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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
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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

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References

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