Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-25T04:38:55.190Z Has data issue: false hasContentIssue false
  • English
  • Français

Bifurcations at a spherical hole in an infinite elastoplastic medium

Published online by Cambridge University Press:  24 October 2008

J. L. Bassani ,
D. Durban  and
J. W. Hutchinson
J. L. Bassani
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
D. Durban
Affiliation:
Department of Aeronautical EngineeringTechnion – Israel Institute of Technology,Haifa, Israel
J. W. Hutchinson
Affiliation:
Division of Applied Sciences, Harvard University, Cambridge, Massachusetts 02138
Get access Rights & Permissions [Opens in a new window]

Abstract

The bifurcation problem of an infinite elastoplastic medium surrounding a spherical cavity and subjected to uniform radial tension or compression at infinity is studied. The material is assumed to be incompressible, and its behaviour is modelled by both hypoelastic (flow theory) and hyperelastic (deformation theory) constitutive relations. No bifurcation was found with the flow theory. Surface bifurcation modes were discovered with the deformation theory in both tension and compression. An independent study is also presented of surface bifurcations of a semi-infinite elastoplastic material under equi-biaxial stress. The critical strain for the half-space coincides with the strain at the spherical cavity at the lowest bifurcation.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 87 , Issue 2 , March 1980 , pp. 339 - 356
Copyright
Copyright © Cambridge Philosophical Society 1980

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Durban, D. and Baruch, M.On the problem of a spherical cavity in an infinite elasto/plastic medium. J. Appl. Mech. 43 (1976), 633–638.CrossRefGoogle Scholar
(2)Hill, R.Bifurcation and uniqueness in non-linear mechanics of continua. Problems of Continuum Mechanics, pp. 155–164 (Soc. Ind. Appl. Maths., 1961).Google Scholar
(3)Hill, R. and Hutchinson, J. W.Bifurcation phenomena in the plane tension test. J. Mech. Phys. Solids 23 (1975), 239–264.CrossRefGoogle Scholar
(4)Young, N. J. B.Bifurcation phenomena in the plane compression test. J. Mech. Phys. Solids 24 (1976), 77–91.CrossRefGoogle Scholar
(5)Durban, D. and Baruch, M.Analysis of an elasto/plastic thick walled sphere loaded by internal and external pressure. Int. J. Non-Linear Mech. 12 (1977), 9–21.CrossRefGoogle Scholar
(6)Hutchinson, J. W. and Neale, K. W. Sheet necking. II. Time-dependent behavior. Mechanics of Sheet Metal Forming, 127–153 (Plenum, 1978).CrossRefGoogle Scholar
(7)Hill, R.Aspects of invariance in solid mechanics. Advances in Appl. Mech. 18 (1978), pp. 1–75.Google Scholar
(8)Stören, S. and Rice, J. R.Localized necking in thin sheets. J. Mech. Phys. Solids 23 (1975), 421–441.CrossRefGoogle Scholar
(9)Haughton, D. M. and Ogden, R. W.On the incremental equations in non-linear elasticity. II. Bifurcation of pressurized spherical shells. J. Mech. Phys. Solids 26 (1978), 111–138.CrossRefGoogle Scholar
(10)Biot, M. A.Mechanics of incremental deformation, p. 211 (New York, Wiley, 1965).Google Scholar
(11)Needleman, A. and Rice, J. R. Limits to ductility set by plastic flow localization. In Mechanics of sheet metal forming, pp, 237–265 (Plenum, 1978).Google Scholar