Hostname: page-component-7479d7b7d-8zxtt Total loading time: 0 Render date: 2024-07-12T13:24:51.503Z Has data issue: false hasContentIssue false
  • English
  • Français

On intrinsic eigenstates in plasticity with generalized variables

Published online by Cambridge University Press:  24 October 2008

R. Hill
R. Hill
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

The classical specification of elastic/plastic or rigid/plastic response in metals is reformulated in generalized variables. The allowed measures of strain are sets of any geometric magnitudes that jointly determine the shape of a material element; the allowed measures of stress are generated by work-conjugacy. The choice of variables affects the parameters and qualitative features of the constitutive framework; these dependences are made explicit by concise formulae of transformation.

Eigenstates intrinsic to the material are considered wherein the strain can change while the conjugate stress is either stationary or coupled differentially with the strain. Such configurations are associated with incipient branching of the strain response to a prescribed variation of the conjugate stress. Sensitivity to the loading environment is evaluated for both elastic/plastic and rigid/plastic materials. This synoptic approach to eigenproblems is illustrated in the context of materials testing.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 93 , Issue 1 , January 1983 , pp. 177 - 189
Copyright
Copyright © Cambridge Philosophical Society 1983

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)Hill, R.On discontinuous plastic states, with special reference to localized necking in thin sheets. J. Mech. Phys. Solids 1 (1952), 19–30.CrossRefGoogle Scholar
(2)Hill, R.A general theory of uniqueness and stability in elastic-plastic solids. J. Mech. Phys. Solids 6 (1958), 236–249.CrossRefGoogle Scholar
(3)Hill, R.Some basic principles in the mechanics of solids without a natural time. J. Mech. Phys. Solids 7 (1959), 209–225.CrossRefGoogle Scholar
(4)Hill, R.Constitutive laws and waves in rigid/plastic solids. J. Mech. Phys. Solids 10 (1962), 89–98.CrossRefGoogle Scholar
(5)Hill, R. On the classical constitutive laws for elastic/plastic solids. Recent progress in applied mechanics - The Folke Odqvist volume (ed. Broberg, B., Hult, J., and Niordson, F.), pp. 241–249 (Almqvist and Wiksell, Stockholm, 1967).Google Scholar
(6)Hill, R.Eigenmodal deformations in elastic/plastic continua. J. Mech. Phys. Solids 15 (1967), 371–386.CrossRefGoogle Scholar
(7)Hill, R.On constitutive inequalities for simple materials. J. Mech. Phys. Solids 16 (1968), 229–242, 315–322.CrossRefGoogle Scholar
(8)Hill, R.On constitutive macro-variables for heterogeneous solids at finite strain. Proc. Roy. Soc. London A 326 (1972), 131–147.Google Scholar
(9)Hill, R.On the elasticity and stability of perfect crystals at finite strain. Proc. Cambridge Philos. Soc. 77 (1975), 225–240.CrossRefGoogle Scholar
(10)Hill, R.Aspects of invariance in solid mechanics. Advances in Applied Mechanics 18 (1978), 1–75.Google Scholar
(11)Hill, R.Theoretical plasticity of textured aggregates. Proc. Cambridge Philos. Soc. 85 (1979), 179–191.CrossRefGoogle Scholar
(12)Hill, R.Invariance relations in thermoelasticity with generalized variables. Proc. Cambridge Philos. Soc. 90 (1981), 373–384.CrossRefGoogle Scholar
(13)Hill, R.Constitutive branching in elastic materials. Proc. Cambridge Philos. Soc. 91 (1982), 167–181.CrossRefGoogle Scholar
(14)Mellor, P. B. Experimental studies of plastic anisotropy in sheet metal. Mechanics of solids: The Rodney Hill 60th anniversary volume (ed. Hopkins, H. G. and Sewell, M. J.), pp. 383–415 (Pergamon Press, Oxford, 1982).CrossRefGoogle Scholar
(15)Swift, H. W.Plastic instability under plane stress. J. Mech. Phys. Solids 1 (1952), 1–18.CrossRefGoogle Scholar