Interaction between a punch and an arbitrary crack or inclusion in a transversely isotropic half-space

Fabrikant, I.; Karapetian, E.; Kalinin, S. V.

doi:10.1007/s00033-017-0894-5

Title: Interaction between a punch and an arbitrary crack or inclusion in a transversely isotropic half-space

Journal Article · Sat Dec 09 00:00:00 EST 2017 · Zeitschrift fuer Angewandte Mathematik und Physik

DOI:https://doi.org/10.1007/s00033-017-0894-5· OSTI ID:1426573

Fabrikant, I. ^[1]; Karapetian, E. ^[2]; Kalinin, S. V. ^[3]

Fabrikant-Research, Montreal, QC (Canada)
Suffolk Univ., Boston, MA (United States). Dept. of Mathematics and Computer Science
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Center for Nanophase Materials Science (CNMS)

Here, we consider the problem of an arbitrary shaped rigid punch pressed against the boundary of a transversely isotropic half-space and interacting with an arbitrary flat crack or inclusion, located in the plane parallel to the boundary. The set of governing integral equations is derived for the most general conditions, namely the presence of both normal and tangential stresses under the punch, as well as general loading of the crack faces. In order to verify correctness of the derivations, two different methods were used to obtain governing integral equations: generalized method of images and utilization of the reciprocal theorem. Both methods gave the same results. Axisymmetric coaxial case of interaction between a rigid inclusion and a flat circular punch both centered along the z-axis is considered as an illustrative example. Most of the final results are presented in terms of elementary functions.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1426573

Journal Information:: Zeitschrift fuer Angewandte Mathematik und Physik, Vol. 69, Issue 1; ISSN 0044-2275

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 1 work

Citation information provided by
Web of Science

References (37)

Stiffness relations for piezoelectric indentation of flat and non-flat punches of arbitrary planform: Applications to probing nanoelectromechanical properties of materials Karapetian, Edgar; Kachanov, Mark; Kalinin, Sergei V. Journal of the Mechanics and Physics of Solids, Vol. 57, Issue 4 https://doi.org/10.1016/j.jmps.2009.01.002	journal	April 2009
Sub-surface AFM imaging using tip generated stress and electric fields Cadena, Maria J.; Chen, Yuhang; Reifenberger, Ronald G. Applied Physics Letters, Vol. 110, Issue 12 https://doi.org/10.1063/1.4977837	journal	March 2017
Simultaneous elastic and electromechanical imaging by scanning probe microscopy: Theory and applications to ferroelectric and biological materials Shin, J.; Rodriguez, B. J.; Baddorf, A. P. Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures, Vol. 23, Issue 5 https://doi.org/10.1116/1.2052714	journal	January 2005
Indentation induced mechanical and electrical response in ferroelectric crystal investigated by acoustic mode AFM Yu, H. F.; Zeng, H. R.; Ma, X. D. physica status solidi (a), Vol. 202, Issue 2 https://doi.org/10.1002/pssa.200409082	journal	January 2005
Single- and Multi-Frequency Detection of Surface Displacements via Scanning Probe Microscopy Romanyuk, Konstantin; Luchkin, Sergey Yu.; Ivanov, Maxim Microscopy and Microanalysis, Vol. 21, Issue 1 https://doi.org/10.1017/S1431927614013622	journal	January 2015
Determination of shear stiffness based on thermal noise analysis in atomic force microscopy: Passive overtone microscopy Drobek, Tanja; Stark, Robert W.; Heckl, Wolfgang M. Physical Review B, Vol. 64, Issue 4 https://doi.org/10.1103/PhysRevB.64.045401	journal	June 2001
Advances in quantitative nanoscale subsurface imaging by mode-synthesizing atomic force microscopy Vitry, P.; Bourillot, E.; Plassard, C. Applied Physics Letters, Vol. 105, Issue 5 https://doi.org/10.1063/1.4892467	journal	August 2014
The band excitation method in scanning probe microscopy for rapid mapping of energy dissipation on the nanoscale Jesse, Stephen; Kalinin, Sergei V.; Proksch, Roger Nanotechnology, Vol. 18, Issue 43 https://doi.org/10.1088/0957-4484/18/43/435503	journal	September 2007
Acoustic microscopy by atomic force microscopy Rabe, U.; Arnold, W. Applied Physics Letters, Vol. 64, Issue 12 https://doi.org/10.1063/1.111869	journal	March 1994
Local Elasticity Response in Ferroelectric Crystals Studied by Afm-Based Novel Probe Techniques Yu, H. F.; Zeng, H. R.; Ding, A. L. Integrated Ferroelectrics, Vol. 78, Issue 1 https://doi.org/10.1080/10584580600663565	journal	November 2006
Piezoelectric nanoindentation Rar, Andrei; Pharr, G. M.; Oliver, W. C. Journal of Materials Research, Vol. 21, Issue 3 https://doi.org/10.1557/jmr.2006.0081	journal	March 2006
Nanoelectromechanics of polarization switching in piezoresponse force microscopy Kalinin, S. V.; Gruverman, A.; Rodriguez, B. J. Journal of Applied Physics, Vol. 97, Issue 7 https://doi.org/10.1063/1.1866483	journal	April 2005
Enhancing higher harmonics of a tapping cantilever by excitation at a submultiple of its resonance frequency Balantekin, M.; Atalar, A. Physical Review B, Vol. 71, Issue 12 https://doi.org/10.1103/PhysRevB.71.125416	journal	March 2005
Elastic phase response of silica nanoparticles buried in soft matter Tetard, Laurene; Passian, Ali; Lynch, Rachel M. Applied Physics Letters, Vol. 93, Issue 13 https://doi.org/10.1063/1.2987460	journal	September 2008
Local thermomechanical characterization of phase transitions using band excitation atomic force acoustic microscopy with heated probe Jesse, S.; Nikiforov, M. P.; Germinario, L. T. Applied Physics Letters, Vol. 93, Issue 7 https://doi.org/10.1063/1.2965470	journal	August 2008
Dual-frequency resonance-tracking atomic force microscopy Rodriguez, Brian J.; Callahan, Clint; Kalinin, Sergei V. Nanotechnology, Vol. 18, Issue 47, Article No. 475504 https://doi.org/10.1088/0957-4484/18/47/475504	journal	October 2007
Mode-synthesizing atomic force microscopy for 3D reconstruction of embedded low-density dielectric nanostructures Vitry, Pauline; Bourillot, Eric; Plassard, Cédric Nano Research, Vol. 8, Issue 7 https://doi.org/10.1007/s12274-015-0728-8	journal	May 2015
Modeling the effect of subsurface interface defects on contact stiffness for ultrasonic atomic force microscopy Sarioglu, A. F.; Atalar, A.; Degertekin, F. L. Applied Physics Letters, Vol. 84, Issue 26 https://doi.org/10.1063/1.1764941	journal	June 2004
An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments Oliver, W. C.; Pharr, G. M. Journal of Materials Research, Vol. 7, Issue 06, p. 1564-1583 https://doi.org/10.1557/JMR.1992.1564	journal	June 1992
High-resolution characterization of piezoelectric ceramics by ultrasonic scanning force microscopy techniques Rabe, U.; Kopycinska, M.; Hirsekorn, S. Journal of Physics D: Applied Physics, Vol. 35, Issue 20 https://doi.org/10.1088/0022-3727/35/20/323	journal	October 2002
Nanoelectromechanics of piezoresponse force microscopy Kalinin, Sergei V.; Karapetian, Edgar; Kachanov, Mark Physical Review B, Vol. 70, Issue 18 https://doi.org/10.1103/PhysRevB.70.184101	journal	November 2004
Relationship between direct and converse piezoelectric effect in a nanoscale electromechanical contact Kalinin, Sergei V.; Mirman, Boris; Karapetian, Edgar Physical Review B, Vol. 76, Issue 21 https://doi.org/10.1103/PhysRevB.76.212102	journal	December 2007
Piezoelectric indentation of a flat circular punch accompanied by frictional sliding and applications to scanning probe microscopy Makagon, Arty; Kachanov, Mark; Karapetian, Edgar International Journal of Engineering Science, Vol. 47, Issue 2 https://doi.org/10.1016/j.ijengsci.2008.07.010	journal	February 2009
Resolution theory, and static and frequency-dependent cross-talk in piezoresponse force microscopy Jesse, S.; Guo, S.; Kumar, A. Nanotechnology, Vol. 21, Issue 40 https://doi.org/10.1088/0957-4484/21/40/405703	journal	September 2010
Band Excitation in Scanning Probe Microscopy: Recognition and Functional Imaging Jesse, S.; Vasudevan, R. K.; Collins, L. Annual Review of Physical Chemistry, Vol. 65, Issue 1 https://doi.org/10.1146/annurev-physchem-040513-103609	journal	April 2014
Nanoelectromechanics of piezoelectric indentation and applications to scanning probe microscopies of ferroelectric materials Karapetian *, E.; Kachanov, M.; Kalinin, S. V. Philosophical Magazine, Vol. 85, Issue 10 https://doi.org/10.1080/14786430412331324680	journal	April 2005
Indentation of spherical and conical punches into piezoelectric half-space with frictional sliding: Applications to scanning probe microscopy Makagon, Arty; Kachanov, Mark; Kalinin, Sergei V. Physical Review B, Vol. 76, Issue 6 https://doi.org/10.1103/PhysRevB.76.064115	journal	August 2007
Local Elasticity Response in Ferroelectric Crystals Studied by Afm-Based Novel Probe Techniques Yu, H. F.; Zeng, H. R.; Ding, A. L. Integrated Ferroelectrics, Vol. 73, Issue 1 https://doi.org/10.1080/10584580500414168	journal	September 2005
Elastic-property measurements of ultrathin films using atomic force acoustic microscopy Kopycinska-Müller, M.; Geiss, R. H.; Müller, J. Nanotechnology, Vol. 16, Issue 6 https://doi.org/10.1088/0957-4484/16/6/013	journal	April 2005
Visualization of Au Nanoparticles Buried in a Polymer Matrix by Scanning Thermal Noise Microscopy Yao, Atsushi; Kobayashi, Kei; Nosaka, Shunta Scientific Reports, Vol. 7, Issue 1 https://doi.org/10.1038/srep42718	journal	February 2017
The emergence of multifrequency force microscopy Garcia, Ricardo; Herruzo, Elena T. Nature Nanotechnology, Vol. 7, Issue 4 https://doi.org/10.1038/nnano.2012.38	journal	April 2012
New modes for subsurface atomic force microscopy through nanomechanical coupling Tetard, L.; Passian, A.; Thundat, T. Nature Nanotechnology, Vol. 5, Issue 2, p. 105-109 https://doi.org/10.1038/nnano.2009.454	journal	December 2009
Atomic force acoustic microscopy methods to determine thin-film elastic properties Hurley, D. C.; Shen, K.; Jennett, N. M. Journal of Applied Physics, Vol. 94, Issue 4 https://doi.org/10.1063/1.1592632	journal	August 2003
Point force and generalized point source on the surface of semi-infinite transversely isotropic material Karapetian, Edgar; Kalinin, Sergei V. Journal of Applied Physics, Vol. 110, Issue 5 https://doi.org/10.1063/1.3624799	journal	September 2011
Probing the temperature dependence of the mechanical properties of polymers at the nanoscale with band excitation thermal scanning probe microscopy Nikiforov, M. P.; Jesse, S.; Morozovska, A. N. Nanotechnology, Vol. 20, Issue 39 https://doi.org/10.1088/0957-4484/20/39/395709	journal	September 2009
Contact stiffness of finite size subsurface defects for atomic force microscopy: Three-dimensional finite element modeling and experimental verification Parlak, Zehra; Levent Degertekin, F. Journal of Applied Physics, Vol. 103, Issue 11 https://doi.org/10.1063/1.2936881	journal	June 2008
Nanoelectromechanics of Piezoresponse Force Microscopy: Contact Properties, Fields Below the Surface and Polarization Switching Kalinin, S. V.; Shin, Junsoo; Kachanov, M. MRS Proceedings, Vol. 784 https://doi.org/10.1557/PROC-784-C2.6	journal	January 2003

Cited By (1)

Boundary element analysis of 3D shell‐like rigid electrically conducting inclusions in anisotropic thermomagnetoelectroelastic solids Pasternak, Iaroslav; Sulym, Heorhiy; Ilchuk, Nataliia ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 99, Issue 7 https://doi.org/10.1002/zamm.201800319	journal	May 2019

Similar Records

Quantitative Characterization of Impacts of Coupled Geomechanics and Flow on Safe and Permanent Geological Storage of CO₂ in Fractured Aquifers

Technical Report · Wed Dec 19 00:00:00 EST 2018 · OSTI ID:1426573

Winterfeld, Philip; Wu, Yu-Shu; Kneafsey, Timothy

Interaction between a cylindrical crack and coaxial rigid cylindrical inclusion

Conference · Sun Dec 31 00:00:00 EST 1995 · OSTI ID:1426573

Demir, I

Free convective heat transfer over a nonisothermal body of arbitrary shape embedded in a fluid-saturated porous medium

Journal Article · Sun Feb 01 00:00:00 EST 1987 · Journal of Heat Transfer (Transcations of the ASME (American Society of Mechanical Engineers), Series C); (United States) · OSTI ID:1426573

Nakayama, A; Koyama, H

Related Subjects

97 MATHEMATICS AND COMPUTING

Title: Interaction between a punch and an arbitrary crack or inclusion in a transversely isotropic half-space

Citation Formats

References (37)

Cited By (1)

Similar Records

Related Subjects