流动无序物质介观模型中永久剪切带的自发形成
Spontaneous formation of permanent shear bands in a mesoscopic model of flowing disordered matter
摘要：
本研究提出了一个连贯的方案，形成永久剪切带的屈服应力材料的流动。这是一个公认的观点，在无序介质中的流动是通过局部塑性事件发生的，对应于小尺寸的重排，产生一个长范围的应力重新分布的系统。在一个最小的介观模型，结合这些当地的动态，我们研究的空间组织当地的塑料事件。本研究中最重要的参数是局部重排后恢复原始结构所需的典型重组时间。与最近的平均场研究一致[Alissot \textit{et al., Eur. Phys. J. E}，2010，\textbf{33}，183]，我们观察到永久剪切带的自发形成，当该重构时间大于重排中的典型应力释放时间时。这些带由保持弹性的固体区域内的大量塑性事件组成。这种非均匀流动行为本质上不同于在没有剪切带的流动中在小剪切速率极限下观察到的瞬态动力学非均匀性[Martens \textit{et al., Phys. Rev. Lett.}，2011，\textbf{106}，156001]。我们详细分析了剪切带的大小，剪切速率和重组时间的依赖关系。此外，我们合理化的平均场版本的空间模型内的情况下，产生一个非单调的流动曲线大重组时间。这解释了在临界剪切速率以下的均匀流的不稳定性，该临界剪切速率对应于曲线的最小值。因此，我们的研究有力地支持了这样一种观点，即在当地的动力学特征的时间尺度是永久剪切带的物理起源。
英文摘要：
This study proposes a coherent scenario of the formation of permanent shear bands in the flow of yield stress materials. It is a well accepted point of view that flow in disordered media is occurring via local plastic events, corresponding to small size rearrangements, that yield a long range stress redistribution over the system. Within a minimalistic mesoscopic model that incorporates these local dynamics, we study the spatial organisation of the local plastic events. The most important parameter in this study is the typical restructuring time needed to regain the original structure after a local rearrangement. In agreement with a recent mean field study [Coussot \textit{et al., Eur. Phys. J. E}, 2010, \textbf{33}, 183] we observe a spontaneous formation of permanent shear bands, when this restructuring time is large compared to the typical stress release time in a rearrangement. The bands consist of a large number of plastic events within a solid region that remains elastic. This heterogeneous flow behaviour is different in nature from the transient dynamical heterogeneities that one observes in the small shear rate limit in flow without shear-banding [Martens \textit{et al., Phys. Rev. Lett.}, 2011, \textbf{106}, 156001]. We analyse in detail the dependence of the shear bands on system size, shear rate and restructuring time. Further we rationalise the scenario within a mean field version of the spatial model, that produces a non monotonous flow curve for large restructuring times. This explains the instability of the homogeneous flow below a critical shear rate, that corresponds to the minimum of the curve. Our study therefore strongly supports the idea that the characteristic time scales involved in the local dynamics are at the physical origin of permanent shear bands.
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