A geometric approach to predicting plasticity in disordered solids

TL;DR

The paper tackles predicting plastic rearrangements in disordered solids from the undeformed configuration. It introduces a geometric filter based on the continuous Nye density $\rho$ to remove spurious plane-wave–induced vortex defects in vibrational modes. Compared with the vortex-based topology method, the Nye-density approach yields stronger correlations with plastic spots identified by $D^2_{\min}$ and remains effective at small strains and for genuine plastic stress drops. Validation on a 2D Kob–Andersen glass under athermal quasi-static shear and on an independent sample demonstrates robustness and suggests extension to three dimensions with reduced computational cost. This work provides a priori identification of plastic-prone regions and offers a framework to integrate geometric incompatibility into elastoplastic models.

Abstract

It was recently shown that vortex-like topological defects with negative winding number in the vibrational modes of a two-dimensional glass under quasistatic shear correlate strongly with plastic events, offering a promising route to predict them. However, many of these vortices, a number that actually grows quadratically with mode frequency, are entirely unrelated to plasticity and arise simply from the underlying plane-wave structure of the modes. This raises doubts about the fundamental relevance of such defects to plastic rearrangements and limits their predictive power. Here, we introduce a geometrical filter based on the Nye dislocation density that, when applied to the vibrational modes, removes these spurious defects and reveals the true plastic precursors. Using simulations of a two-dimensional model glass, we show that this filtered approach consistently outperforms the conventional vortex-based method, particularly at small strains and when focusing on genuine plastic stress drops, offering a more robust tool to predicting plasticity in glasses from their undeformed initial state.

Figures (14)

• Figure 1: Filtering out spurious defects in the eigenvector field of a simulated glass. Example of an eigenvector field in which and denote, respectively, the $-1$ and $+1$ topological vortex defects defined in wu2023topology. The background colormap displays the norm $\rho$ of the continuous Nye vector, Eq. \ref{['nye']}. The green vectors indicate half of the phonon wavelength associated with this eigenvector.
• Figure 2: Geometric Nye density versus average winding number.(a) Average local Nye density $\bar{\rho}(x,y)$, Eq. \ref{['localnye']}, corresponding to the first $n=20$ vibrational modes. Red crosses and disks correspond to the plastic spots, identified using $D^2_{\text{min}}$, for a small strain $\gamma=0.005$ for direct and inverse shear. (b) Same representation where the color map indicates the average value of the topological winding number $\bar{q}(x,y)$.
• Figure 3: Correlation with plastic soft spots.(a)-(c) Radial pair correlation functions between plastic spots (P), Nye density $\alpha$, and $\pm 1$ topological defects. Different colors correspond to different modes involved in the average. The global strain value is fixed to $\gamma=0.005$. (d)-(f) Same analysis for fixed value of $n=20$ and different values of the strain used to compute the non-affine $D^2_{\text{min}}$ measure.
• Figure 4: Identifying the real plastic events.(a) Stress-strain curve under shear and zoom on the first plastic event. Red and black curves correspond respectively to $xy$ and inverse ($-xy$) shear. (b) Colored clusters are the plastic spots corresponding to the first five plastic events (PEs) in the stess-strain curve. The background color is the averaged Nye density computed using the first $n=20$ vibrational modes. (c) In black, the same plastic soft spots identified with $D^2_{\text{min}}$. The background color is the average winding number from the first $n=20$ modes. (d)-(f) Radial pair correlation functions between the plastic spots (P), the average Nye density ($\alpha$) and the $\pm 1$ topological charge. Different colors correspond to different PE considered as indicated in the legend. Red arrows in panel (e) and (f) indicate respectively a weak correlation/anti-correlation consistent with the results of wu2023topology.
• Figure 5: Nye density for ideal cases.(a) Lowest eigenvector field of an ideal dislocation HUANG2025106274. (b) Lowest eigenvector field for an Eshelby inclusion HUANG2025106274. (c) Eigenvector field for an ideal vortex. (d) Eigenvector field for an ideal anti-vortex. In all panels, the background color refer to the value of the local Nye density, while and denote, respectively, the $-1$ and $+1$ topological vortex defects.