Theoretical Models for Stress-Strain Curves of Elastomer Materials

Fang Ding; Huan Zhang; Ming-ming Ding; Tong-fei Shi; Yun-qi Li; Li-jia An

doi:10.11777/j.issn1000-3304.2019.19132

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Theoretical Models for Stress-Strain Curves of Elastomer Materials

Research Article | 更新时间：2021-01-26

- Theoretical Models for Stress-Strain Curves of Elastomer Materials
  增强出版
- Acta Polymerica Sinica Vol. 50, Issue 12, Pages: 1357-1366(2019)
- 作者机构：
  
  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
- 作者简介：
- 基金信息：
- DOI：10.11777/j.issn1000-3304.2019.19132
  CLC：
- Published：2019-12，
  
  Published Online：23 August 2019，
  
  Received：9 July 2019，
  
  Revised：23 July 2019，
扫描看全文
Fang Ding, Huan Zhang, Ming-ming Ding, Tong-fei Shi, Yun-qi Li, Li-jia An. Theoretical Models for Stress-Strain Curves of Elastomer Materials. [J]. Acta Polymerica Sinica 50(12):1357-1366(2019)
DOI：

Fang Ding, Huan Zhang, Ming-ming Ding, Tong-fei Shi, Yun-qi Li, Li-jia An. Theoretical Models for Stress-Strain Curves of Elastomer Materials. [J]. Acta Polymerica Sinica 50(12):1357-1366(2019) DOI： 10.11777/j.issn1000-3304.2019.19132.

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.

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.

关键词

本构模型应力-应变关系聚合物弹性体力学性能

Keywords

Constitutive modelStress-strain curveElastomerMechanical properties

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College of Materials Science and Engineering, Qingdao University

Department of Polymer Science and Engineering, Zhejiang University

State Key Laboratory of Supramolecular Structure and Materials, College of Chemistry, Jilin University

Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Zhejiang University

Zheda Institute of Advanced Materials and Chemical Engineering

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