THE EUROPEAN PHYSICAL JOURNAL E c○ EDP Sciences

Abstract. A new formalism is used for a Monte Carlo determination of the elastic constants of a twodimensional net of fixed connectivity. The net is composed of point-like atoms each of which is tethered to six neighbors by a bond limiting the distance between them to a certain maximal separation, but having zero energy at all smaller lengths. We measure the elastic constants for many values of the ratio γ between the maximal and actual extensions of the net. When the net is very stretched (γ ∼ 1), a simple transformation maps the system into a triangular hard disks solid, and we show that the elastic properties of both systems coincide. We also show that the crossover to a Gaussian elastic behavior, expected for the non-stressed net, occurs when the net is looser (γ ∼ 3). PACS. 62.20.Dc Elasticity, elastic constants – 05.10.-a Computational methods in statistical physics and nonlinear dynamics – 65.50.+m Thermodynamic properties and entropies Materials like rubber and gels are formed when polymers or monomers are cross-linked into macroscopically large networks. Due to the small energetic differences (of the order of kT)between the allowed microscopic configurations of these materials, their physics is primaril