New two-parameter constitutive models for rubber-like materials: Revisiting the relationship between single chain stretch and continuum deformation

IF 4.4 2区 工程技术 Q1 MECHANICS
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Abstract

The connection between macroscopic deformation and microscopic chain stretch is a key element in constitutive models for rubber-like materials that are based on the statistical mechanics of polymer chains. A new micro-macro chain stretch relation is proposed, using the Irving–Kirkwood–Noll procedure to construct a Cauchy stress tensor from forces along polymer chains. This construction assumes that the deformed polymer network remains approximately isotropic for low to moderate macroscopic stretches, a starting point recently adopted in the literature to propose a non-affine micro-macro chain stretch relation (Amores et al., 2021). Requiring the constructed Cauchy stress to be consistent with the stress tensor derived from the strain energy density results in a new chain stretch relation involving the exponential function. A hybrid chain stretch relation combining the new chain stretch with the well-known affine relation is then proposed to account for the whole range of stretches in experimental datasets. Comparison of the model predictions to experimental data in the literature shows that the two new micro-macro chain stretch relations in this work result in two-parameter constitutive models that outperform those based on existing chain stretches with no increase in the number of fitting parameters used.

类橡胶材料的新双参数构成模型:重新审视单链拉伸与连续变形之间的关系
宏观变形与微观链拉伸之间的联系是基于聚合物链统计力学的类橡胶材料构成模型的关键要素。本文提出了一种新的微观-宏观链拉伸关系,利用 Irving-Kirkwood-Noll 程序从聚合物链上的力构建考希应力张量。这种构造假定变形聚合物网络在低到中等宏观拉伸时保持近似各向同性,这是最近文献中提出非正交微宏观链拉伸关系时采用的出发点(Amores 等人,2021 年)。要求构建的柯西应力与应变能密度导出的应力张量一致,会产生一种涉及指数函数的新链式拉伸关系。然后提出了一种混合链拉伸关系,将新的链拉伸关系与众所周知的仿射关系相结合,以解释实验数据集中的全部拉伸范围。将模型预测结果与文献中的实验数据进行比较后发现,这项研究中的两种新的微宏观链拉伸关系所产生的双参数构成模型优于基于现有链拉伸关系的模型,而且所用拟合参数的数量没有增加。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
7.00
自引率
7.30%
发文量
275
审稿时长
48 days
期刊介绍: The European Journal of Mechanics endash; A/Solids continues to publish articles in English in all areas of Solid Mechanics from the physical and mathematical basis to materials engineering, technological applications and methods of modern computational mechanics, both pure and applied research.
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