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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
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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

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References

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