改进的黏弹材料应力松弛模型

为了用较少的参数准确描述粘弹材料的应力松弛实验数据,并且唯象解释松弛速率与应力的幂律关系,用假塑性粘壶与弹簧串联,得到改进的Maxwell模型。改进的Maxwell模型再与弹簧并联,给出改进的Zener模型。取定应变时,可得出松弛速率与应力满足幂律关系。求解本构方程得到它们的应力松弛函数。结果表明,常见的幂律型松弛可视为改进后模型的解,幂律函数的指数与反映材料非线性强弱的参数建立了关系,而Debye型松弛是幂律型松弛的一种极限情况。用给出的松弛函数对聚异丁烯的松弛模量进行了研究,拟合过程简单,准确度较高。

The modified relaxation models for viscoelastic materials

Based on pseudoplastic dashpots, the modified Maxwell model and modified Zener model were discussed. Their relaxation functions show that the common power-law relaxation can be seen as those modified models and the Debye relaxation is the limit case of power-law relaxation. Moreover, the relaxation rate and stress exhibite power-law relation. The relaxation modulus of polyisobutylene was studied by modified power-law relaxation function. The method proposed may be useful in various fields of relaxation theory.