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Research Papers

# Indentation of a Transversely Isotropic Thermoporoelastic Half-Space by a Rigid Circular Cylindrical Punch

[+] Author and Article Information
Yilan Huang, Guozhan Xia

Department of Engineering Mechanics,
Zhejiang University,
Hangzhou 310027, China

Weiqiu Chen

Department of Engineering Mechanics,
Zhejiang University,
Hangzhou 310027, China;
State Key Laboratory of CAD & CG,
Zhejiang University,
Hangzhou 310058, China;
Key Laboratory of Soft Machines and
Smart Devices of Zhejiang Province,
Zhejiang University,
Hangzhou 310027, China;
Soft Matter Research Center,
Zhejiang University,
Hangzhou 310027, China

Xiangyu Li

State Key Laboratory of Traction Power,
Southwest Jiaotong University,
Chengdu 610031, China;
Applied Mechanics and Structure Safety Key
Laboratory of Sichuan Province,
School of Mechanics and Engineering,
Southwest Jiaotong University,
Chengdu 610031, China

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received May 16, 2017; final manuscript received August 18, 2017; published online September 8, 2017. Editor: Yonggang Huang.

J. Appl. Mech 84(11), 111001 (Sep 08, 2017) Paper No: JAM-17-1256; doi: 10.1115/1.4037739 History: Received May 16, 2017; Revised August 18, 2017

## Abstract

Exact solutions to the three-dimensional (3D) contact problem of a rigid flat-ended circular cylindrical indenter punching onto a transversely isotropic thermoporoelastic half-space are presented. The couplings among the elastic, hydrostatic, and thermal fields are considered, and two different sets of boundary conditions are formulated for two different cases. We use a concise general solution to represent all the field variables in terms of potential functions and transform the original problem to the one that is mathematically expressed by integral (or integro-differential) equations. The potential theory method is extended and applied to exactly solve these integral equations. As a consequence, all the physical quantities of the coupling fields are derived analytically. To validate the analytical solutions, we also simulate the contact behavior by using the finite element method (FEM). An excellent agreement between the analytical predictions and the numerical simulations is obtained. Further attention is also paid to the discussion on the obtained results. The present solutions can be used as a theoretical reference when practically applying microscale image formation techniques such as thermal scanning probe microscopy (SPM) and electrochemical strain microscopy (ESM).

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## Figures

Fig. 1

Schematic diagram of a flat-ended indenter in frictionless contact with a transversely isotropic thermoporoelastic half-space

Fig. 2

Dimensionless axial displacement w caused by q10

Fig. 3

Dimensionless axial stress σz caused by q10

Fig. 4

Dimensionless circumferential stress σϕ caused by q10

Fig. 5

Dimensionless porous pressure P caused by q10

Fig. 6

Contour of axial displacement w caused by q10

Fig. 7

Contour of axial stress σz caused by q10

Fig. 8

Dimensionless radial displacement u caused by w0

Fig. 9

Dimensionless axial displacement w caused by w0

Fig. 10

Dimensionless circumferential stress σϕ caused by w0

Fig. 11

Dimensionless shear stress τρz caused by w0

Fig. 12

Contour of axial displacement w caused by w0

Fig. 13

Contour of axial stress σz caused by w0

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