Laboratory description of clay normally distinguishes the scale of atoms from the scale of clay particles and aggregates. Contemporary constitutive models for clay tend to ignore this scale separation, and rather focus on phenomenology. By considering scale separation, this paper introduces a robust physics-based phenomenological constitutive model for clay that qualitatively captures their broad spectrum of rate-dependent mechanical features. The model is derived using the thoroughly rigorous hydrodynamic procedure. While some imagine that by considering rigour and physics, their models would get complicated, the resulting set of equations reveal a surprising degree of simplicity. The derivation strongly benefits from the principle of two-stage irreversibility, which describes energy flow within the material from the continuum scale down to the atomistic micro-scale, through the meso-scale of clay aggregates. While thermal and meso-related temperatures capture atomistic and clay aggregate fluctuating motions, a sink term from the latter to the former underpins the direction of the energy flow. The model’s standout feature is in pinpointing new transport coefficients that drive both volumetric and shear plastic flows in a thermodynamically coupled manner. A novel scheme is then proposed to calibrate these coefficients from conventional steady-state observations. Thanks to the formulation the model shows a remarkable level of predictiveness, despite being relatively simple mathematically. In particular, the model readily explains the broad spectrum of rate-dependent phenomena during transient loading, along with creep and relaxation processes. Given the generality of hydrodynamics, it is anticipated that the new model could be expanded to capture fluid-solid transitions between liquid-like soft mud and plastic-like stiff clay responses, contingent on water content variations.

中文翻译：

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粘土的简单流体动力学模型


粘土的实验室描述通常将原子的尺度与粘土颗粒和聚集体的尺度区分开来。当代粘土本构模型往往忽略这种尺度分离，而是关注现象学。通过考虑尺度分离，本文引入了一种基于物理的稳健粘土唯象本构模型，该模型定性地捕获了其广泛的与速率相关的力学特征。该模型是使用彻底严格的流体动力学程序导出的。虽然有些人认为，通过考虑严格性和物理原理，他们的模型会变得复杂，但所得的方程组却显示出惊人的简单性。这一推导极大地受益于两阶段不可逆性原理，该原理描述了材料内的能量流，从连续体尺度到原子微观尺度，通过粘土骨料的介观尺度。虽然热和介观相关温度捕捉原子和粘土骨料波动运动，但从后者到前者的汇项支撑了能量流的方向。该模型的突出特点是精确确定新的传输系数，以热力学耦合的方式驱动体积和剪切塑料流动。然后提出了一种新颖的方案来根据传统的稳态观测来校准这些系数。尽管数学上相对简单，但由于公式化，该模型显示出显着的预测能力。特别是，该模型很容易解释瞬态载荷期间广泛的速率相关现象以及蠕变和松弛过程。 考虑到流体动力学的普遍性，预计新模型可以扩展到捕获液体状软泥和塑料状硬粘土响应之间的流固转变，这取决于含水量的变化。