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On the elasticity and stability of perfect crystals at finite strain

  • R. Hill (a1)
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.

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References
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(1)Hill, R.On constitutive inequalities for simple materials. I. J. Mech. Phys. Solids 16 (1968), 229242.
(2)Hill, R.On constitutive macro-variables for heterogeneous solids at finite strain. Proc. R. Soc. Ser. A 326 (1972), 131147.
(3)Born, M.On the stability of crystal lattices. I. Proc. Cambridge Philos. Soc. 36 (1940), 160172.
(4)Stakgold, I.The Cauchy relations in a molecular theory of elasticity. Quart. Appt. Math. 8 (1950), 169186.
(5)Born, M. and Huang, K.Dynamical Theory of Crystal Lattices (Oxford: Clarendon Press, 1954).
(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.
(7)Milstein, F.Theoretical strength of a perfect crystal. Phys. Rev. Ser. B 3 (1971), 11301141.
(8)Milstein, F.Theoretical strength of a perfect crystal with exponentially attractive and repulsive interatomic interactions. J. Appt. Phys. 44 (1973), 38333840.
(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.
(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.
(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.
(12)Hill, R.Constitutive inequalities for isotropic elastic solids under finite strain. Proc. Roy. Soc. Ser. A 314 (1970), 457472.
(13)Hill, R.Eigenmodal deformations in elastic/plastic continua. J. Mech. Phys. Solids 15 (1967), 371386.
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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