Effective medium theory of random regular networks

Disordered spring networks can exhibit rigidity transitions, due to either the removal of material in over-constrained networks or the application of strain in under-constrained ones. While an effective medium theory (EMT) exists for the former, there is none for the latter. We, therefore, formulate an EMT for random regular, under-constrained spring networks with purely geometrical disorder to predict their stiffness via the distribution of tensions. We find a linear dependence of stiffness on strain in the rigid phase and a nontrivial dependence on both the mean and standard deviation of the tension distribution. While EMT does not yield highly accurate predictions of shear modulus due to spatial heterogeneities, it requires only the distribution of tensions for an intact system, therefore making it an ideal starting point for experimentalists quantifying the mechanics of such networks. Copyright (C) 2022 EPLA

Automated summary

This study proposes an effective medium theory for random regular spring networks with purely geometrical disorder to predict their stiffness through the distribution of tensions. The study finds a linear dependence of stiffness on strain in the rigid phase and a nontrivial dependence on both the mean and standard deviation of the tension distribution. Although the theory does not accurately predict shear modulus due to spatial heterogeneities, it serves as an ideal starting point for experimentalists to quantify the mechanics of such networks.