描述屈服前固体行为与屈服后液体行为的代数型触变弹黏塑性本构方程
An algebraic thixotropic elasto-viscoplastic constitutive equation describing pre-yielding solid and post-yielding liquid behaviours
AI总结：
针对传统弹黏塑性本构模型屈服前假设理想化的问题，提出基于结构参数的代数型触变非线性弹黏塑性模型，参数更少且能精准预测多种实验现象，可为Bingham模型提供物理解释。
摘要：
构建合适的弹黏塑性本构方程颇具挑战，尤其是描述屈服前固体行为与屈服后液体行为的模型。Oldroyd 1946年的公式是最早解释该行为的模型之一，但其关于屈服前为简单线性弹性且准静态变形的假设，使得该模型过于理想化。同时，屈服前准静态变形的假设，也意味着在非准静态条件下，屈服前可能存在黏性和塑性变形。大多数早期模型都沿用了Oldroyd提出的屈服前线性弹性假设。\n本文讨论了基于结构参数的触变型非线性弹黏塑性本构模型，该模型适用于可逆与不可逆触变材料。研究中考虑了屈服前的非线性弹性和塑性行为。尽管该模型只是简单的代数方程，但它能使用相同参数、结合不同剪切历史，同时解释低剪切速率下的黏度平台和零剪切速率黏度发散的现象。该模型还能预测实验中可观测到的瞬态和稳态剪切带现象。此外，模型能有效预测启动流动过程中与等待时间相关的应力过冲、剪切斜坡加载中的应力滞后、剪切速率突降测试结果以及黏度分岔现象。在稳态下，根据剪切历史的不同，模型可退化为Bingham模型、Herschel-Bulkley型模型或牛顿流体模型。与现有模型所需的6到7个参数相比，本文的不可逆模型仅需4个参数，可逆模型仅需5个参数。凭借更少的参数，该模型对最新实验结果的预测效果良好。本框架有望为Bingham模型提供一种可能的物理解释。
英文摘要：
Formulating an appropriate elasto-viscoplastic constitutive equation is challenging, especially for a model describing pre-yielding solid and post-yielding liquid behaviours. Oldroyds 1946 formulation was one of the first models explaining it, however, assumptions of a simple linear elastic and quasi-static deformation before yielding made his model idealistic. At the same time, the quasi-static pre-yielding deformation assumption open-up the possibility for pre-yielding viscous and plastic deformation in the absence of quasi-static conditions. Most early models followed Oldroyds pre-yielding linear elastic assumption. Here, we discuss the structural parameters based thixotropic non-linear elasto-viscoplastic constitutive model valid for reversible and irreversible thixotropic materials. In this work, we have considered non-linear elastic and plastic behaviours before yielding. Despite being a simple algebraic equation, our model explains both the viscosity plateau at low shear rates and the diverging zero shear rate viscosity, using the same parameters but different shear histories. Our model also predicts experimentally observable transient and steady-state shear banding. Furthermore, our model effectively predicts waiting-time-dependent stress overshoot during startup flow, stress hysteresis in shear ramps, sudden stepdown shear rate test results, and viscosity bifurcation phenomena. At the steady state, it reduces to either Bingham, Herschel Bulkley type, or Newtonian fluids model, depending on shear histories. Our model requires only four and five for the irreversible and reversible model, respectively, compared to six or seven parameters required by the existing model. With fewer parameters, our model favourably predicts recent experimental results. The current framework has the potential to provide a possible physical interpretation of the Bingham model.
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