Unifying Plasticity in Ordered and Disordered Matter using Topological and Geometrical Descriptors

TL;DR

This paper introduces topological and geometrical density fields to identify and predict plastic deformation regions in both crystalline and amorphous materials, unifying their plasticity descriptions.

Contribution

It proposes a novel framework using dislocation, disclination, and incompatibility densities that generalize plasticity sources across different material structures.

Findings

Fields strongly correlate with $D^2_{min}$ in simulated and experimental systems.

These fields distinguish rotational and translational contributions to plasticity.

Rotational defects dominate in three-dimensional systems.

Abstract

Identifying the regions responsible for plastic flow in amorphous solids remains an open problem, since structural disorder seems to prevent the direct application of concepts such as dislocations, topological defects that successfully describe irreversible deformations in crystalline systems. Here, we introduce fields of dislocation, disclination, and incompatibility densities, that reduce to the standard sources of plasticity in crystals and assess their predictive power in amorphous materials. We find that, in a simulated two-dimensional glass as well in two- and three-dimensional experimental granular systems, these fields exhibit strong spatial correlations with $D^2_{\text{min}}$, the standard measure used to locate plastic events under shear in disordered solids. Unlike $D^2_{\text{min}}$, these fields also allow to disentangle rotational and translational contributions to the plastic events, revealing that rotational defects becoming dominant in three dimensions. Our approach paves the way for a unified description of plasticity in crystalline and amorphous solids.