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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
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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

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References

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