Scaling properties of the elastic stiffness moduli of a random rigid-nonrigid network near the rigidity threshold: Theory and simulations

The critical properties of the elastic stiffness moduli of random rigid-nonrigid networks near the rigidity threshold $p_c$ are investigated by constructing a scaling theory in terms of two scaling parameters. The theory is tested by simulations of a series of two-dimensional long-strip, two-component random networks at $p_c$, in which both components have finite bond-stretching and angle-bending force constants. The simulations also serve to determine the precise form of the scaling variables. Some new physical properties have emerged that will need to be understood theoretically and tested experimentally.