Topological defects govern plasticity and shear band formation in two-dimensional amorphous solids

TL;DR

This study reveals that topological defects in the displacement field of 2D amorphous solids predict plasticity and shear band formation, linking microscopic topological changes to macroscopic mechanical behavior.

Contribution

It introduces a topological framework to understand plasticity and shear band formation in 2D amorphous materials, highlighting the role of topological defects as predictive tools.

Findings

Topological defects predict the onset of plastic flow.

Defects cause local order breakdown and structural changes.

Shear bands form through defect clustering and shape transformation.

Abstract

Understanding the fundamental mechanisms behind plastic instabilities and shear band formation in amorphous media under applied deformation remains a long-standing challenge. Leveraging on the mathematical concept of topology, we revisit this problem using two-dimensional experimental amorphous granular packings subjected to pure shear. We demonstrate that topological defects (TDs) in the displacement vector field act as carriers of plasticity, enabling the prediction of both the onset of plastic flow and the global mechanical response of the system. At the microscopic level, we show that these TDs are responsible for the dynamical breakdown of local orientational order, thereby linking topological excitations to short-range structural changes. Finally, we establish that the spatial localization and cooperative alignment of TDs underlie the formation of macroscopic shear bands, which drive plastic flow under large shear loads. This process is mediated by the quasi-periodic annihilation of large defect clusters and their geometric transformation from an approximately isotropic to a strongly anisotropic shape. Our results provide a unified framework for understanding plastic deformation and shear band formation in two-dimensional amorphous systems by connecting topology, short-range order, and mechanical response.