2013/04/24 by J. Ashwin, Ashwin J., Oleg Gendelman +3 · 1 citation
Chemistry · Engineering · Materials Science · Mathematics · Physics and Astronomy · #Amorphous solid #Chemistry #Composite material #Condensed matter physics #Crystallography #Geometry #Instability #Material Dynamics and Properties #Materials science #Mathematics #Mechanics #Metallic Glasses and Amorphous Alloys #Physics #Plasticity #Principal axis theorem #Shear (geology) #Shear band #Shear stress #Theoretical and Computational Physics #Yield (engineering) #cond-mat.mtrl-sci #cond-mat.soft
paper · pdf · doi:10.1103/physreve.88.022310
published as Phys. Rev. E 88, 022310 (2013)
arxiv created 2013/04/24 · openalex publication_date 2013/08/20 · arxiv updated 2015/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
It is well known experimentally that well-quenched amorphous solids exhibit a plastic instability in the form of a catastrophic shear localization at a well-defined value of the external strain. The instability may develop to a shear band that in some cases is followed by a fracture. It is also known that the values of the yield strain (and yield stress), as well as the direction of the shear band with respect to the principal stress axis, vary considerably with variations in the external loading conditions. In this paper we present a microscopic theory of these phenomena for two-dimensional athermal amorphous solids that are strained quasistatically. We present analytic formulas for the yield strains for different loading conditions, as well as for the angles of the shear bands. We explain that the external loading conditions determine the eigenvalues of the quadrupolar Eshelby inclusions which model the nonaffine displacement field. These inclusions model elementary plastic events and determine both the yield strain and the direction of the shear band. We show that the angles of the shear bands with respect to the principal stress axis are limited theoretically between 30° and 60°. Available experimental data conform to this prediction.