分数指数模型的热力学分析及其应用

本文论证了两种经典粘弹性固体模型的等价性并指出了其存在的问题。给出了热力学对分数指数模型 1]参数的限制条件。计算与实验结果比较表明:因为该模型具有适当多的参数,采用同一组参数可以做到同时与同一材料的蠕变和松弛试验结果很好吻合;并能做到松弛模量和蠕变柔量的Stieltjes卷积近似等于单位阶跃函数;在很宽广的频率范围内能同时很好地模拟真实材料的存储模量和损耗模量。由于其计算速度快,能与大多数真实材料的性能实验结果相拟合,可以广泛应用于工程实际中的粘弹性静力和动力问题的计算。

THERMODYNAMIC ANALYSIS AND APPLICATION OF FRACTIONAL EXPONENTIAL MODEL

In this paper, the equivalence of two classical viscoelastic models for solids is proved and the shortcomings of these models are pointed out. The restrictions of thermodynamics upon parameters of the fractional exponential model 1] are given. It is shown by the comparison of calculations and experiments that since the model contains proper parameters, the model can simultaneously fit the experimental data of the creep and the relaxation processes of the same material with high accuracy by using the same set of parameters; the Stieltjes convolution of the creep compliance and the relaxation modulus of the model can equal the unit-step function approximately and in considerable wide frequency range the model can fit the storage modulus and the dissipation modulus very well. Since it has the advantage of high calculating speed and it can fit the experimental results of most real materials, the model can be widely used in the analysis of static or dynamic viscoelastic problems in engineering.