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Constitutive branching in elastic materials

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

In finite elasticity a homogeneous strain is not always determined uniquely by the conjugate stress. The phenomenon is investigated for any constitutive work-function, and in both its global and local aspects. Uniqueness is lost in specific critical states. Basic properties of their aggregates in the stress and strain spaces are derived, and shown to be fundamental for the material response near individual critical states. The geometry of local branches is analyzed in detail. Further properties resulting from material isotropy are obtained. The general theory is illustrated by examples typifying the responses of metal crystals and rubberlike polymers.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 92 , Issue 1 , July 1982 , pp. 167 - 181
Copyright
Copyright © Cambridge Philosophical Society 1982

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References

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