Yielding in dense active matter

TL;DR

This work tackles yielding in dense active matter by combining AQRD-driven simulations with a modified elastoplastic framework that incorporates the correlation length of the input drive. It reveals that ultrastable packings, brittle under shear, flow ductilely when driven by correlated random fields, with yielding behavior tunable by the input-field length scale $\xi$ and factorizable through a scaling parameter $\kappa$. A rotated Eshelby-style elastoplastic model reproduces the main trends, showing that rearrangement orientations and their correlations align with the input field, and that output plasticity can be partially predicted from the input field alone in several regimes. The findings challenge mean-field expectations and suggest new routes for programmable control of flow in dense amorphous materials by tailoring the driving-field statistics, with implications for designing reconfigurable granular materials and biologically inspired composites.

Abstract

High-density granular active matter is a useful model for dense animal collectives and could be useful for designing reconfigurable materials that can flow or solidify on command. Recent work has demonstrated key similarities and differences between the mechanical response of dense active matter and its sheared passive counterpart, yet a constitutive law that predicts precisely how dense active matter flows or fails remains elusive. Here we study the yielding transition in dense active matter in the limit of slow driving and large persistence times, across a wide range of material preparations. Under shear, materials prepared to be very low energy or ultrastable are brittle, and well-described by elastoplastic constitutive laws. We show that under random active forcing, however, ultrastable materials are always ductile. We develop a modified elastoplastic model that captures and explains these observations, where the key parameter is the correlation length of the input active driving field. We also observe large parameter regimes where the plastic flow is surprisingly well-predicted by the input active driving field and not highly dependent on the structural disorder, suggesting new strategies for control.

Figures (12)

• Figure 1: (A) Input displacement field induced in linear response due to Lees-Edwards boundary conditions under AQS. (B) Example input displacements applied to particles with the smallest $\xi =1$ under AQRD. (C) Stress vs. strain curves for $k_\lambda=5$ (brittle) in purple and $k_\lambda=1000$ (ductile) in yellow for $N=5000$. Solid lines represent AQS and dotted lines represent AQRD (AQRD effective stress $\tilde{\sigma}/ \sqrt{\kappa}$ and strain $\tilde{\gamma} \sqrt{\kappa}$ given by Eq. \ref{['scaling']}) with $\xi/\mathcal{L}=0.01$. Ultrastable systems ($k_\lambda=5$) show no large discontinuous stress drops under AQRD. Inset shows the same curves averaged over an ensemble of $20$ packings. (D): Average maximum stress drop $\Delta \sigma_{max}^*$ for a system size of $N= 5000$ vs the material preparation parameter $k_{\lambda}$ (lower $k_{\lambda}$ is more ordered/stable) for different input field correlation lengths in AQRD (colors) and AQS (black squares). (E) Average maximum stress drop $\Delta\sigma_{max^*}$ for AQRD with $k_\lambda= 5$ versus input correlation length $\xi/\mathcal{L}$ for different system sizes.
• Figure 2: (A) Standard orientation of Eshelby propagator for a yielding site Eshelby_1957schall2007structural. (B) Rotated Eshelby propagator for a yielding site in the modified EPM. (C) Stress vs. strain curves for three values of the EPM disorder $R$ in a system of $N=1048576$ ($\mathcal{L} = 1024$). Solid lines represent standard AQS EPM and dashed lines are for the EPM with randomly-oriented Eshelby kernels with $\xi = 8$ and $\xi/\mathcal{L}=0.007$. (D) Average maximum stress drop $\langle \Delta\sigma_{max}\rangle$ (averaged over initial stress realizations and orientational disorder) vs $R$ (low $R$ means less disorder/more stable). (E) Average maximum stress drop $\Delta\sigma_{max}$ versus the correlation length of Eshelby orientations $\xi/\mathcal{L}$, for different values of the system size $N$ with disorder $R = 0.15$.
• Figure 3: (A, C, E) Intensity plots of $D^{2}_{min}$ for the largest stress drop in an example member of the ensemble for $\xi/\mathcal{L}= 0.05 ,0.15,0.25$ in a system of $N=2500$ and $k_\lambda = 5$. The darkest spots identify particles experiencing highly nonaffine rearrangements in a neighborhood of $5 \bar{r}$, as defined in Appendix \ref{['A:yieldingcorr']}. (B, D, F) Spatial representation of modified EPM colored by number of yielding events per site for $\xi/\mathcal{L} = 0.023, 0.094, 0.25$ and $N=16384$ ($\mathcal{L}=128$).
• Figure 4: (A,B,C) Intensity plots for the yielding angles $\theta^y$ of particles with high $D^{2}_{min}$ in the largest observed avalanches in AQRD under $\xi/\mathcal{L} =0.05, 0.15$ and $0.25$ in a system with $k_\lambda =5$ and $N=2500$. (D)$X^y$ (defined in Appendix \ref{['sec:Identifying_rearrangers']}) in units of particle diameter versus $\xi/\mathcal{L}$ averaged over an ensemble of 20 systems and 80 stress drops for $N=2500$ ($L_y\approx L_x\approx50$).
• Figure 5: (A,B,C) Example input displacement fields for AQRD with $\xi/\mathcal{L} = 0.05, 0.15, 0.25$ in a system of $N=2500$ particles. The length of the arrow indicates the magnitude of the displacement and the color indicates the orientation of each displacement vector. Clusters of high local shear strain identified as described in the main text are outlined in black. (D) Average length (major axis of best fit ellipsoid) of clusters of high local shear strain vs $\xi/\mathcal{L}$.