发表机构
Kyoto University; Kanazawa University; Kyoto MPI Inc.（京都大学; 金泽大学; 京都MPI公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对从实验可观测应力推断黏弹性本构方程的难题，提出偏应力闭合建模方法，经Giesekus和Larson模型验证可有效捕捉相关流动响应并明确其有效范围。
AI 中文摘要
标准流变学测量仅能得到选定的应力分量，因此从实验可观测的量推断张量本构方程十分复杂。我们提出一种基于偏应力张量（迹为零）而非额外应力张量的本构建构方法。利用包含剪切应力、剪切下的第一和第二法向应力差，以及单轴拉伸下的拉伸应力的流变数据，可构建出不含不确定各向同性应力的偏应力状态。偏应力动力学由通过符号回归推断出的闭合模型表示，该模型需满足材料客观性和给定的线性麦克斯韦响应约束。为验证所提方法，从Giesekus模型和Larson模型的应力响应中推断出的两个闭合模型，成功捕捉了变形速率约为逆弛豫时间下平面拉伸以及混合剪切/单轴拉伸下未训练的瞬态流动响应。在训练数据对应的线性响应区及变形速率范围内，这些闭合模型的稳态流变函数与原始模型一致，而在训练范围外的更大变形速率下则出现偏差和发散响应。这些结果表明，所提的偏应力构建方法为可观测的线性和非线性黏弹性动力学的本构建模提供了实用途径，同时明确了其在强变形下的有效范围。
英文摘要
Standard rheological measurements yield only selected stress components; thus, inferring tensorial constitutive equations from experimentally accessible observables is complicated. We propose a constitutive formulation written in terms of a deviatoric stress tensor, whose trace is zero, rather than the extra stress tensor. From rheometric data including shear stress, first and second normal stress differences under shear, and elongational stress under uniaxial elongation, we can construct a deviatoric stress state without the indeterminate isotropic stress. The deviatoric-stress dynamics is represented by a closure inferred through symbolic regression, constrained to satisfy material objectivity and a given linear Maxwell response. To demonstrate the proposed formulation, two closures inferred from stress responses of the Giesekus and Larson models successfully captured untrained transient-flow responses under planar elongation and mixed shear/uniaxial elongations at deformation rates around an inverse relaxation time. Steady rheological functions of the closures agreed with the original models in the linear-response regime and over a deformation-rate range connected to the training data, whereas deviations and divergent responses appeared at larger deformation rates outside the training regime. These results demonstrate that the proposed deviatoric-stress formulation provides a practical route for constitutive modeling of observable linear and nonlinear viscoelastic dynamics, while clarifying its range of validity under strong deformation.
Comments11 pages, 4 figures
