Hostname: page-component-77c89778f8-5wvtr Total loading time: 0 Render date: 2024-07-21T11:53:44.609Z Has data issue: false hasContentIssue false
  • English
  • Français

On finite anti-plane shear for imcompressible elastic materials

Published online by Cambridge University Press:  17 February 2009

James K. Knowles
James K. Knowles
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper is concerned with deformations corresponding to antiplane shear in finite elastostatics. The principal result is a necessary and sufficient condition for a homogeneous, isotropic, incompressible material to admit nontrivial states of anti-plane shear. The condition is given in terms of the strain energy density characteristic of the material and is illustrated by means of special examples.

Type
Research Article
Information
The ANZIAM Journal , Volume 19 , Issue 4 , December 1976 , pp. 400 - 415
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Achenbach, J. D., ‘Bifurcation of a running crack in anti-plane strain’, International Journal of Solids and Structures, 11 (1975), 1301.CrossRefGoogle Scholar
[2]Achenbach, J. D. and Bazant, Z. P., ‘Elastodynamic near-tip stress and displacement fields for rapidly propagating cracks in orthotropic materials’, J. Appl. Mech. 42 (1975), 252.CrossRefGoogle Scholar
[3]Adkins, J. E., ‘Some generalizations of the shear problem for isotropic incompressible materials’, Proceedings of the Cambridge Philosophical Society, 50 (1954), 334.Google Scholar
[4]Amazigo, J. C., ‘Fully plastic crack in an infinite body under anti-plane shear’, International Journal of Solids and Structures, 10 (1974), 1003.CrossRefGoogle Scholar
[5]Amazigo, J. C., ‘Fully plastic center-cracked strip under anti-plane shear’, International Journal of Solids and Structures, 11 (1975), 1291.CrossRefGoogle Scholar
[6]Bers, L., Mathematical aspects of subsonic and transonic gas dynamics, Surveys in Applied Mathematics, Vol. 3, Wiley, New York, 1958.Google Scholar
[7]Courant, R. and Hilbert, D., Methods of Mathematical Physics, Vol. 2, Interscience, New York, 1962.Google Scholar
[8]Green, A. E. and Adkins, J. E., Large Elastic Deformations, Clarendon Press, Oxford, 1960.Google Scholar
[9]Hult, J. A. H. and McClintock, F. A., ‘Elastic-plastic stress and strain distribution around sharp notches under repeated shear’, Proceedings of the Ninth International Congress of Applied Mechanics, Brussels, 8 (1956), 51.Google Scholar
[10]Knowles, J. K., ‘The finite anti-plane shear field near the tip of a crack for a class of incompressible elastic solids’ to appear in international Journal of Fracture, 13 (1977).CrossRefGoogle Scholar
[11]Knowles, J. K. and Sternberg, E., ‘An asymptotic finite-deformation analysis of the elastostatic field near the tip of a crack’, Journal of Elasticity, 3 (1973), 67.CrossRefGoogle Scholar
[12]Knowles, J. K. and Sternberg, E., ‘Finite-deformation analysis of the elastostatic field near the tip of a crack: Reconsideration and higher order results’, Journal of Elasticity, 4 (1974), 201.CrossRefGoogle Scholar
[13]Lo, K. K., ‘Finite deformation crack in an infinite body under anti-plane simple shear’, to appear in International Journal of Solids and Structures.Google Scholar
[14]Rice, J. R., ‘Stresses due to a sharp notch in a work-hardening elastic-plastic material loaded by longitudinal shear’, J. Appl. Mech., 34 (1967) 287.CrossRefGoogle Scholar
[15]Truesdell, C. and Noll, W., ‘The nonlinear field theories of mechanics’, Handbuch der Physik, Vol. 3/1, Springer, Berlin, 1965.Google Scholar