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

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 $\xi$ and the width $L$ of the network whose length $N$ is very large ($N\gg L,N\gg \xi$). For $L$ and $\xi$ large enough, the ratio $\frac{\mu }{C_{11}}$ is found to depend only on the ratio $\frac{\xi }{L}$. For $\frac{\xi }{L}<1\mathrm{}$, the ratio tends to a value 0.46 ± 0.02, which corresponds to a rather low (though positive) value of Poisson's ratio $\sigma$ namely, $\sigma =0.08\mathrm{}\pm 0.04$.