Effective medium theory of random regular networks

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