Transition rates for slip-avalanches in soft athermal disks under quasi-static simple shear deformations

Abstract

We study slip-avalanches in two-dimensional soft athermal disks by quasi-static simulations of simple shear deformations. Sharp drops in shear stress, or slip-avalanches, are observed intermittently during steady state. Such the stress drop is caused by restructuring of the contact networks, accompanied by drastic changes of the interaction forces, ∆ f . The changes of the forces happen heterogeneously in space, indicating that collective non-affine motions of the disks are most pronounced when slip-avalanches occur. We analyze and predict statistics for the force changes, ∆ f , by transition rates of the force and contact angle, where slip-avalanches are characterized by their wide power-law tails. We find that the transition rates are described as a q-Gaussian distribution regardless of the area fraction of the disks. Because the transition rates quantify structural changes of the force-chains, our findings are an important step towards a microscopic theory of slip-avalanches in the experimentally accessible quasi-static regime.The mechanics of amorphous solids, e.g. glasses, ceramics, colloidal suspensions, and granular materials, is of crucial importance in engineering science 1 . Continuously shearing amorphous solids, one observes plastic deformations after a yielding point, where stress exhibits intermittent fluctuations around a mean In this Communication, we investigate microscopic structural changes of force-chain networks by QS simulations. As a model of amorphous solids, we simulate disordered soft athermal disks in two dimensions. In our system, slip-avalanches are caused by restructuring of the force-chain networks (accompanied by drastic changes of the forces between the disks) under shear. These structural changes of force-chains are analyzed by introducing transition rates as previously studied for isotropic deformations 31 . The transition rates describe the development of force distributions through a master equation. We find that (i) despite J o u r n a l N a me , [ y e a r ] , [ v o l . ] , 1-5 | 1 arXiv:1809.10487v1 [cond-mat.soft]

Un-jamming due to energetic instability: statics to dynamics

“…In order to describe solid-like granular matter on the macroscopic scale, concepts from elasto-and visco-plastic theories were used [15,16,21,[26][27][28][29][30][31][32][33][34][35] including instabilities, yield and failure [29,[36][37][38][39][40][41][42][43][44][45]. Recently, statistical mechanics/ physics concepts [19,46], helped to better understand the probabilities for plastic deformations [17-21, 34, 47-49], force network change/growth [50,51], stress-based meso ensembles [52], or stress-relaxation [11,[22][23][24]. A traditional subject of research are stress-fluctuations [53][54][55][56], and the quest for the "effective temperature" [47,48,57,58] of thermal or a-thermal granular packings [48,52,59].…”

“…There-among other considerations-it is shown that (finite) granular systems can remain elastic for tiny strain, then have localized plastic events at larger strain with probability increasing, before (global) yield takes place with particular probabilities as cast into a meso-scale, stochastic master-equation approach, in Refs. [50,153,154].…”

“…The ratios d 1 , d 2 , and d 3 , close to jamming, change slightly for further unloading, which reflects a minute change of the probability density function of overlaps (contact forces)-not detailed here, see Refs. [50,153,154].…”

Jamming and irreversibility

“…4. It is plausible that contact changes are a proxy for irreversible rearrangements, but this must be verified-while rearrangements involve contact changes, not all rearrangements are irreversible [22,[30][31][32][33][34][35].…”

A static discrete element method with discontinuous deformation analysis

“…To better model the static problem, various static discrete element models have been proposed, in which different formulations are employed to remove inertial effects in DEM . As a consequence, the integration of the equation of motion is avoided, and the system evolves through a series of static equilibrium states under varied loads.…”