Site percolation on central-force elastic networks

1987; American Physical Society; Volume: 35; Issue: 16 Linguagem: Inglês

10.1103/physrevb.35.8579

ISSN

1095-3795

Autores

M. F. Thorpe, Edward J. Garboczi,

Tópico(s)

Force Microscopy Techniques and Applications

Resumo

The elastic properties of model random networks are studied, in which a fraction ${p}_{s}$ of the sites are randomly present and are connected to their remaining nearest neighbors by Hooke springs with force constant \ensuremath{\alpha}. The one-site-defect problem is solved exactly using Green's-function techniques specialized to the static elastic limit. The location of ${p}_{s}^{\mathrm{*}}$, the critical point at which all the elastic moduli vanish, and f(${p}_{s}$), 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 Cauchy's relation (${C}_{12}$=${C}_{44}$) is strictly disobeyed, even in the one-site-defect limit.

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