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The micromechanics of nonlinear plastic modes
Soft Condensed Matter · Submitted 17 Mar 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Nonlinear plastic modes (NPMs) are collective displacements that are indicative of imminent plastic instabilities in elastic solids. | background 1.00 | 0.07 | 0.03 | asserted 0.99 |
| s1 | In this work we formulate the atomistic theory that describes the reversible evolution of NPMs and their associated stiffnesses under external deformations. | contribution 0.94 | 0.94 | 0.03 | asserted 0.99 |
| s2 | 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. | method 0.67 | 0.78 | 0.03 | asserted 0.93 |
| s3 | 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. | result 0.99 | 0.93 | 0.89 | asserted 1.00 |
| s4 | In particular, destabilizing modes vary with a singular rate, whereas NPMs' exhibit no such singularity. | result 1.00 | 0.87 | 0.34 | asserted 1.00 |
| s5 | As a result, NPMs converge much earlier than destabilizing eigenmodes to their common final form at plastic instabilities. | result 0.95 | 0.87 | 0.18 | asserted 1.00 |
| s6 | 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. | interpretation 1.00 | 0.70 | 0.30 | asserted 0.95 |
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The paper
Original 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.
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How the literature uses it
2 arXiv papers cite this in 8 sentences
Papers citing it · 5 sentences without a confident label
Cites it as background 2 papers
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These excitations are thus termed quasi-localized modes (QLMs), and identify glassy defects that become unstable under applied shear, generating structural rearrangements and non-affine motion [ref] .
Searching for structural predictors of plasticity in dense active packings · Linear response and augmented Hessian framework · 0.86
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As previously noted, several recent works (Refs. [ref] ) have formulated and studied NPMs and PHMs as faithful representations of structural instabilities in model glasses.
Bond-space operator disentangles quasi-localized and phononic modes in structural glasses · Relevant modes and spatial decay · 0.98
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