黄屹澜^1，， 夏国展^1，， 陈伟球^{2，3，4，*}， 李翔宇^5，6，

（  1、浙江大学工程力学系， 浙江杭州，310027 ；       2、浙江大学工程力学系， 浙江杭州，310027；       3、浙江省软体机器人与智能器件研究重点实验室， 浙江杭州 310027；       4、浙江大学软物质科学研究中心(SMRC)， 浙江杭州 310027；       5、牵引动力国家重点实验室，四川成都 610031；       6、四川省应用力学与结构安全重点实验室，西南交通大学力学与工程学院， 四川成都 610031；  ）

摘要： 给出了横观各向同性热多孔材料半空间在刚性圆形平底压头作用下接触响应的三维精确解，考虑了弹性场、流场以及热场之间的相互耦合作用。基于用准调和函数表示的通解，采用势理论方法首先将原问题化为一组积分或积分-微分方程，导出了其解析解，然后利用势理论的最新成果进一步得到三维全场精确解。为了进行有效性验证，也开展了有限元模拟，所得结果与精确解一致。本文给出的精确解将为微观成像技术走向定量化应用提供重要的理论支撑。
关键词： 热多孔材料；接触问题；通解；势理论方法；三维精确解

Yilan Huang^1,， Guozhan Xia^1,， Weiqiu Chen^1,2,3,*， Xiangyu Li^4,5,

（  1、Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027；       2、Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou 310027；       3、Soft Matter Research Center, Zhejiang University, Hangzhou 310027；       4、State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu 610031；       5、Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031；  ）

Abstract： An exact solution to the three-dimensional contact problem of a rigid flat-ended circular cylindrical indenter punching onto a transversely isotropic thermoporoelastic half-space is presented. The couplings among the elastic, hydrostatic, and thermal fields are considered. A concise general solution to represent all field variables in terms of quasi-harmonic functions is employed. With the generalized potential theory method, the original problem is transformed to the one that is mathematically expressed by a set of integral or integro-differential equations, which can be solved exactly. By further making use of the new results in the potential theory method, all three-dimensional field variables are derived analytically and explicitly. For validation, finite element simulation of the contact response is also conducted, and an excellent agreement with the exact solution is obtained. The present solution can be used as a basis for quantitative application of microscale image formation techniques including thermal scanning probe microscopy and electrochemical strain microscopy.

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