Micropolar elastic percolation: The superelastic problem

Abstract

This paper deals with the critical elastic behavior of a two-dimensional micropolar (or "granular") network with randomly rigid or elastic bonds. It presents a new derivation of Feng's inequalities $1<\mathrm{}{s}^{\prime }<s$ in the context of micropolar elasticity (where $s$ is the conductivity exponent, $s^{\prime }$ the elastic-moduli exponent). In addition, an exact calculation on a fractal model suggests that $s^{\prime }=s-{\Delta }^S$, where ${\Delta }^S$ is a correction of order 20%. This correction results from the rotations of the rigid clusters, and differs from the "eccentricity" correction ${\Delta }^E$ found in the elastic case.