Issue 25, 2025

Continuum mechanics of differential growth in disordered granular matter

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 Poisson's ratio. This theory has implications for various experimental protocols, including non-uniform heating or wetting, which lead to spatially varying expansion fields.

Graphical abstract: Continuum mechanics of differential growth in disordered granular matter

Article information

Article type
Paper
Submitted
01 Dec 2024
Accepted
27 May 2025
First published
06 Jun 2025
This article is Open Access
Creative Commons BY-NC license

Soft Matter, 2025,21, 5153-5161

Continuum mechanics of differential growth in disordered granular matter

N. S. Livne, T. Samanta, A. Schiller, I. Procaccia and M. Moshe, Soft Matter, 2025, 21, 5153 DOI: 10.1039/D4SM01429D

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