Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-15T02:01:58.659Z Has data issue: false hasContentIssue false
  • English
  • Français

A continuum model of many-body interactions in a perfect crystal

Published online by Cambridge University Press:  24 October 2008

G. P. Parry
G. P. Parry
Affiliation:
School of Mathematics, University of Bath
Get access Rights & Permissions [Opens in a new window]

Abstract

Theoretical and numerical calculations of the mechanical properties of single crystals usually presuppose pairwise interactions between the atoms of the lattice. It follows from this assumption that the Cauchy relations hold in respect of the Green measure of strain. Here we account for many-body interactions between the atoms of the lattice. The main result is that a continuum model of n-body interactions must possess completely symmetric (n − 1)th order Green strain moduli. Existing strain energy functions, used to model crystal elasticity, are thereby given some physical significance.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 85 , Issue 2 , March 1979 , pp. 379 - 385
Copyright
Copyright © Cambridge Philosophical Society 1979

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)Born, M.On the stability of crystal lattices. I. Proc. Cambridge Philos. Soc. 36 (1940), 160–172.CrossRefGoogle Scholar
(2)Ericksen, J. L.Nonlinear elasticity of diatomic crystals. Internal. J. Solid Structures 6 (1970), 951–958.CrossRefGoogle Scholar
(3)Ericksen, J. L. Special topics in Elastostatics. In Advances in Applied Mechanics, vol. 17, ed. Yih, Chia-Shun (New York and London, Academic Press, 1977).Google Scholar
(4)Hill, R.On the elasticity and stability of perfect crystals at finite strain. Proc. Cambridge Philos. Soc. 77 (1975), 225–240.Google Scholar
(5)Huang, K., Milstein, F. and Baldwin, J. A. Jr. Theoretical strength of a perfect crystal in a state of simple shear. Phys. Rev. B 10 (1974), 3635–3646.CrossRefGoogle Scholar
(6)Inglebert, G. and Zarka, J. Instabilités d'un monocristal parfait (Internal report. Laboratoire de Mecanique des Solides, Ecole Polytechnique, Palaiseau, 1976).Google Scholar
(7)Macmillan, N. H. and Kelly, A.The mechanical properties of perfect crystals. I. The ideal strength. Proc. Roy. Soc. Ser. A 330 (1972), 291–308.Google Scholar
(8)Parry, G. P.On the elasticity of monatomic crystals. Math. Proc. Cambridge Philos. Soc. 80 (1976), 189–211.CrossRefGoogle Scholar
(9)Parry, G. P. Ph.D. thesis. Cambridge University (1976).Google Scholar
(10)Truesdell, C.A theorem on the isotropy groups of a hyperelastic material. Proc. Nat. Acad. Sci. U.S.A. 52 (1964), 1081–1083.CrossRefGoogle ScholarPubMed