考虑结构演变的各向同性粘弹性介质非线性流动模型生成的蠕变曲线

IF 0.3 Q4 MECHANICS Moscow University Mechanics Bulletin Pub Date : 2024-10-05 DOI:10.3103/S002713302470016X
A. V. Khokhlov
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引用次数: 0

摘要

我们继续对上一篇文章中提出的各向同性粘弹性介质剪切流动的非线性麦克斯韦型构造方程进行系统分析研究。该方程考虑了变形过程与结构演变之间的相互作用,即链交联、分子团聚和结晶的形成和断裂动力学对粘度和剪切模量的影响,以及变形对动力学的影响。构成方程由递增材料函数和六个正参数控制。假定应力恒定(以模拟蠕变条件),我们对两个未知函数(即应变和交联密度)提出了两个非线性微分方程组,并以显式形式获得了其精确的通解。我们研究了该模型在任意材料函数和材料参数条件下产生的蠕变曲线的特性,并分析了蠕变曲线和交联密度对时间、应力水平、初始交联密度以及模型的材料参数的依赖性。因此,我们证明该模型不仅能描述剪切稀化流体简单剪切流动的基本现象,还能模拟固体体的蠕变、松弛和其他现象。
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Creep Curves Generated by a Nonlinear Flow Model of Tixotropic Viscoelastoplastic Media Taking into Account Structure Evolution

We continue the systematic analytical study of the nonlinear Maxwell-type constitutive equation for shear flow of tixotropic viscoelastoplastic media formulated in the previous article. It accounts for interaction of deformation process and structure evolution, namely, the influence of the kinetics of formation and breakage of chain cross-links, agglomerations of molecules, and crystallites on viscosity and shear modulus and deformation influence on the kinetics. The constitutive equation is governed by an increasing material function and six positive parameters. Assuming that the stress is constant (in order to simulate creep conditions), we formulate the set of two nonlinear differential equations for two unknown functions (namely, strain and cross-links density) and obtain its exact general solution in explicit form. We examine the properties of creep curves generated by the model for arbitrary material function and material parameters and analyze dependence of creep curves and cross-links density on time, stress level, initial cross-links density, and material parameters governing the model. Thus, we prove that the model not only describes basic phenomena observed for simple shear flow of shear thinning fluids, but can simulate creep, relaxation, and other phenomena observed for solid bodies.

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来源期刊
CiteScore
0.60
自引率
0.00%
发文量
9
期刊介绍: Moscow University Mechanics Bulletin  is the journal of scientific publications, reflecting the most important areas of mechanics at Lomonosov Moscow State University. The journal is dedicated to research in theoretical mechanics, applied mechanics and motion control, hydrodynamics, aeromechanics, gas and wave dynamics, theory of elasticity, theory of elasticity and mechanics of composites.
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