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Constitutive branching in elastic materials

Published online by Cambridge University Press:  24 October 2008

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

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
Copyright
Copyright © Cambridge Philosophical Society 1982

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References

REFERENCES

(1)Chadwick, P. and Ogden, R. W.A theorem of tensor calculus and its application to isotropic elasticity. Arch. Rational Mech. Anal. 44 (1971), 5468.CrossRefGoogle Scholar
(2)Hill, R.On constitutive inequalities for simple materials. J. Mech. Phys. Solids 16 (1968), 229242.CrossRefGoogle Scholar
(3)Hill, R.Constitutive inequalities for isotropic elastic solids under finite strain. Proc. Roy. Soc. London, Ser. A, 314 (1970), 457472.Google Scholar
(4)Hill, R.On the elasticity and stability of perfect crystals at finite strain. Math. Proc. Cambridge Philos. Soc. 77 (1975), 225240.CrossRefGoogle Scholar
(5)Hill, R.Aspects of invariance in solid mechanics. Advances in Applied Mechanics 18 (1978), 175.Google Scholar
(6)Milstein, F. and Farber, B.A theoretical fcc → bcc transition under [100] tensile loading. Phys. Rev. Letters 44 (1980), 277282.CrossRefGoogle Scholar
(7)Parry, G. P.On the relative strengths of intrinsic stability criteria. Quart. J. Mech. Appl. Math. 31 (1978), 17.CrossRefGoogle Scholar
(8)Sewell, M. J.A general theory of equilibrium paths through critical points. Proc. Roy. Soc. London, Ser. A, 306 (1968), 201238.Google Scholar
(9)Thompson, J. M. T.A general theory for the equilibrium and stability of discrete con-servative systems. Z. Angew. Math. Phys. 20 (1969), 7975846.CrossRefGoogle Scholar