The micromechanics of nonlinear plastic modes

TL;DR

This paper develops an atomistic theory for nonlinear plastic modes (NPMs) in elastic solids, revealing their distinct dynamical behavior near instabilities and highlighting their advantage in predicting plastic failure points.

Contribution

It formulates the reversible evolution of NPMs under deformation and compares their dynamics to linear eigenmodes, demonstrating NPMs' superior predictive capabilities.

Findings

NPMs do not exhibit singular scaling near instabilities.

Destabilizing eigenmodes vary with a singular rate.

NPMs converge earlier to their final form at plastic instabilities.

Abstract

Nonlinear plastic modes (NPMs) are collective displacements that are indicative of imminent plastic instabilities in elastic solids. In this work we formulate the atomistic theory that describes the reversible evolution of NPMs and their associated stiffnesses under external deformations. The deformation-dynamics of NPMs is compared to those of the analogous observables derived from atomistic linear elastic theory, namely destabilizing eigenmodes of the dynamical matrix and their associated eigenvalues. The key result we present and explain is that the dynamics of NPMs and of destabilizing eigenmodes under external deformations follow different scaling laws with respect to the proximity to imminent instabilities. In particular, destabilizing modes vary with a singular rate, whereas NPMs' exhibit no such singularity. As a result, NPMs converge much earlier than destabilizing eigenmodes to their common final form at plastic instabilities. This dynamical difference between NPMs and linear destabilizing eigenmodes underlines the usefulness of NPMs for predicting the locus and geometry of plastic instabilities, compared to their linear-elastic counterparts.