一种采用分数阶导数的新流变模型理论

提出了一种采用分数阶导数的新流变模型理论，它将分数微积分理论和经典模型理论的方法统一起来，使得模型的物理概念来明确，使已有分散的分数阶导数模型工作系统化，使问题的解法系统化，它克服了经典模型理论和实验结果吻合不好的严重缺点，仅采用很少几个元件组合就可获得很好的效果，利用这种模型理论，可望构造出各种与实验结果吻合很好的新固体和流体模型，这种新模型理论可以满意地描述物体的瞬时弹性、延迟弹性、粘性流、塑性等性能。

A New Rheological ModelTheory with Fractional Order Derivatives

A new theory of rheological model with fractional order derivatives is proposed in this paper, which unifies the methods of fractional calculus model and the classical model theory, and makes the physic conceptions of the model more clear. It makes the existing scattered individual works of fractional calculus models systemic and makes the methods of solution systemic. It overcomes the serious shortcoming of the classical model theory that the results cannot fit the experimental data very well. Excellent results can be obtained by using the combination of a few numbers of elements of the model. By using this kind of model theory, various models of solids and liquids may be constituted, which can fit the experimental data with high accuracy. Various properties of materials, such as instantaneous elasticity, delayed elasticity, viscous flow and plasticity, etc., can be described satisfactoriy by this new model theory.