# Linking microscopic and macroscopic response in disordered solids

## TL;DR

This paper introduces a local modulus concept for disordered solids that links microscopic bond responses to macroscopic mechanical properties, enabling efficient analysis of bond contributions to overall stiffness.

## Contribution

It proposes a local modulus for individual bonds, providing new insights into how microscopic bond changes influence global mechanical responses in disordered solids.

## Key findings

- Local modulus $L_{i}$ helps understand bond contributions to global properties.
- Efficient computation of bond contributions to bulk and shear moduli.
- Reveals correlations between bond contributions to different moduli.

## Abstract

The modulus of a rigid network of harmonic springs depends on the sum of the energies in each of the bonds due to the applied distortion: compression in the case of the bulk modulus, $B$, or shear in the case of the shear modulus, $\mathcal{G}$. The distortion need not be global and we introduce a local modulus, $L_{i}$, associated with changing the equilibrium length of a single bond, $i$, in the network. We show that $L_{i}$ is useful for understanding many aspects of the mechanical response of the entire system. For example, it allows an understanding, and efficient computation, of how each bond in a network contributes to global properties such as $B$ and $\mathcal{G}$ and sheds light on how a particular bond's contribution to one modulus is, or is not, correlated with its contribution to another.