Site percolation on central-force elastic networks

M. F. Thorpe, E. J. Garboczi

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Abstract

The elastic properties of model random networks are studied, in which a fraction ps of the sites are randomly present and are connected to their remaining nearest neighbors by Hooke springs with force constant. The one-site-defect problem is solved exactly using Green's-function techniques specialized to the static elastic limit. The location of ps*, the critical point at which all the elastic moduli vanish, and f(ps), the fraction of zero-frequency modes, agree well with the predictions of constraint-counting theory. In contrast to previously studied bond-depletion problems, it is shown both analytically and numerically that Cauchys relation (C12=C44) is strictly disobeyed, even in the one-site-defect limit.

Original languageEnglish (US)
Pages (from-to)8579-8586
Number of pages8
JournalPhysical Review B
Volume35
Issue number16
DOIs
StatePublished - Jan 1 1987

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ASJC Scopus subject areas

  • Condensed Matter Physics

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