聚合物弹性体材料应力-应变关系的理论研究

Theoretical Models for Stress-Strain Curves of Elastomer Materials

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EightChain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.

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 stressstrain 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.