Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-27T02:05:19.160Z Has data issue: false hasContentIssue false
  • English
  • Français

On the elasticity of monatomic crystals

Published online by Cambridge University Press:  24 October 2008

Gareth P. Parry
Gareth P. Parry
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

This is an exploration of the mechanical consequences of the symmetry inherent in a monatomic elastic crystal lattice. The investigation is based on a theorem by means of which the square of the right stretch tensor is uniquely decomposed. Generality is assured by the affine equivalence of all monatomic lattices. Response functions appropriate to perfect monatomic crystals are thereby constructed, and some simple deformation paths are considered.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 80 , Issue 1 , July 1976 , pp. 189 - 211
Copyright
Copyright © Cambridge Philosophical Society 1976

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Ericksen, J. L.Nonlinear elasticity of diatomic crystals. Intermit. J. Solid Structures 6 (1970), 951–958.CrossRefGoogle Scholar
(2)Hill, R. Private communication.Google Scholar
(3)Hill, R.On constitutive inequalities for simple materials. I. J. Mech. Phys. Solids 16 (1968), 229–242.CrossRefGoogle Scholar
(4)Hill, R.On the elasticity and stability of perfect crystals at finite strain. Proc. Cambridge Philos. Soc. 77 (1975), 225–240.CrossRefGoogle Scholar
(5)Hua, L. K. & Reiner, I.On the generators of the symplectic modular group. Trans. Amer. Math. Soc. 65 (1949), 415–426.CrossRefGoogle Scholar
(6)Macmillan, N. H. & Kelly, A.The mechanical properties of perfect crystals. I. The ideal strength. Proc. Roy. Soc. Ser. A 330 (1972), 291–308.Google Scholar
(7)Milstein, F. et al. Theoretical strength of a perfect crystal in a state of simple shear. Phys. Rev. B 10 (1974), 3635–3646.Google Scholar
(8)Noll, W.A mathematical theory of the mechanical behaviour of continuous media. Arch. Rational Mech. Anal. 2 (1958), 197–226.CrossRefGoogle Scholar
(9)Truesdell, C.A theorem on the isotropy groups of a hyperelastic material. Proc. Nat. A. Sci. U.S.A. 52 (1964), 1081–1083.CrossRefGoogle ScholarPubMed
(10)Truesdell, C. & Noll, W.The non-linear field theories of mechanics, p. 41. (Springer-Verlag, 1965.)Google Scholar