Poisson's ratio and angle bending in spring networks

TL;DR

This paper derives a simple analytic expression showing that in spring networks with equal spring and bond-reorientation strengths, the Poisson's ratio is zero regardless of the network's geometry.

Contribution

It provides a novel analytic result linking the ratio of interaction strengths to the Poisson's ratio in spring networks.

Findings

Poisson's ratio becomes zero when spring and bond-reorientation strengths are equal.

Poisson's ratio is independent of network geometry under this condition.

The result simplifies understanding of mechanical responses in spring networks.

Abstract

The Poisson's ratio of a spring network system has been shown to depend not only on the geometry but also on the relative strength of angle-bending forces in comparison to the bond-compression forces in the system. Here we derive the very simple analytic result that in systems where the spring interaction strength is equal to the bond-reorientation interaction, the Poisson's ratio identically goes to zero and is independent of the network geometry.