单向应力条件下松弛时间率相关的非线性粘弹性本构模型

基于单向拉伸实验研究和内变量理论 ,提出了一种新的简单的一维非线性粘弹性本构关系 .对两种粘弹性材料 ,即高密度聚乙烯和聚丙烯进行了不同加载速率作用下的拉伸实验研究 ,实验结果表明 ,两种材料的应力应变关系与加载速率相关 ;对材料的应力应变实验数据进行拟合发现 ,材料的松弛时间具有很强的应变率相关性 ,当应变率发生数量级变化时 ,材料的松弛时间也发生数量级的变化 .采用内变量理论 ,导出了在单轴应力条件下松弛时间率相关的非线性粘弹性本构关系的迭代形式 ,并给出其收敛条件 .当采取一次迭代形式时 ,本构关系退化为松弛时间率相关的Maxwell模型 .数值拟合的结果表明 ,一次迭代形式的本构关系就可以很好地拟合和预测实验结果 .

NONLINEAR VISCOELASTIC CONSTITUTIVE RELATIONS BASED ON THE RATE SENSITIVE RELAXATION TIME UNDER THE CONDITION OF UNIAXIAL STRESS

A new simple nonlinear viscoelastic constitutive model under uniaxial tension is proposed by means of experimental method and internal-variable theory.The te nsion tests of two viscoelastic materials,i.e.,polypropylene (PP) and hig h-density polyethylene (HDPE),are carried out at different strain rate.The exp erimental date shows that the relation between stress and strain depends distin ctly on strain rate.The result of curve fitting for experiment data indicates th at the relaxation time of the materials is rate sensitive.When strain rate chan ges in orders of magnitude,the value of relaxation time varies in the same orde r.Under the condition of uniaxial stress,a new nonlinear viscoelastic constitut ive relation with iteration form is studied by adopting internal-variable theor y ,and the convergence condition is derived.If the degree of iteration is taken t o be one,then the corresponding constitutive relation reduces to Maxwell model wi t h rate related relaxation time. Such a nonlinear viscoelastic model can be used to fit and predict the constitutive relation of PP and HDPE perfectly.