Effective-medium theory of percolation on central-force elastic networks. III. The superelastic problem

The effective-medium theory developed in previous papers is extended to the superelastic problem, where a fraction p of the bonds in a central-force elastic network have a spring constant αₛ and a fraction 1-p of the bonds have a spring constant αw. The superelastic limit is obtained as αw/αₛ{→}0 such that αw remains finite. In this paper we present comparisons between effective-medium theory and numerical simulations for the triangular net with nearest-neighbor central forces and the square net with nearest- and next-nearest-neighbor central forces. Some unexpected symmetries are found in these models.