Cauchy relations for central-force random networks

Abstract

For many years it has been known that the elastic moduli of networks whose only interatomic forces are central pair potentials and whose atoms occupy centers of inversion at equilibrium obey the Cauchy relations. Recently it has been shown analytically that such networks with one bond missing (thus eliminating all centers of inversion at atomic sites) still obey the Cauchy relations exactly, while similar networks with one site missing do not. The usual hypothesis that must be satisfied in order for the Cauchy relations to hold must be generalized. This paper presents a possible hypothesis and explores its implications via computer simulation of three different two-dimensional random networks.