Yield stress fluids (YSFs) display a dual nature highlighted by the existence of a critical stress ${\sigma }_{\text{y}}$ such that YSFs are solid for stresses $\sigma$ imposed below ${\sigma }_{\text{y}}$, whereas they flow like liquids for $\sigma >{\sigma }_{\text{y}}$. Under an applied shear rate $\dot{\gamma }$, the solid-to-liquid transition is associated with a complex spatiotemporal scenario that depends on the microscopic details of the system, on the boundary conditions, and on the system size. Still, the general phenomenology reported in the literature boils down to a simple sequence that can be divided into a short-time response characterized by the so-called “stress overshoot,” followed by stress relaxation towards a steady state. Such relaxation can be either (1) long-lasting, which usually involves the growth of a shear band that can be only transient or that may persist at steady state or (2) abrupt, in which case the solid-to-liquid transition resembles the failure of a brittle material, involving avalanches. In the present paper, we use a continuum model based on a spatially resolved fluidity approach to rationalize the complete scenario associated with the shear-induced yielding of YSFs. A key feature of our model is to provide a scaling for the coordinates of the stress overshoot, i.e., stress ${\sigma }_{\text{M}}$ and strain ${\gamma }_{\text{M}}$ as a function of $\dot{\gamma }$, which shows good agreement with experimental and numerical data extracted from the literature. Moreover, our approach shows that the power-law scaling ${\sigma }_{\text{M}}\left(\dot{\gamma }\right)$ is intimately linked to the growth dynamics of a fluidized boundary layer in the vicinity of the moving boundary. Yet such scaling is independent of the fate of that layer, and of the long-term behavior of the YSF, i.e., whether the steady-state flow profile is homogeneous or shear-banded. Finally, when including the presence of “long-range” correlations, we show that our model displays a ductile to brittle transition, i.e., the stress overshoot reduces into a sharp stress drop associated with avalanches, which impacts the scaling ${\sigma }_{\text{M}}\left(\dot{\gamma }\right)$. This generalized model nicely captures subtle avalanche-like features of the transient shear banding dynamics reported in experiments. Our work offers a unified picture of shear-induced yielding in YSFs, whose complex spatiotemporal dynamics are deeply connected to nonlocal effects.

中文翻译：

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软玻璃材料中剪切启动的连续模型

屈服应力流体 (YSF) 显示出临界应力的存在所突出的双重性质 ${\sigma }_{\text{是}}$ 这样 YSF 就可以承受压力 $\sigma$ 下面强加 ${\sigma }_{\text{是}}$，而它们像液体一样流动 $\sigma >{\sigma }_{\text{是}}$. 在施加的剪切速率下$\dot{\gamma }$，固体到液体的转变与复杂的时空情景有关，该情景取决于系统的微观细节、边界条件和系统大小。尽管如此，文献中报道的一般现象学归结为一个简单的序列，可以分为以所谓的“应力超调”为特征的短时响应，然后是向稳定状态的应力松弛。这种松弛可以是 (1) 持久的，这通常涉及剪切带的增长，该剪切带可能只是暂时的或可能在稳定状态下持续存在，或者 (2) 突然，在这种情况下，固体到液体的转变类似于脆性材料的失效，包括雪崩。在本文中，我们使用基于空间解析流动性方法的连续模型来合理化与 YSF 的剪切诱导屈服相关的完整场景。我们模型的一个关键特征是为应力超调的坐标提供缩放，即应力${\sigma }_{\text{米}}$ 和应变 ${\gamma }_{\text{米}}$ 作为一个函数 $\dot{\gamma }$，这与从文献中提取的实验和数值数据显示出良好的一致性。此外，我们的方法表明幂律缩放${\sigma }_{\text{米}}\left(\dot{\gamma }\right)$与移动边界附近流化边界层的生长动力学密切相关。然而，这种缩放与该层的命运和 YSF 的长期行为无关，即稳态流动剖面是均匀的还是剪切带。最后，当包括“长程”相关性的存在时，我们表明我们的模型显示出韧性到脆性的转变，即应力超调减少为与雪崩相关的急剧应力下降，这会影响缩放${\sigma }_{\text{米}}\left(\dot{\gamma }\right)$. 这个广义模型很好地捕捉了实验中报告的瞬态剪切带动力学的微妙雪崩状特征。我们的工作提供了 YSF 中剪切诱导屈服的统一图景，其复杂的时空动力学与非局部效应密切相关。