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).

References

References
1.
Gerber
,
C.
, and
Lang
,
H. P.
,
2007
, “
How the Doors to the Nanoworld Were Opened
,”
Nat. Nanotechnol.
,
1
(
1
), pp.
3
5
.
2.
Kalinin
,
S. V.
, and
Gruverman
,
A.
,
2007
,
Scanning Probe Microscopy: Electrical and Electromechanical Phenomena at the Nanoscale
,
Springer
,
New York
.
3.
Meyer
,
E.
,
Hug
,
H. J.
, and
Bennewitz
,
R.
,
2013
,
Scanning Probe Microscopy: The Lab on a Tip
,
Springer
,
New York
.
4.
Li
,
J.
,
Li
,
J. F.
,
Yu
,
Q.
,
Chen
,
Q. N.
, and
Xie
,
S.
,
2015
, “
Strain-Based Scanning Probe Microscopies for Functional Materials, Biological Structures, and Electrochemical Systems
,”
J. Materiomics
,
1
(1), pp.
3
21
.
5.
Hammiche
,
A.
,
Bozec
,
L.
,
Conroy
,
M.
,
Pollock
,
H. M.
,
Mills
,
G.
,
Weaver
,
J. M. R.
, and
Song
,
M.
,
2000
, “
Highly Localized Thermal, Mechanical, and Spectroscopic Characterization of Polymers Using Miniaturized Thermal Probes
,”
J. Vac. Sci. Technol. B
,
18
(
3
), pp.
1322
1332
.
6.
Nelson
,
B. A.
, and
King
,
W. P.
,
2007
, “
Measuring Material Softening With Nanoscale Spatial Resolution Using Heated Silicon Probes
,”
Rev. Sci. Instrum.
,
78
(
2
), p.
023702
.
7.
Jesse
,
S.
,
Kumar
,
A.
,
Arruda
,
T. M.
,
Kim
,
Y.
,
Kalinin
,
S. V.
, and
Ciucci
,
F.
,
2012
, “
Electrochemical Strain Microscopy: Probing Ionic and Electrochemical Phenomena in Solids at the Nanometer Level
,”
MRS Bull.
,
37
(
7
), pp.
651
658
.
8.
Eshghinejad
,
A.
,
Esfahani
,
E. N.
,
Wang
,
P.
,
Xie
,
S.
,
Geary
,
T. C.
,
Adler
,
S. B.
, and
Li
,
J. Y.
,
2016
, “
Scanning Thermo-Ionic Microscopy for Probing Local Electrochemistry at the Nanoscale
,”
J. Appl. Phys.
,
119
, p.
205110
.
9.
Esfahani
,
E. N.
,
Eshghinejad
,
A.
,
Ou
,
Y.
,
Zhao
,
J. J.
,
Adler
,
S.
, and
Li
,
J.
,
2017
, “
Scanning Thermo-Ionic Microscopy: Probing Nanoscale Electrochemistry Via Thermal Stress-Induced Oscillation
,”
arXiv:1703.06184
.
10.
Biot
,
M. A.
,
1941
, “
General Theory of Three‐Dimensional Consolidation
,”
J. Appl. Phys.
,
12
(
2
), pp.
155
164
.
11.
Biot
,
M. A.
,
1956
, “
General Solutions of the Equations of Elasticity and Consolidation for a Porous Material
,”
ASME J. Appl. Mech.
,
23
(
1
), pp.
91
96
.
12.
Roeloffs
,
E.
,
1996
, “
Poroelastic Techniques in the Study of Earthquake-Related Hydrologic Phenomena
,”
Adv. Geophys.
,
37
, pp.
135
195
.
13.
Smit
,
T. H.
,
Huyghe
,
J. M.
, and
Cowin
,
S. C.
,
2002
, “
Estimation of the Poroelastic Parameters of Cortical Bone
,”
J. Biomech.
,
35
(
6
), pp.
829
835
.
14.
Coussy
,
O.
,
2004
,
Poromechanics
,
Wiley
, Chichester, UK.
15.
Fabrikant
,
V. I.
,
1989
,
Applications of Potential Theory in Mechanics: A Selection of New Results
,
Kluwer
,
Dordrecht, The Netherlands
.
16.
Fabrikant
,
V. I.
,
1991
,
Mixed Boundary Value Problems of Potential Theory and Their Applications in Engineering
,
Kluwer
,
Dordrecht, The Netherlands
.
17.
Chen
,
W. Q.
,
2000
, “
On Piezoelastic Contact Problem for a Smooth Punch
,”
Int. J. Solids Struct.
,
37
(
16
), pp.
2331
2340
.
18.
Chen
,
W. Q.
,
Pan
,
E. N.
,
Wang
,
H. M.
, and
Zhang
,
C. Z.
,
2010
, “
Theory of Indentation on Multiferroic Composite Materials
,”
J. Mech. Phys. Solids
,
58
(
10
), pp.
1524
1551
.
19.
Li
,
X. Y.
,
Wu
,
F.
,
Jin
,
X.
, and
Chen
,
W. Q.
,
2015
, “
3D Coupled Field in a Transversely Isotropic Magneto-Electro-Elastic Half Space Punched by an Elliptic Indenter
,”
J. Mech. Phys. Solids
,
75
, pp.
1
44
.
20.
Chen
,
W. Q.
, and
Ding
,
H. J.
,
2004
, “
Potential Theory Method for 3D Crack and Contact Problems of Multi-Field Coupled Media: A Survey
,”
J. Zhejiang Univ., Sci., A
,
5
(
9
), pp.
1009
1021
.
21.
Chen
,
W. Q.
,
2015
, “
Some Recent Advances in 3D Crack and Contact Analysis of Elastic Solids With Transverse Isotropy and Multi-Field Coupling
,”
Acta Mech. Sin.
,
31
(
5
), pp.
601
626
.
22.
Karapetian
,
E.
, and
Kalinin
,
S. V.
,
2013
, “
Indentation of a Punch With Chemical or Heat Distribution at Its Base Into Transversely Isotropic Half-Space: Application to Local Thermal and Electrochemical Probes
,”
J. Appl. Phys.
,
113
(
18
), p.
187201
.
23.
Yang
,
J.
, and
Jin
,
X.
,
2014
, “
Indentation of a Flat Circular Punch With Uniform Heat Flux at Its Base Into Transversely Isotropic Magneto-Electro-Thermo-Elastic Half Space
,”
J. Appl. Phys.
,
115
(
8
), p.
083516
.
24.
Wang
,
Z. P.
,
Wang
,
T.
,
Li
,
P. D.
,
Li
,
X. Y.
, and
Chen
,
W. Q.
,
2016
, “
Three-Dimensional Fundamental Thermo-Elastic Solutions Applied to Contact Problems
,”
J. Appl. Phys.
,
120
(
17
), p.
174904
.
25.
Ashida
,
F.
,
Noda
,
N.
, and
Okumura
,
I. A.
,
1993
, “
General Solution Technique for Transient Thermoelasticity of Transversely Isotropic Solids in Cylindrical Coordinates
,”
Acta Mech.
,
101
(
1–4
), pp.
215
230
.
26.
Ding
,
H. J.
,
Guo
,
F. L.
, and
Hou
,
P. F.
,
2000
, “
A General Solution for Piezothermoelasticity of Transversely Isotropic Piezoelectric Materials and Its Applications
,”
Int. J. Eng. Sci.
,
38
(
13
), pp.
1415
1440
.
27.
Chen
,
W. Q.
,
2001
, “
On the General Solution for Piezothermoelasticity for Transverse Isotropy With Application
,”
ASME J. Appl. Mech.
,
67
(
4
), pp.
705
711
.
28.
Li
,
X. Y.
,
Chen
,
W. Q.
, and
Wang
,
H. Y.
,
2010
, “
General Steady-State Solutions for Transversely Isotropic Thermoporoelastic Media in Three Dimensions and Its Application
,”
Eur. J. Mech. A
,
29
(
3
), pp.
317
326
.
29.
Wang
,
J. H.
,
Chen
,
C. Q.
, and
Lu
,
T. J.
,
2008
, “
Indentation Responses of Piezoelectric Films
,”
J. Mech. Phys. Solids
,
56
(
12
), pp.
3331
3351
.
30.
Wu
,
Y. F.
,
Yu
,
H. Y.
, and
Chen
,
W. Q.
,
2012
, “
Mechanics of Indentation for Piezoelectric Thin Films on Elastic Substrate
,”
Int. J. Solids Struct.
,
49
(
1
), pp.
95
110
.
31.
Barber
,
J. R.
,
1971
, “
The Effect of Thermal Distortion on Constriction Resistance
,”
Int. J. Heat Mass Transfer
,
14
(
6
), pp.
751
766
.
32.
Barber
,
J. R.
,
1971
, “
The Solution of Heated Punch Problems by Point Source Methods
,”
Int. J. Eng. Sci.
,
9
(
12
), pp.
1165
1170
.
33.
ABAQUS
,
2014
, “
Abaqus Analysis User’s Guide
,” Dassault Systèmes Simulia Corp., Vélizy-Villacoublay, France.
34.
Abousleiman
,
Y.
, and
Ekbote
,
S.
,
2002
,
Porothermoelasticity in Transversely Isotropic Porous Materials
,”
IUTAM Symposium on Theoretical and Numerical Methods in Continuum Mechanics of Porous Materials
, Stuttgart, Germany, Sept. 5–10, pp.
145
152
.
35.
Kanj
,
M.
, and
Abousleiman
,
Y.
,
2005
, “
Porothermoelastic Analyses of Anisotropic Hollow Cylinders With Applications
,”
Int. J. Numer. Anal. Methods Geomech.
,
29
(
2
), pp.
103
126
.
You do not currently have access to this content.