在定义的3种分数阶微积分的基础上,给出了分数阶Laplace变换公式、基于分数阶微积分的软体元件及其本构方程.用软体元件替代整数阶Poynting-Thomson模型中的牛顿体元件,得到与之相对应的分数阶Poynting-Thomson模型.用分数阶Laplace变换推导出分数阶Poynting-Thomson模型的本构关系,并引入H-Fox特殊函数得出它的蠕变方程和松弛方程.通过一个研究实例,将分数阶Poynting-Thomson模型与整数阶Poynting-Thomson模型进行对比分析,结果表明分数阶Poynting-Thomson模型比一般的组合流变模型拟合精度高,能够克服整数阶模型在蠕变曲线拐点附近与试验数据不能很好吻合的弊端,反映了蠕变的非线性渐变过程,能更有效地描述岩土材料的流变本构特性.%Based on the definitions of three fractional calculus, Fractional Laplace transform formula, soft-matter element and its constitutive equations were presented. A fractional calculus Poynting-Thomson model was defined derived from the integer calculus Poynting-Thomson model, by substituting soft-matter element for the Newtonian element. The constitutive relations of fractional Poynting-Thomson model was abtained by fractional Laplace Transform, and creep equation and relaxation equation for the fractional calculus Poynting-Thomson model were derived by using the discrete inverse Laplace transform method and H-Fox function. It is shown by comparing the fitting results of the integer calculus Poynting-Thomson model and the fractional calculus Poynting-Thomson model, that the fractional calculus Poynting-Thomson gains the higher precision and overcomes the shortcoming of low fitting precision of the integer calculus Poynting-Thomson model at the inflexion of the creep curve. The fractional calculus Poynting-Thomson model may reflect the nonlinear creep process in gradual change, and may describe more efficiently rheological constitutive properties of geomatterials.
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