Exact indentation response of a transversely isotropic thermoporoelastic half-space under a rigid circular cylindrical punch

• 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.

Keywords： thermoporoelastic medium contact problem general solution potential theory method three-dimensional exact solution