We theoretically study the effect of external deformation on activated structural relaxation and aspects of the nonlinear mechanical response of glassy hard sphere fluids in the context of elastically collective nonlinear Langevin equation theory. This microscopic force-based approach describes activated relaxation as a coupled local–nonlocal event involving caging and longer range collective elasticity, with the latter becoming more important and ultimately dominant with increasing packing fraction under equilibrium conditions. The central new question we address is how this physical picture of activated relaxation, and the relative importance of local caging vs collective elasticity physics, depends on external deformation. Theoretical predictions are presented for deformation-induced enhancement of mobility, the onset of relaxation speed up at remarkably low values of stress, strain, or shear rate, apparent power law thinning of the steady state structural relaxation time and viscosity, a non-vanishing activation barrier in the shear thinning regime, an apparent Herschel–Bulkley form of the rate dependence of the steady state shear stress, exponential growth of different measures of a dynamic yield or flow stress with the packing fraction, and reduced fragility and dynamic heterogeneity under deformation. The results are contrasted with experiments and simulations, and qualitative or better agreement is found. An overarching conclusion is that deformation strongly reduces the importance of longer range collective elastic effects relative to the local caging aspect for most, but not all, physical questions, with deformation-dependent fragility and dynamic heterogeneity phenomena being qualitatively sensitive to collective elasticity. Overall, nonlinear rheology is predicted to be a more local problem than quiescent structural relaxation, albeit with deformation-modified activated processes still important.

中文翻译：

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集体弹性对强变形下硬球流体和胶体悬浮液中激活的结构弛豫，屈服和稳态流的作用

我们在弹性集体非线性Langevin方程理论的背景下，从理论上研究了外部变形对活化结构弛豫的影响以及玻璃态硬球流体的非线性力学响应。这种基于微观力的方法将活化松弛描述为局部非局部耦合事件，涉及笼养和较远范围的集体弹性，后者变得更为重要，并最终在平衡条件下随着堆积分数的增加而占主导地位。我们要解决的中心新问题是激活松弛的物理图景，以及局部笼统与集体弹性物理的相对重要性如何取决于外部变形。提出了理论预测，以预测变形引起的流动性增强，在应力，应变或剪切速率极低的值下，松弛的开始速度加快，稳态结构松弛时间和粘度的表观幂律变薄，剪切变薄状态下的活化势垒不消失，明显的Herschel-Bulkley形式的稳态剪切应力的速率依赖性，动态屈服或流动应力的不同度量随填充分数的指数增长以及变形下的脆性和动态异质性降低。将结果与实验和仿真进行对比，发现定性或更佳的一致性。总体结论是，对于大多数（但不是全部）物理问题，相对于局部笼统方面而言，变形极大地降低了较远范围的集体弹性效应的重要性，变形相关的脆弱性和动态异质性现象对集体弹性定性敏感。总的来说，尽管流变改性的活化过程仍然很重要，但非线性流变学预计比静态结构弛豫更局限。