Year: 2019
Type: article
Abstract: We present results on a mesoscale model for amorphous matter in athermal, quasistatic (a-AQS), steady-state shear flow. In particular, we perform a careful analysis of the scaling with the lateral system size $L$ of (i) statistics of individual relaxation events in terms of stress relaxation $S$, and individual event mean-squared displacement $M$, and the subsequent load increments $\mathrm{\ensuremath{\Delta}}\ensuremath{\gamma}$, required to initiate the next event; (ii) static properties of the system encoded by $x={\ensuremath{\sigma}}_{y}\ensuremath{-}\ensuremath{\sigma}$, the distance of local stress values from threshold; and (iii) long-time correlations and the emergence of diffusive behavior. For the event statistics, we find that the distribution of $S$ is similar to, but distinct from, the distribution of $M$. We find a strong correlation between $S$ and $M$ for any particular event, with $S\ensuremath{\sim}{M}^{q}$ with $q\ensuremath{\approx}0.65$. The exponent $q$ completely determines the scaling exponents for $P(M)$ given those for $P(S)$. For the distribution of local thresholds, we find $P(x)$ is analytic at $x=0$, and has a value ${P(x)|}_{x=0}={p}_{0}$ which scales with lateral system length as ${p}_{0}\ensuremath{\propto}{L}^{\ensuremath{-}0.6}$. The size dependence of the average load increment $\ensuremath{\langle}\mathrm{\ensuremath{\Delta}}\ensuremath{\gamma}\ensuremath{\rangle}$ appears to be asymptotically controlled by the plateau behavior of $P(x)$ rather than by a subsequent apparent power-law behavior. Extreme value statistics arguments lead thus to a scaling relation between the exponents governing $P(x)$ and those governing $P(S)$. Finally, we study the long-time correlations via single-particle tracer statistics. The value of the diffusion coefficient is completely determined by $\ensuremath{\langle}\mathrm{\ensuremath{\Delta}}\ensuremath{\gamma}\ensuremath{\rangle}$ and the scaling properties of $P(M)$ (in particular from $\ensuremath{\langle}M\ensuremath{\rangle}$) rather than directly from $P(S)$ as one might have naively guessed. Our results (i) further define the a-AQS universality class, (ii) clarify the relation between avalanches of stress relaxation and diffusive behavior, and (iii) clarify the relation between local threshold distributions and event statistics.
Source: Physical review. E
Language: English
Subfield: Materials Chemistry
Field: Materials Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2945811725