论文标题
驱动的无定形固体中剪切转化密度的特性
Properties of the density of shear transformations in driven amorphous solids
论文作者
论文摘要
触发连续雪崩的应变载荷$Δγ$是无定形固体缓慢变形的关键。它的时间平均值$ \langleΔγ\ rangle $显示出非平凡的系统大小依赖性，构成了屈服过渡的区别特征之一。这种依赖的细节尚未完全理解。我们通过理论分析和无定形固体的弹性模型的模拟来解决这个问题。准确确定$ \langleΔγ\ rangle $的尺寸依赖性导致对局部距离对不稳定性$ x $的稳态分布的精确评估。我们发现，通常假定的表格$ p（x）\ sim x^θ$（$θ$是所谓的伪差异指数）在低$ x $时并不准确，并且在一般$ x $中，通常倾向于$ p（x）$倾向于系统size依赖性\ textit \ textit {fitexit {finite {finite}限制为$ x \ x \ x \ 0 $。我们确定了这种有限尺寸的依赖的后果，这是对随机步行的精确结果的影响，并披露了参考位点感觉到的机械噪声的替代解释。我们在二维弹性模型中测试了我们的预测，显示了小$ x $ $ p（x）$饱和对$ \langleΔγ\ rangle $和相关规模的尺寸依赖性的关键影响。
The strain load $Δγ$ that triggers consecutive avalanches is a key observable in the slow deformation of amorphous solids. Its temporally averaged value $\langle Δγ\rangle$ displays a non-trivial system-size dependence that constitutes one of the distinguishing features of the yielding transition. Details of this dependence are not yet fully understood. We address this problem by means of theoretical analysis and simulations of elastoplastic models for amorphous solids. An accurate determination of the size dependence of $\langle Δγ\rangle$ leads to a precise evaluation of the steady-state distribution of local distances to instability $x$. We find that the usually assumed form $P(x)\sim x^θ$ (with $θ$ being the so-called pseudo-gap exponent) is not accurate at low $x$ and that in general $P(x)$ tends to a system-size-dependent \textit{finite} limit as $x\to 0$. We work out the consequences of this finite-size dependence standing on exact results for random-walks and disclosing an alternative interpretation of the mechanical noise felt by a reference site. We test our predictions in two- and three-dimensional elastoplastic models, showing the crucial influence of the saturation of $P(x)$ at small $x$ on the size dependence of $\langle Δγ\rangle$ and related scalings.
