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

Abstract

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 ${\alpha }_s$ and a fraction 1-p of the bonds have a spring constant ${\alpha }_w$. The superelastic limit is obtained as ${\alpha }_w$/${\alpha }_s$→0 such that ${\alpha }_w$ 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.