Role of local response in manipulating the elastic properties of disordered solids by bond removal

TL;DR

This study investigates how local bond responses can be used to strategically remove bonds in disordered solids, enabling the design of auxetic materials with tailored elastic properties without causing cracks.

Contribution

It introduces a method that considers local bond responses to improve bond removal strategies for manipulating elastic properties in disordered networks.

Findings

Pruning can effectively tune bulk and shear moduli.

Auxetic materials can be designed without cracking.

Spatial correlation lengths diverge near the isostatic limit.

Abstract

We explore the range over which the elasticity of disordered spring networks can be manipulated by the removal of selected bonds. By taking into account the local response of a bond, we demonstrate that the effectiveness of pruning can be improved so that auxetic (i.e., negative Poisson's ratio) materials can be designed without the formation of cracks even while maintaining the global isotropy of the network. The bulk, $B$, and shear, $G$, moduli scale with the number of bonds removed and we estimate the exponents characterizing these power laws. We also find that there are spatial correlation lengths in the change of $B$ and $G$ upon removing different bonds that diverge as the network approaches the isostatic limit where the excess coordination number $\Delta Z\rightarrow0$.