We formulate a particle and force level, activated dynamics-based statistical mechanical theory for the continuous startup nonlinear shear rheology of ultradense glass-forming hard sphere fluids and colloidal suspensions in the context of the elastically collective nonlinear Langevin equation approach and a generalized Maxwell model constitutive equation. Activated structural relaxation is described as a coupled local-nonlocal event involving caging and longer range collective elasticity which controls the characteristic stress relaxation time. Theoretical predictions for the deformation-induced enhancement of mobility, the onset of relaxation acceleration at remarkably low values of stress, strain, or shear rate, apparent power law thinning of the steady-state structural relaxation time and viscosity, a nonvanishing activation barrier in the shear thinning regime, an apparent Herschel–Buckley form of the shear rate dependence of the steady-state shear stress, exponential growth of different measures of a yield or flow stress with packing fraction, and reduced fragility and dynamic heterogeneity under deformation were previously shown to be in good agreement with experiments. The central new question we address here is the defining feature of the transient response—the stress overshoot. In contrast to the steady-state flow regime, understanding the transient response requires an explicit treatment of the coupled nonequilibrium evolution of structure, elastic modulus, and stress relaxation time. We formulate a new quantitative model for this aspect in a physically motivated and computationally tractable manner. Theoretical predictions for the stress overshoot are shown to be in good agreement with experimental observations in the metastable ultradense regime of hard sphere colloidal suspensions as a function of shear rate and packing fraction, and accounting for deformation-assisted activated motion appears to be crucial for both the transient and steady-state responses.

中文翻译：

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超致密玻璃形成流体和胶体悬浮液中剪切流变学和应力超调的微观激活动力学理论

我们在弹性集体非线性朗之万方程方法和广义麦克斯韦本构模型的背景下，为超致密玻璃形成硬球流体和胶体悬浮液的连续启动非线性剪切流变学制定了粒子和力水平、基于激活动力学的统计力学理论方程。激活的结构松弛被描述为一个耦合的局部-非局部事件，涉及笼罩和控制特征应力松弛时间的较长范围的集体弹性。变形引起的流动性增强的理论预测，在非常低的应力、应变或剪切率值下开始松弛加速，稳态结构松弛时间和粘度的表观幂律变薄，剪切稀化状态下的非消失活化势垒，稳态剪切应力的剪切速率依赖性的明显 Herschel-Buckley 形式，屈服或流动应力的不同测量值随堆积分数的指数增长，以及脆性和动态异质性降低变形下的 先前显示与实验非常一致。我们在这里解决的核心新问题是瞬态响应的定义特征——应力过冲。与稳态流态相反，理解瞬态响应需要明确处理结构、弹性模量和应力松弛时间的耦合非平衡演化。我们以物理动机和计算上易于处理的方式为这方面制定了一个新的定量模型。