用不同屈服面建模弹黏塑性自由表面流动

中文摘要 AI 辅助

弹黏塑性提供了一种统一方式来描述可能兼具类固体和类流体行为的屈服应力流体。本文提出一个有限应变过应力型弹黏塑性框架以方便纳入不同屈服面。在此框架内比较了几种屈服面选择并评估相关挑战，考虑了三种代表性屈服面。对于冯·米塞斯屈服面，该公式自然恢复了以单一临界屈服应力为特征的宾汉和赫谢尔 - 巴克利流变学。详细讨论了德鲁克 - 普拉格屈服面的奇异性及特殊处理方法，表明修正剑桥黏土模型在适当条件下可规避此奇异性并得到预期解。在混合欧拉 - 拉格朗日格式中实现的此框架能有效模拟二维或三维弹黏塑性流动，无需正则化固液转变或单独处理自由表面。数值基准模拟说明了屈服面几何形状如何影响速度剖面、柱塞形成和可压缩性。

英文摘要

Elasto-viscoplasticity provides a unified way of describing yield-stress fluids which may exhibit both solid-like and fluid-like behavior. In this work, we present a finite strain overstress-type elasto-viscoplastic framework designed to facilitate the incorporation of different yield surfaces. Within this framework, we compare several yield-surface choices and assess the associated challenges. We consider three representative yield surfaces: (i) pressure-independent, (ii) pressure-sensitive frictional and (iii) capped surfaces, corresponding to von Mises, Drucker--Prager, and modified Cam--clay models, respectively. In the case of von Mises, the proposed formulation naturally recovers the well-known Bingham and Herschel--Bulkley rheologies which are characterized by a single critical yield stress. We discuss in detail the singularity of the Drucker--Prager yield surface which requires a special treatment. In particular, we show that the modified Cam--clay model can be used to conveniently circumvent this singularity under the right conditions, retrieving the expected solution of Drucker--Prager. Implemented within a hybrid Eulerian--Lagrangian scheme, the general framework presented here enables efficient simulations of elasto-viscoplastic flows in two or three spatial dimensions, not requiring regularizing the solid-fluid transition nor a separate free-surface treatment. Numerical benchmark simulations illustrate how yield surface geometry affects velocity profiles, plug formation and compressibility.

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12 pages, 11 figures