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On the comparison of stability criteria in anisotropic materials

Published online by Cambridge University Press:  24 October 2008

Gareth. P. Parry
Gareth. P. Parry
Affiliation:
University of Bath
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Abstract

The convexity of the internal energy, regarded as a function of any tensor strain measure, determines the stability of a material in a particular loading environment. Such convexity criteria reflect properties of the material alone and therefore have the alternative interpretation of constitutive inequalities. An assessment of the relative strengths of these criteria is therefore of interest because it provides an ordering of the constitutive inequalities. Existing comparison theorems, allowing such an assessment, suppose that work-conjugate measures of stress and strain are coaxial. The main content of this paper is a theorem which makes no such supposition and so enables a comparison of criteria of convexity, and an ordering of constitutive inequalities, for arbitrarily anisotropic materials.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 86 , Issue 3 , November 1979 , pp. 529 - 538
Copyright
Copyright © Cambridge Philosophical Society 1979

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References

REFERENCES

(1)Truesdell, C.Z. angew. Math. Mech. 36 (1956), 97.Google Scholar
(2)Hill, R.Proc. R. Soc. A 314, (1970), 457.Google Scholar
(3)Hill, R. and Milstein, F.Phys. Rev. B 15 (1976), 3087.Google Scholar
(4)Parry, G. P.Quart. J. Mech. Appl. Math. 31 (1978), 1.CrossRefGoogle Scholar
(5)Hill, R.Math. Proc. Cambridge Phil. Soc. 77 (1975), 2–25.CrossRefGoogle Scholar
(6)Chadwick, P. and Ogden, R. W.Arch. Rational Mech. Analysis 44 (1971), 54.Google Scholar
(7)Ericksen, J. L.Int. J. Solids Structures 6, 951 (1970).Google Scholar
(1)Parry, G. P.A continuum model of many-body interactions in a perfect crystal. Math. Proc. Cambridge Philos. Soc. 85 (1979), 379.CrossRefGoogle Scholar
(2)Zucker, I. J. and Paik, D.Three body forces and the third order elastic constants of the rare gas crystals. J. Phys. C 12 (1979), 771.Google Scholar