Plasticity in amorphous solids is mediated by topological defects in the displacement field

TL;DR

This paper reveals that topological defects in the nonaffine displacement field, rather than static structure, govern plasticity in amorphous solids, linking microscopic defect dynamics to macroscopic yielding behavior.

Contribution

It introduces a novel method to identify and characterize dislocation-like topological defects in the displacement field of glasses, connecting defect behavior to plastic instability.

Findings

Topological defects correlate with plastic events and yield peaks.

Burgers vectors of defects predict shear band formation at 45 degrees.

Defects result from violation of Cauchy-Born rules in amorphous solids.

Abstract

The microscopic mechanism by which amorphous solids yield plastically under an externally applied stress or deformation has remained elusive in spite of enormous research activity in recent years. Most approaches have attempted to identify atomic-scale structural "defects" or spatio-temporal correlations in the undeformed glass that may trigger plastic instability. In contrast, here we show that the topological defects which correlate with plastic instability can be identified, not in the static structure of the glass, but rather in the nonaffine displacement field under deformation. These dislocation-like topological defects (DTDs) can be quantitatively characterized in terms of Burgers circuits (and the resulting Burgers vectors) which are constructed on the microscopic nonaffine displacement field. We demonstrate that (i) DTDs are the manifestation of incompatibility of deformation in glasses as a result of violation of Cauchy-Born rules (nonaffinity); (ii) the resulting average Burgers vector displays peaks in correspondence of major plastic events, including a spectacular non-local peak at the yielding transition, which results from self-organization into shear bands due to the attractive interaction between anti-parallel DTDs; (iii) application of Schmid's law to the DTDs leads to prediction of shear bands at 45 degrees for uniaxial deformations, as widely observed in experiments and simulations.