一种基于分子链统计理论的橡胶超弹性混合本构模型

A Hyperelastic Mixed Constitutive Model for Rubber Based on Molecular Chain Statistical Theory

橡胶材料因其独特的超弹性在实际中广泛应用,通过解析应力-应变关系可以为橡胶力学性能的工程应用提供理论指导。为了更准确地描述橡胶材料力学性能,提出一种适用于橡胶材料的超弹性混合本构模型。新模型基于Gaussian模型与八链模型,引入有关拉伸比的权重函数将二者耦合,在拉伸比较小的情况下,新模型退化成Gaussian形式,在拉伸比较大的情况下,新模型可以依靠权重函数改善八链模型在小变形区域的不足。针对取向硬化的应力-应变曲线、无取向硬化的应力-应变曲线、不同拉伸比应力-应变曲线三种力学特征曲线,从单轴拉伸、等双轴拉伸和纯剪切三类实验数据进行预测验证。结果表明,新模型同时保留了Gaussian模型在小变形范围和八链模型在大变形范围内的预测优势,且对拉伸比和应力应变曲线形式没有依赖性,均能给出高精度的预测结果,突破了Gaussian模型和八链模型的使用限制,为橡胶超弹性力学性能的预测提供了新的思路。

Rubber materials are widely used in practice because of their unique hyperelasticity.The analysis of the stress-strain relationship can provide theoretical guidance for the engineering application of rubber mechanical properties.In order to describe the mechanical properties of rubber materials more accurately,a hybrid hyperelastic constitutive model was proposed in this paper.The new model is based on the Gaussian model and 8-chain model,which are coupled by the weight function related to the stretching ratio.When the stretching ratio is small,the new model degenerates into Gaussian form;When the stretching ratio is large,the new model can improve the deficiency of 8-chain model in small deformation by regulating of the weight function.We select experiment data from three aspects to verify the applicability of the new model:Stress-strain curve of orientation hardening,stress-strain curve of non-oriented hardening,stress-strain curve of different stretch ratios.We carry on the fitting verification from uniaxial tension,biaxial tension and pure shear experiments,respectively.The results show that the new model retains the advantages of Gaussian model in small deformation range and 8-chain model in large deformation range at the same time and has no dependence on stretching ratios and stress-strain curve forms.It breaks through the limitation of Gaussian model and 8-chain model,and provides a new idea for prediction of rubber hyperelastic mechanical properties.