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Path sensitivity of material response at intrinsic eigenstates in classical plasticity

Published online by Cambridge University Press:  24 October 2008

R. Hill
R. Hill
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
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Abstract

Categories of rigid/plastic response are investigated along arbitrary paths of homogeneous deformation. Successive yield surfaces are presumed to be convex and self-similar relative to certain canonical measures of stress and finite strain. After a general analysis attention is focussed on path-sensitive response in configurations where the canonical rate of hardening vanishes. The analysis is subsequently extended to other types of eigenstate, especially those associated with actual or prospective loading devices. The results are illustrated in the context of formability tests on sheet metal.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 103 , Issue 2 , March 1988 , pp. 371 - 381
Copyright
Copyright © Cambridge Philosophical Society 1988

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References

REFERENCES

[1]Hill, R.. On constitutive macro-variables for heterogeneous solids at finite strain. Proc. Roy. Soc. London Ser. A 326 (1972), 131–147.Google Scholar
[2]Hill, R.. Aspects of invariance in solid mechanics. Adv. in Appl. Mech. 18 (1978), 1–75.Google Scholar
[3]Hill, R.. Theoretical plasticity of textured aggregates. Math. Proc. Cambridge Philos. Soc. 85, (1979), 179–191.CrossRefGoogle Scholar
[4]Hill, R.. Constitutive branching in elastic materials. Math. Proc. Cambridge Philos. Soc. 91 (1982), 167–181.CrossRefGoogle Scholar
[5]Hill, R.. On intrinsic eigenstates in plasticity with generalized variables. Math. Proc. Cambridge Philos. Soc. 93 (1983), 177–189.Google Scholar
[6]Swift, H. W.. Plastic instability under plane stress. J. Mech. Phys. Solids 1 (1952), 1–18.CrossRefGoogle Scholar