Realizing negative Poisson's ratio in unstressed spring networks

TL;DR

This paper demonstrates that negative Poisson's ratio can be achieved in unstressed spring networks through structural disorder, length-dependent spring stiffness, and nonaffine contributions, even in perfect crystals.

Contribution

It introduces a method to realize negative Poisson's ratio in spring networks by tuning spring stiffness based on length and disorder, revealing new design principles.

Findings

Negative Poisson's ratio increases with disorder

Length-dependent spring stiffness enables negative Poisson's ratio

Nonaffine contributions are crucial for negative Poisson's ratio

Abstract

When randomly displacing the nodes of a crystalline and unstressed spring network, we find that the Possion's ratio decreases with the increase of structural disorder and even becomes negative. Employing our finding that longer springs tend to contribute more to the shear modulus but less to the bulk modulus, we are able to achieve negative Poisson's ratio with lower structural disorder by attributing each spring a length dependent stiffness. Even with perfect crystalline structure, the network can have negative Possion's ratio, if the stiffness of each spring is set by its virtual length after a virtual network distortion. We also reveal that the nonaffine contribution arising from the structural or spring constant disorder produced in some cooperative way by network distortion is essential to the emergence of negative Poisson's ratio.