Behavior of depleted elastic networks: Comparison of effective-medium and numerical calculations

Machine simulations and effective-medium theories are used to examine the influence of transverse (i.e., noncentral) forces on the elastic percolation transition in two dimensions. We consider models in which the transverse forces arise from (1) contact interactions between pairs of macroscopic particles and (2) bond-bending forces involving three-site interactions. In the first class of models, effective-medium theory is shown to describe with surprising accuracy the dependence of the bulk and shear moduli on the bond occupation parameter p. In all cases we find that, as p is decreased, the ratio of the bulk to the shear modulus approaches a value that is independent of the systems initial parameters, but which does depend on the microscopic details of the model. Finally, we consider the description of depleted elastic systems from a continuum viewpoint. Two distinct effective-medium theories are shown to predict behavior consistent with that obtained in our microscopic analysis. Here, however, the ratio of the bulk to shear modulus at threshold varies over a continuous range of values.