Eigenvalue analysis of stress-strain curve of two-dimensional amorphous solids of dispersed frictional grains with finite shear strain

TL;DR

This paper uses eigenvalue analysis of the Hessian matrix to accurately predict the stress-strain behavior of two-dimensional amorphous granular solids under finite shear strain, revealing no precursors to stress drops.

Contribution

It introduces a method to analyze stress-strain curves via eigenvalues without considering slip, matching simulations and showing no early warning signals for stress drops.

Findings

Eigenvalue analysis accurately reproduces stress-strain curves.

Eigenvalues do not serve as precursors to stress-drop events.

The method works despite plastic deformations from stress avalanches.

Abstract

The stress-strain curve of two-dimensional frictional dispersed grains interacting with a harmonic potential without considering the dynamical slip under a finite strain is determined by using eigenvalue analysis of the Hessian matrix. After the configuration of grains is obtained, the stress-strain curve based on the eigenvalue analysis is in almost perfect agreement with that obtained by the simulation, even if there are plastic deformations caused by stress avalanches. Unlike the naive expectation, the eigenvalues in our model do not indicate any precursors to the stress-drop events.