Rigorous solution for the elasticity of diluted Gaussian spring networks

1 November 2000

journal article
research article
Published by American Physical Society (APS) in Physical Review E

Vol. 62 (5) , 7490-7493
https://doi.org/10.1103/physreve.62.7490

Abstract

We present a rigorous solution of the elasticity of the diluted Gaussian spring networks (DGSNs) at zero temperature. We show that the deformation of a diluted DGSN is homogeneous provided that the displacements of the particles on the boundary are homogeneous. It follows that at zero temperature the nonvanishing elastic stiffness coefficients are proportional to the hydrostatic pressure in both two and three dimensions. Follows a rigorous proof of the equivalence of the elasticity of the DGSN and the conductance of the random resistor network at zero temperature.

Keywords

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