张亚鹏^*， 高峰

（  中国矿业大学力学与建筑学院；  ）

摘要： 本文利用分数阶微积分的展开式建立多孔介质的本构模型。多孔介质由于在其形状上具有统计自相似性，因此其可以应用分数维进行描述，所以它可以用分数阶微积分进行描述。目前基于分数微积分的研究仅仅是在形式上的应用，没有太多数学的推导，许多也是经验性的公式，本文利用严格的数学工具进行推导，类似平面问题的推导，但此时采用分数阶展开进行描述，得到多孔介质的分数阶理论，并类似平面问题的位移解的推导得到多孔介质位移解得推导，为多孔介质在分数阶理论上提出一些重要的依据。
关键词： 分数阶微积分；本构模型；泰勒展开式；多孔介质

Zhang Yapeng^*， Gao Feng

（  School of Mechanics & Civil Engineering, China University Of Mining And Technology；  ）

Abstract： In this paper we use the tayor's series of fractional calculus to build the constitutive model of the Porous media, Due to its shape in porous media with statistical self-similarity, accordingly its application of fractal dimension can describe, so it can use fractional calculus are described herein，At present, based on the mechanics of fractional calculus study only limited in form of applied.there is not to much reduction on mathsematics,and many functions is experimential funchtions，Similar planar problem, but meanwhile the derivation of fractional launched by describing get porous medium of fractional theory, and similar to the throne of planar problem of porous media displacement is derived to deduction, a displacement for porous medium in fractional theory put forward some important basis.

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