Universal Poisson's ratio in a two-dimensional random network of rigid and nonrigid bonds.

Abstract

Two different elastic moduli near the percolation threshold of a two-dimensional random honey-comb network of rigid and nonrigid bonds were calculated as a function of the correlation length $\ensuremath{\xi}$ and the width $L$ of the network whose length $N$ is very large ($N\ensuremath{\gg}L,N\ensuremath{\gg}\ensuremath{\xi}$). For $L$ and $\ensuremath{\xi}$ large enough, the ratio $\frac{\ensuremath{\mu}}{{C}_{11}}$ is found to depend only on the ratio $\frac{\ensuremath{\xi}}{L}$. For $\frac{\ensuremath{\xi}}{L}<1$, the ratio tends to a value 0.46 \ifmmode\pm\else\textpm\fi{} 0.02, which corresponds to a rather low (though positive) value of Poisson's ratio $\ensuremath{\sigma}$ namely, $\ensuremath{\sigma}=0.08\ifmmode\pm\else\textpm\fi{}0.04$.