有限变形下橡胶材料非线性高弹-粘弹性本构模型

A Nonlinear Hyper-Viscoelastic Constitutive Model for Rubber Material with Finite Strain

基于唯象学原理提出一种适用于橡胶材料在有限应变条件下的非线性高弹-粘弹性本构模型。该模型将应力拆分为两部分:基于Yeoh模型计算得到的高弹性应力和由Boltzmann叠加原理计算得到的带有率依赖性的粘弹性应力。该本构模型中具有应变依赖性的高弹性应力通过修正Zener模型中的非线性弹簧表示,具有时间及应变依赖性的粘弹性应力通过修正Zener模型中的非线性Maxwell模型表示。利用此本构模型模拟不同应变下的拉伸、回复、应力松弛及多步松弛的复杂加载过程,与试验结果的吻合性良好,说明该本构模型合理、可靠。

A nonlinear hyper-viscoelastic constitutive model for rubber Material with finite strain was proposed. The total stress was divided into two parts：the first part was hyperelastic stress calculated by Yeoh hyperelastic model,and the second part was rate dependent viscoelastic stress calculated by Boltzmann superposition principle. The hyperelastic stress depended strain was described by the nonlinear spring in the modified Zener model,while the viscoelastic stress depended rate and pre-deformation was characterized by the nonlinear dashpot in the modified Zener model. Loading and unloading uniaxial tensile test,stress relaxation test,and multistep relaxation test were used to verify the effectiveness and reliability of the proposed constitutive model. A good agreement between test data and calculated data indicated that the model was reliable and reasonable.