0
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

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).

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Gerber, C. , and Lang, H. P. , 2007, “ How the Doors to the Nanoworld Were Opened,” Nat. Nanotechnol., 1(1), pp. 3–5. [CrossRef]
Kalinin, S. V. , and Gruverman, A. , 2007, Scanning Probe Microscopy: Electrical and Electromechanical Phenomena at the Nanoscale, Springer, New York. [CrossRef]
Meyer, E. , Hug, H. J. , and Bennewitz, R. , 2013, Scanning Probe Microscopy: The Lab on a Tip, Springer, New York.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef] [PubMed]
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. [CrossRef]
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. [CrossRef]
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.
Biot, M. A. , 1941, “ General Theory of Three‐Dimensional Consolidation,” J. Appl. Phys., 12(2), pp. 155–164. [CrossRef]
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.
Roeloffs, E. , 1996, “ Poroelastic Techniques in the Study of Earthquake-Related Hydrologic Phenomena,” Adv. Geophys., 37, pp. 135–195. [CrossRef]
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. [CrossRef] [PubMed]
Coussy, O. , 2004, Poromechanics, Wiley, Chichester, UK.
Fabrikant, V. I. , 1989, Applications of Potential Theory in Mechanics: A Selection of New Results, Kluwer, Dordrecht, The Netherlands.
Fabrikant, V. I. , 1991, Mixed Boundary Value Problems of Potential Theory and Their Applications in Engineering, Kluwer, Dordrecht, The Netherlands.
Chen, W. Q. , 2000, “ On Piezoelastic Contact Problem for a Smooth Punch,” Int. J. Solids Struct., 37(16), pp. 2331–2340. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Chen, W. Q. , 2001, “ On the General Solution for Piezothermoelasticity for Transverse Isotropy With Application,” ASME J. Appl. Mech., 67(4), pp. 705–711. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Barber, J. R. , 1971, “ The Effect of Thermal Distortion on Constriction Resistance,” Int. J. Heat Mass Transfer, 14(6), pp. 751–766. [CrossRef]
Barber, J. R. , 1971, “ The Solution of Heated Punch Problems by Point Source Methods,” Int. J. Eng. Sci., 9(12), pp. 1165–1170. [CrossRef]
ABAQUS, 2014, “ Abaqus Analysis User’s Guide,” Dassault Systèmes Simulia Corp., Vélizy-Villacoublay, France.
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.
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. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

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

Grahic Jump Location
Fig. 2

Dimensionless axial displacement w caused by q10

Grahic Jump Location
Fig. 3

Dimensionless axial stress σz caused by q10

Grahic Jump Location
Fig. 4

Dimensionless circumferential stress σϕ caused by q10

Grahic Jump Location
Fig. 5

Dimensionless porous pressure P caused by q10

Grahic Jump Location
Fig. 6

Contour of axial displacement w caused by q10

Grahic Jump Location
Fig. 7

Contour of axial stress σz caused by q10

Grahic Jump Location
Fig. 8

Dimensionless radial displacement u caused by w0

Grahic Jump Location
Fig. 9

Dimensionless axial displacement w caused by w0

Grahic Jump Location
Fig. 10

Dimensionless circumferential stress σϕ caused by w0

Grahic Jump Location
Fig. 11

Dimensionless shear stress τρz caused by w0

Grahic Jump Location
Fig. 12

Contour of axial displacement w caused by w0

Grahic Jump Location
Fig. 13

Contour of axial stress σz caused by w0

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In