. Ogden, Non-linear elastic deformations, Ellis Horwood, 1984
A. E. Green and W. Zerna, Theoretical elasticity, Oxford University Press, 1968
A. E. Green and J. E. Adkins, Large elastic deformations, Oxford University Press, 1970
R. T. Shield, The rotation associated with large strains, SIAM J. Appl. Math. 25, 483–491 (1973)
A. Franek, J. Kratochvil, and L. Travnicek, Inhomogeneous inverse problem in finite elasticity, J. Elasticity 14, 363–372 (1984)
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
73C50
Retrieve articles in all journals
with MSC:
73C50
Additional Information
Article copyright:
© Copyright 1986
American Mathematical Society
