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On the elasticity and stability of perfect crystals at finite strain

Published online by Cambridge University Press:  24 October 2008

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

Abstract

The concept of ideal strength of perfect crystals as an instability phenomenon is critically reviewed in the context of generalized moduli associated with arbitrary measures of stress and strain. Further aspects of elastic response to finite strain are discussed in relation to the classical model of an atomic lattice.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1975

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References

REFERENCES

(1)Hill, R.On constitutive inequalities for simple materials. I. J. Mech. Phys. Solids 16 (1968), 229242.CrossRefGoogle Scholar
(2)Hill, R.On constitutive macro-variables for heterogeneous solids at finite strain. Proc. R. Soc. Ser. A 326 (1972), 131147.Google Scholar
(3)Born, M.On the stability of crystal lattices. I. Proc. Cambridge Philos. Soc. 36 (1940), 160172.CrossRefGoogle Scholar
(4)Stakgold, I.The Cauchy relations in a molecular theory of elasticity. Quart. Appt. Math. 8 (1950), 169186.CrossRefGoogle Scholar
(5)Born, M. and Huang, K.Dynamical Theory of Crystal Lattices (Oxford: Clarendon Press, 1954).Google Scholar
(6)Born, M. and Fürth, R.On the stability of crystal lattices. III. An attempt to calculate the tensile strength of a cubic lattice by purely static considerations. Proc. Cambridge Philos. Soc. 36 (1940), 454465.CrossRefGoogle Scholar
(7)Milstein, F.Theoretical strength of a perfect crystal. Phys. Rev. Ser. B 3 (1971), 11301141.CrossRefGoogle Scholar
(8)Milstein, F.Theoretical strength of a perfect crystal with exponentially attractive and repulsive interatomic interactions. J. Appt. Phys. 44 (1973), 38333840.CrossRefGoogle Scholar
(9)Macmillan, N. H. and Kelly, A.The mechanical properties of perfect crystals. I. The ideal strength. Proc. R. Soc. Ser. A 330 (1972), 291308.Google Scholar
(10)Macmillan, N. H. and Kelly, A.The mechanical properties of perfect crystals. II. The stability and mode of fracture of highly stressed ideal crystals. Proc. Roy. Soc. Ser. A 330 (1972), 309317.Google Scholar
(11)Macmillan, N. H. and Kelly, A.Some limitations in the use of Morse potentials for calculating ideal strengths of metals. Materials Science and Engineering 12 (1973), 7986.CrossRefGoogle Scholar
(12)Hill, R.Constitutive inequalities for isotropic elastic solids under finite strain. Proc. Roy. Soc. Ser. A 314 (1970), 457472.Google Scholar
(13)Hill, R.Eigenmodal deformations in elastic/plastic continua. J. Mech. Phys. Solids 15 (1967), 371386.CrossRefGoogle Scholar