Signatures of the spatial extent of plastic events in the yielding transition in amorphous solids

Dynamic phase diagram of plastically deformed amorphous solids at finite temperature

“…Meanwhile, for T < T c (L), we have the usual AQS regime scaling, s c (L) ∼ L d/((θ+1)(2−τ )) and consequently the scaling relation d f = d/((θ + 1)(2 − τ )) [21]. Though this works well for the shuffled kernel simulations, we note that for our full 2d simulations, there are small corrections due to finite-size scaling effects in p(x) as described previously [47]. Our finding, that there are "anomalous" stress fluctuations (i.e.…”

“…10). We expect the velocity dependent plateau to occur at x ≈ τ • ẋ, while the system-size dependent terminal plateau should scale as x ∼ L −d [44,47]. We approximate the plateau as occurring at x p = (τ ẋ + 0.02L −2 ), which effectively collapses the plateau onset in Fig.…”

Avalanches in the athermal quasistatic limit of sheared amorphous solids: an atomistic perspective

“…They concluded that the decrease in τ is likely associated with mainshocks which are primarily responsible for the presence of a bump. The influence of spatial extent of avalanches on τ has also been reported in an elastoplastic model, where the mean field value of τ = 1.5 was found for point-like events while τ = 1.37 when all events where considered [24].…”

“…a plateau develops in the limit x → 0. Recently, Korchinski et al proposed a modified scaling law that takes these developments into account, This scaling relation relies on the presence of a plateau for small x and on the presence of spatial correlations of local stresses [24]. These scaling laws allow θ to be inferred from the avalanche size distributions.…”