论文标题
在无定形固体的平均磁场弹性塑性模型中衰老
Aging in a mean field elastoplastic model of amorphous solids
论文作者
论文摘要
我们构建了在任意时间依赖性扰动下的无定形固体动力学的平均弹性塑料描述，这是基于Lin和Wyart [Phys的工作。 Rev. X 6，011005（2016）]用于稳定剪切。局部应力是由整个材料中的屈服事件的幂律分布的机械噪声驱动的，与研究噪声是高斯的精心研究的Hébraud-Lequeux模型相比。我们首先使用映射到平均第一个传递时间问题，在没有剪切的情况下研究相图，这显示了被捕状态和流体状态之间的过渡。然后，我们引入了一种针对低收益率制度的边界层缩放技术，我们首先应用该技术来研究接近停滞过渡时的稳态收益率的缩放率。这些量表是进一步开发的，以研究玻璃制度的老化行为，以表征机械噪声频谱的指数$μ$的不同值。我们发现，作为$ 1 <μ<2 $的幂律的收益率衰减，$μ= 1 $的指数伸展指数，$μ<1 $的指数呈指数，这反映了远场和近场事件的相对重要性，因为压力传播器的范围是不同的。将平均场预测与晶格弹性模型的老化模拟的比较显示出极好的定量一致性，直到时间简单地重新缩放。
We construct a mean-field elastoplastic description of the dynamics of amorphous solids under arbitrary time-dependent perturbations, building on the work of Lin and Wyart [Phys. Rev. X 6, 011005 (2016)] for steady shear. Local stresses are driven by power-law distributed mechanical noise from yield events throughout the material, in contrast to the well-studied Hébraud-Lequeux model where the noise is Gaussian. We first use a mapping to a mean first passage time problem to study the phase diagram in the absence of shear, which shows a transition between an arrested and a fluid state. We then introduce a boundary layer scaling technique for low yield rate regimes, which we first apply to study the scaling of the steady state yield rate on approaching the arrest transition. These scalings are further developed to study the aging behaviour in the glassy regime, for different values of the exponent $μ$ characterizing the mechanical noise spectrum. We find that the yield rate decays as a power-law for $1<μ<2$, a stretched exponential for $μ=1$ and an exponential for $μ<1$, reflecting the relative importance of far-field and near-field events as the range of the stress propagator is varied. Comparison of the mean-field predictions with aging simulations of a lattice elastoplastic model shows excellent quantitative agreement, up to a simple rescaling of time.
