Continuum mechanics of differential growth in disordered granular matter

TL;DR

This paper develops a geometric continuum theory for disordered granular materials undergoing growth, predicting anomalous displacement responses to stimuli, supported by molecular dynamics simulations, and revealing a link between odd parameters and Poisson's ratio.

Contribution

It introduces a novel geometric theory of odd-dipole-screening incorporating growth fields, extending understanding of granular matter responses to stimuli.

Findings

The theory predicts anomalous displacement fields due to non-uniform growth.

Simulations confirm the predicted displacement responses.

A relationship between odd parameters and Poisson's ratio is identified.

Abstract

Disordered granular matter exhibits mechanical responses that occupy the boundary between fluids and solids, lacking a complete description within a continuum theoretical framework. Recent studies have shown that, in the quasi-static limit, the mechanical response of disordered solids to external perturbations is anomalous and can be accurately predicted by the theory of odd-dipole-screening. In this work, we investigate responsive granular matter, where grains change size in response to stimuli such as humidity, temperature, or other factors. We develop a geometric theory of odd dipole-screening, incorporating the growth field into the equilibrium equation. Our theory predicts an anomalous displacement field in response to non-uniform growth fields, confirmed by molecular dynamics simulations of granular matter. Although the screening parameters in our theory are phenomenological and not derived from microscopic physics, we identify a surprising relationship between the odd parameter and Poissons ratio. This theory has implications for various experimental protocols, including non-uniform heating or wetting, which lead to spatially varying expansion field.