论文标题
Athermal无定形固体中衰老线性响应的平均现场描述
Mean field description of aging linear response in athermal amorphous solids
论文作者
论文摘要
我们研究了无形无定形固体的平均场弹性塑性模型中对应变的线性响应，并结合了由塑料事件引起的幂律机械噪声光谱。在模型的“堵塞”方案中，塑料活性表现出非平凡的慢性弛豫，称为衰老，我们发现应力在随着年龄依赖的高原而在随着物质年龄的增长而不完全依赖于年龄依赖的高原。我们在分析上确定了这种老化线性响应的缩放行为，发现关键缩放指数是通用的，并且独立于噪声指数$μ$。对于$μ> 1 $，我们找到了简单的老化，其中压力放松时间尺度与材料的年龄$ t _ {\ rm w} $线性缩放。在$μ= 1 $的情况下，与物理弹性传播器介导的相互作用相对应，我们发现$ t _ {\ rm w}^{1/2} $缩放是由塑料活动的拉伸指数衰减产生的。我们将这些预测与在对机械平衡的缓慢耗散放松期间的模型堵塞系统的计算机模拟系统中的线性响应进行了比较，并与该理论找到了良好的一致性。
We study the linear response to strain in a mean field elastoplastic model for athermal amorphous solids, incorporating the power-law mechanical noise spectrum arising from plastic events. In the "jammed" regime of the model, where the plastic activity exhibits a non-trivial slow relaxation referred to as aging, we find that the stress relaxes incompletely to an age-dependent plateau, on a timescale which grows with material age. We determine the scaling behaviour of this aging linear response analytically, finding that key scaling exponents are universal and independent of the noise exponent $μ$. For $μ>1$, we find simple aging, where the stress relaxation timescale scales linearly with the age $t_{\rm w}$ of the material. At $μ=1$, which corresponds to interactions mediated by the physical elastic propagator, we find instead a $t_{\rm w}^{1/2}$ scaling arising from the stretched exponential decay of the plastic activity. We compare these predictions with measurements of the linear response in computer simulations of a model jammed system of repulsive soft athermal particles, during its slow dissipative relaxation towards mechanical equilibrium, and find good agreement with the theory.
