分数算子描述的粘弹性材料的本构关系研究

Study on Constitutive Relation of Viscoelastic Material Described by Fractional Operator

从分数导数的定义出发,提出了在经典粘弹性模型理论中采用Abel粘壶取代传统牛顿粘壶的新观点。将有机硅高分子材料在MTS831.10材料试验机上进行动态力学行为试验,对试验结果分别用经典粘弹性模型和分数导数模型进行拟合。结果表明,分数导数Kelvin模型可以同时精确地拟合高分子材料的存储模量和损耗模量随频率变化的曲线,而且其形式简单、统一,在计算过程中需要调整的参数很少。

From the definition of fractional order derivative, the new idea that replacing the traditional Newton dashpot with Abel dashpot is proposed here. The experiment of dynamic behavior of solid polymers in MTS831.10 Testing System has been carried out. And the data of test has also been fitted by traditional viscoelastic model and fractional Kelvin model respectively. The analysis results show that the fractional Kelvin model could accurately simulate the curves of storage modulus and dissipation modulus of solid polymers, moreover, it has a simple and uniform form, only a few of the parameters should be adjusted in the calculation process.