橡胶材料非线性高弹-粘弹性本构模型

本文提出的修正Zener模型，即以非线性弹簧与粘壶代替原来的线性弹簧与粘壶，得到一种适合橡胶材料在单轴作用下的非线性高弹-粘弹性本构模型。该模型可同时描述加载、卸载及应力松弛行为。模型将应力分解为弹性应力与粘性应力。弹性应力由Yeoh高弹性模型得到；粘性应力由加载及卸载过程的瞬时应力通过积分变换得到。此外考虑到应力松弛的作用，因此将粘性应力分解成两部分：一是在加载、卸载过程所用时间内由应变的改变所导致的粘性力；二是在该时间内由应力松弛所产生的反作用力。最后，将实验结果与该模型的计算结果进行对比，结果表明计算结果与实验结果具有良好的一致性，说明该本构模型可靠、合理。

An nonlinear visco-hyperelastic constitutive model for carbon black filled natural rubber materials

A nonlinear visco-hyperelastic constitutive model that can describe loading condition, unloading condition, and stress relaxation process simultaneously was developed for carbon black filled natural rubber materials under uniaxial deformation based on the modified Zener model. The linear dashpot and spring is replaced by nonlinear dashpot and spring. The total stress was decomposed into hyperelastic stress and viscoelastic stress. Hyperelastic stress was determined by the Yeoh model, and viscoelastic stress was determined by the instantaneous stress of loading and unloading conditions by integration method. Besides, considering the stress relaxation, viscoelastic stress was divided into two parts: one part represented the viscoelastic stress that obtained from loading and unloading conditions, the other part represented the reaction force of stress relaxation. Comparison between simulated data and experimental data was made to confirm the reliability of the proposed constitutive model. The result showed that the simulated data were in agreement with the experimental data, indicating the model was reliable and reasonable.