doi:10.11777/j.issn1000-3304.2019.19132

引用本文: 丁芳, 张欢, 丁明明, 石彤非, 李云琦, 安立佳. 聚合物弹性体材料应力-应变关系的理论研究[J]. 高分子学报. doi: 10.11777/j.issn1000-3304.2019.19132 shu

Citation: Fang Ding, Huan Zhang, Ming-ming Ding, Tong-fei Shi, Yun-qi Li and Li-jia An. Theoretical Models for Stress-Strain Curves of Elastomer Materials[J]. Acta Polymerica Sinica. doi: 10.11777/j.issn1000-3304.2019.19132 shu

聚合物弹性体材料应力-应变关系的理论研究

1.
中国科学院合成橡胶及其高性能复合材料重点实验室
2.
高分子化学与物理国家重点实验室
中国科学院长春应用化学研究所　长春 130022
3.
中国科学技术大学应用化学与工程学院　合肥 230026

通讯作者: 李云琦, E-mail: yunqi@ciac.ac.cn

摘要: 通过解析应力-应变关系可以得到弹性体材料组成结构与性能的定量关系. 迄今为止，已发展出三十余种常见本构模型. 明确这些模型的基本假设、边界条件、曲线特征和适用体系既能为聚合物弹性体材料力学性能的工程应用提供指导，又能进一步深化对材料宏观性能与微观组成和结构联系的理解，提升高性能弹性体材料的设计能力. 本文分析了包含唯象、统计力学及其变体模型的发展关系、应力-应变曲线特征，采用非线性拟合模拟模型两两间的关系并计算其最佳确定系数和Fréchet距离，给出了不同模型的相似度和定量等价性评估. 研究发现Gent和Warner模型、Three-Chain和Eight-Chain等5对模型可以实现数学等价，而一些参数多、计算复杂的模型可以用相对简单的模型在曲线特征上单向替代.

关键词:

English

Theoretical Models for Stress-Strain Curves of Elastomer Materials

3.
School of Applied Chemistry and Engineering, University of Science and Technology of China, Hefei 230026

Corresponding author:

Received Date: 2019-07-09
Accepted Date: 2019-07-23
Available Online: 2019-01-01

Abstract: Based on the analysis of uniaxial stress-strain curves, the quantitative relationship between the composition, structure and properties of elastomers can be obtained. So far, more than 30 constitutive models have been developed. Here, we summarized the fundamental assumptions, boundary conditions, general ranges for model parameters and the characteristics of stress-strain curves of these typical models. Equations associated with phenomenological models, statistical mechanics models and their deviations were listed. Through the analysis of the best non-linear fitting of these modeling stress-strain curves using the coefficient of determination and Fréchet distance, the similarity and mathematical equivalence of models were quantified. It was found that Gent model and Warner model, Three-Chain model and Eight-Chain model have mutual equivalence in the depiction of stress-strain curves with strain hardening. Other models can undirectionally replace some models with less parameters and computational complexity. This work can help the selection of the proper constitutive models to simulate complex stress-strain behaviors of elastomer materials.

Key words:

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Figure 1. (a) Schematic uniaxial tensile stress-strain curve; (b) Schematic diagram of types of stress-strain curves

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Figure 2. Schematic diagram for the timeline of the constitutive models. Year for model proposed, major factors and the forms in the construction of strain energy functions were illustrated.

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Figure 3. Schematic diagram of uniaxial tensile stress-strain curves for different constitutive models: (a, b) phenomenological models and (c, d) statistical mechanics models

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Figure 4. Similarity assessment for constitutive models. Histogram for R² (a) and δ_dF (c). Example for the best-fitting between models and their fitting similarity parameters evaluated by R² (a) and δ_dF (b). (d) Network correlation graph of the constitutive models: the edge connection of the model is displayed according to δ_dF < 0.1. The arrow in edge indicates the direction of the model fitting, the size of the vertices is proportional to the number of edges, the color of the edge is negatively correlated with δ_dF, and red edges show the equivalence of two models. (The online version is colorful.)

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Table 1. Classification of different constitutive models that can be used to interpret typical stress-strain curves

Model Type	Stress-strain curves	Constitutive models
Phenomenological model	Convex curve	MR, NH, GT, VL
Phenomenological model	S-shape curve	Warner, VdW, Yeoh, Gent, PS, Beda, Beatty, LP, KA, Ogden, Bechir, HM, MD
Statistical mechanics model	Convex curve	Affine, Phantom, CJ, MCC, ET, NT, SlT
Statistical mechanics model	S-shape curve	EV, TC, EC, BC, DG, SpT