非线性粘弹性本构关系及其应用

给出了三维Ｓｔｉｅｌｔｊｅｓ卷积形式的简化非线性粘弹性本构关系和三维本构关系的弹性回复对应原理，采用简化非线怀本构关系和本构关系的弹性回复对应原理，通过对改性聚丙烯的准静态实验，提出了一种寻求非线性瞬时弹性应力应变关系的新方法；预测了不同应变率情况下的非线性粘弹性应力应变曲线；证明了简化非线性粘弹性本构关系对聚合物一类材料的适用性；表明了应力应变曲线的应变率相依性是遗传性时间效应的直接结果，从而非线性粘弹性本构关系中不必包括应变率作为独立变量。

Nonlinear Viscoelastic Constitutive Theory and Its Applications

Simplified three-dimensional nonlinear viscoelastic constitutive relations in the form of Stieltjes convolution and the three-dimensional elasticity recovery correspondence principle in the constitutive relations are given. By using the simplified constitutive relations and the elasticity recovery correspondence principle, through the quasi-static experiments of modified polypropylene, a new approach for finding the instantaneous elastic stress-strain relation is proposed. The nonlinear viscoelastic stress-strain curves under different strain rates are predicted. The practicability of simplified nonlinear viscoelastic constitutive relations for a class of materials as polymers is verified. It is shown that the dependence of the strain rate of the stress-strain curves under different strain rates is the direct result of the hereditary time effect, so that it is unnecessary to include the strain rate in the constitutive relations as an independent variable.