A unified full field solution for indentation of an anisotropic piezoelectric half-plane by multiple rigid punches

References

• J. R. Willi, Hertzian contact of anisotropic bodies, J. Mech. Phys. Solids., vol. 14, no. 3, pp. 163–176, 1966.
   Web of Science ®Google Scholar
• C. W. Fan, and C. Hwu, Punch problems for an anisotropic elastic half-plane, ASME J. Appl. Mech., vol. 63, no. 1, pp. 69–76, 1996. DOI: 10.1115/1.2787211.
   Web of Science ®Google Scholar
• V. T. Nguyen, and C. Hwu, Boundary element method for two-dimensional frictional contact problems of anisotropic elastic solids, Eng. Anal. Bound. Elem., vol. 108, pp. 49–59, 2019. DOI: 10.1016/j.enganabound.2019.08.010.
   Web of Science ®Google Scholar
• V. T. Nguyen, and C. Hwu, Indentation by multiple rigid punches on two-dimensional anisotropic elastic or viscoelastic solids, Int. J. Mech. Sci., vol. 178, pp. 105595, 2020. DOI: 10.1016/j.ijmecsci.2020.105595.
   Web of Science ®Google Scholar
• Y. T. Zhou, and T. W. Kim, Closed-form solutions for the contact problem of anisotropic materials indented by two collinear punches, Int. J. Mech. Sci., vol. 89, pp. 332–343, 2014. DOI: 10.1016/j.ijmecsci.2014.09.017.
   Web of Science ®Google Scholar
• A. E. Giannakopoulos, and S. Suresh, Theory of indentation of piezoelectric materials, Acta. Mater., vol. 47, no. 7, pp. 2153–2164, 1999. DOI: 10.1016/S1359-6454(99)00076-2.
   Web of Science ®Google Scholar
• W. Q. Chen, and H. J. Ding, Indentation of a transversely isotropic piezoelectric half-space by a rigid sphere, Acta. Mech. Sol. Sin., vol. 12, pp. 114–120, 1999.
   Web of Science ®Google Scholar
• A. E. Giannakopoulos, Strength analysis of spherical indentation of piezoelectric materials, ASME J. Appl. Mech., vol. 67, no. 2, pp. 409–416, 2000. DOI: 10.1115/1.1304913.
   Web of Science ®Google Scholar
• W. Q. Chen, T. Shioya, and H. J. Ding, The elasto-electric field for a rigid conical punch on a transversely isotropic piezoelectric half-space, ASME J. Appl. Mech., vol. 66, no. 3, pp. 764–771, 1999. DOI: 10.1115/1.2791738.
   Web of Science ®Google Scholar
• S. V. Kalinin, E. Karapetian, M. Kachanov, Nanoelectromechanics of piezoresponse force microscopy, Phys. Rev. B., vol. 70, no. 18, pp. 18401, 2004.
   Web of Science ®Google Scholar
• W. Q. Chen, On piezoelastic contact problem for a smooth punch, Int. J. Solids. Struct., vol. 37, no. 16, pp. 2331–2340, 2000. DOI: 10.1016/S0020-7683(98)00307-2.
   Web of Science ®Google Scholar
• E. Karapetian, M. Kachanov, and S. V. Kalinin, Nanoelectromechanics of piezoelectric indentation and applications to scanning probe microscopy of ferroelectric materials, Philos. Mag., vol. 85, no. 10, pp. 1017–1051, 2005. DOI: 10.1080/14786430412331324680.
   Web of Science ®Google Scholar
• R. K. Zhu, W. J. Ming, Y. Y. Liu, K. Pan, and C. H. Lei, The intrinsic piezoresponse in piezoelectric medium under contact-mode piezoresponse force microscopy, Int. J. Mech. Sci., vol. 145, pp. 400–409, 2018. DOI: 10.1016/j.ijmecsci.2018.07.018.
   Web of Science ®Google Scholar
• T. J. Liu, and C. Zhang, Axisymmetric conducting indenter on a functionally graded piezoelectric coating, Int. J. Mech. Sci., vol. 115–116, pp. 34–44, 2016. DOI: 10.1016/j.ijmecsci.2016.06.008.
   Web of Science ®Google Scholar
• Z. R. Chen, and S. W. Yu, Micro-scale adhesive contact of a spherical rigid punch on a piezoelectric half-space, Compos. Sci. Technol., vol. 65, no. 9, pp. 1372–1381, 2005. DOI: 10.1016/j.compscitech.2004.12.007.
   Web of Science ®Google Scholar
• X. Guo, and F. Jin, A generalized JKR-model for two-dimensional adhesive contact of transversely isotropic piezoelectric half-space, Int. J. Solids. Struct., vol. 46, no. 20, pp. 3607–3619, 2009. DOI: 10.1016/j.ijsolstr.2009.06.012.
   Web of Science ®Google Scholar
• F. Jin, S. Yan, X. Guo, and X. Wang, On the contact and adhesion of a piezoelectric half-space under a rigid punch with an axisymmetric power-law profile, Mech. Mat., vol. 129, pp. 189–197, 2019. DOI: 10.1016/j.mechmat.2018.11.018.
   Web of Science ®Google Scholar
• E. Karapetian, M. Kachanov, and S. V. Kalinin, Stiffness relations for piezoelectric indentation of flat and non-flat punches of arbitrary planform: Applications to probing nanoelectromechanical properties of materials, J. Mech. Phys. Solids., vol. 57, no. 4, pp. 673–688, 2009. DOI: 10.1016/j.jmps.2009.01.002.
   Web of Science ®Google Scholar
• Y. T. Zhou, S. J. Pang, and Z. Zhong, Tribological behavior of a flat or circular stamp sliding on piezoelectric/piezomagnetic composites, Int. J. Appl. Mechanics., vol. 09, no. 02, pp. 1750018, 2017. DOI: 10.1142/S1758825117500181.
   Google Scholar
• A. Makagon, M. Kachanov, E. Karapetian, and S. V. Kalinin, Piezoelectric indentation of a flat circular punch accompanied by frictional sliding and applications to scanning probe microscopy, Int. J. Eng. Sci., vol. 47, no. 2, pp. 221–239, 2009. DOI: 10.1016/j.ijengsci.2008.07.010.
   Web of Science ®Google Scholar
• A. S. Vasiliev, Penetration of a spherical conductive punch into a piezoelectric half-space with a functionally graded coating, Int. J. Eng. Sci., vol. 142, pp. 230–241, 2019. DOI: 10.1016/j.ijengsci.2019.06.006.
   Web of Science ®Google Scholar
• E. A. Berndt, and I. Sevostianov, Action of a smooth flat charged punch on the piezoelectric half-space possessing symmetry of class 6, Int. J. Eng. Sci., vol. 103, pp. 77–96, 2016. DOI: 10.1016/j.ijengsci.2016.03.005.
   Web of Science ®Google Scholar
• Y. T. Zhou, and K. Y. Lee, Theory of moving contact of anisotropic piezoelectric materials via real fundamental solutions approach, Eur. J. Mech. A. Solid., vol. 35, pp. 22–36, 2012. DOI: 10.1016/j.euromechsol.2012.01.001.
   Web of Science ®Google Scholar
• Y. T. Zhou, and K. Y. Lee, Frictional contact of anisotropic piezoelectric materials indented by flat and semi-parabolic stamps, Arch Appl Mech., vol. 83, no. 1, pp. 73–95, 2013. DOI: 10.1007/s00419-012-0633-5.
   Web of Science ®Google Scholar
• Y. T. Zhou, and K. Y. Lee, Investigation of frictional sliding contact problems of triangular and cylindrical punches on monoclinic piezoelectric materials, Mech. Mat., vol. 69, no. 1, pp. 237–250, 2014. DOI: 10.1016/j.mechmat.2013.10.008.
   Web of Science ®Google Scholar
• Y. T. Zhou, and T. W. Kim, Two electrically-conducting stamps on the surface of piezoelectric materials, Int. J. Eng. Sci., vol. 81, pp. 146–162, 2014. DOI: 10.1016/j.ijengsci.2014.04.013.
   Web of Science ®Google Scholar
• L. R. Tembleque, A. Sáez, and M. H. Aliabadi, Indentation response of piezoelectric films under frictional contact, Int. J. Eng. Sci., vol. 107, pp. 36–53, 2016. DOI: 10.1016/j.ijengsci.2016.07.005.
   Web of Science ®Google Scholar
• H. Fan, K. Y. Sze, and W. Yang, Two-dimensional contact on a piezoelectric half-space, Int. J. Solids. Struct., vol. 33, no. 9, pp. 1305–1315, 1996. DOI: 10.1016/0020-7683(95)00098-4.
   Web of Science ®Google Scholar
• L. R. Tembleque, F. C. Buroni, and A. Sáez, 3D BEM for orthotropic frictional contact of piezoelectric bodies, Comput Mech., vol. 56, no. 3, pp. 491–502, 2015. DOI: 10.1007/s00466-015-1183-9.
   Web of Science ®Google Scholar
• X. Y. Li, and M. Z. Wang, On the anisotropic piezoelastic contact problem for an elliptical punch, Acta. Mech., vol. 186, no. 1-4, pp. 87–98, 2006. DOI: 10.1007/s00707-006-0365-0.
   Web of Science ®Google Scholar
• L. R. Tembleque, F. C. Buroni, and A. Sáez, Boundary element analysis of the frictionless indentation of piezoelectric films, Eur. J. Comput. Mech., vol. 25, no. 1-2, pp. 24–37, 2016. DOI: 10.1080/17797179.2016.1181030.
   Google Scholar
• İ. Çömez, Thermoelastic contact problem of a magneto-electro-elastic layer indented by a rigid insulating punch, Mech. Adv. Mater. Struct., pp. 1–15, 2021. DOI: 10.1080/15376494.2021.1995087.
   Web of Science ®Google Scholar
• H. F. Tiersten, Linear Piezoelectric Plate Vibrations, Springer, Boston, 1969.
   Google Scholar
• H. S. Tzou, H. J. Lee, and S. M. Arnold, Smart materials, precision sensors/actuators, smart structures, and structronic systems, Mech. Adv. Mater. Struct., vol. 11, no. 4–5, pp. 367–393, 2004. DOI: 10.1080/15376490490451552.
   Web of Science ®Google Scholar
• Z. Suo, C. M. Kuo, D. M. Barnett, and J. R. Willis, Fracture mechanics for piezoelectric ceramics, J. Mech. Phys. Solids., vol. 40, no. 4, pp. 739–765, 1992. DOI: 10.1016/0022-5096(92)90002-J.
   Web of Science ®Google Scholar
• Mitsutoshi. Abe, Toru. Ikeda, Masaaki. Koganemaru, and Noriyuki. Miyazaki, Stress intensity factor analysis of a three-dimensional interfacial corner between anisotropic piezoelectric multi-materials under several boundary conditions on the corner surfaces, Eng. Fract. Mech., vol. 171, pp. 1–21, 2017. DOI: 10.1016/j.engfracmech.2016.12.009.
   Web of Science ®Google Scholar
• J. A. Manyo, G. E. Ntamack, and L. Azrar, 3D-dynamic modeling of cross-ply magneto-electro-elastic laminates based on the pseudo-Stroh formalism, Mech. Adv. Mater. Struct., vol. 28, no. 13, pp. 1337–1354, 2021. DOI: 10.1080/15376494.2019.1668094.
   Web of Science ®Google Scholar
• C. Hwu, W. R. Chen, and T. S. Lo, Green’s function of anisotropic elastic solids with piezoelectric or magneto-electro-elastic inclusions, Int. J. Fract., vol. 215, no. 1–2, pp. 91–103, 2019. DOI: 10.1007/s10704-018-00338-6.
   Web of Science ®Google Scholar
• C. L. Hsu, C. Hwu, and Y. C. Shiah, Three-dimensional boundary element analysis for anisotropic elastic solids and its extension to piezoelectric and magnetoelectroelastic solids, Eng. Anal. Bound. Elem., vol. 98, pp. 265–280, 2019. DOI: 10.1016/j.enganabound.2018.10.022.
   Web of Science ®Google Scholar
• T. C. T. Ting, Anisotropic Elasticity: Theory and Applications, Oxford Science Publications, New York, 1996.
   Google Scholar
• C. Hwu, Anisotropic Elastic Plates, Springer, New York, 2010.
   Google Scholar
• N. I. Muskhelishvili, Some Basic Problem of the Mathematical Theory of Elasticity, Noordhoff Publisher, Groningen, 1954.
   Google Scholar
• N. N. Rogacheva, The Theory of Piezoelectric Shells and Plates, CRC Press, London, 1994.
   Google Scholar
• I. S. Sokolnikoff, Mathematical Theory of Elasticity, McGraw-Hill, New York, 1956.
   Google Scholar
• C. Hwu, Anisotropic Elasticity with Matlab, Springer, Cham, 2021.
   Google Scholar
• C. Hwu, and C. W. Fan, Sliding punches with or without friction along the surface of an anisotropic elastic half-plane, Q. J. Mech. Appl. Math., vol. 51, no. 1, pp. 159–177, 1998. DOI: 10.1093/qjmam/51.1.159.
   Google Scholar
• J. E. Dennis, and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Inc., Englewood Cliffs, 1996.
   Google Scholar
• C. Hwu, and T. L. Kuo, Interface corners in piezoelectric materials, Acta Mech., vol. 214, no. 1-2, pp. 95–110, 2010. DOI: 10.1007/s00707-010-0318-5.
   Web of Science ®Google Scholar
• L. L. Ke, J. Yang, S. Kitipornchai, and Y. S. Wang, Electro-mechanical frictionless contact behavior of a functionally graded piezoelectric layered half-plane under a rigid punch, Int. J. Solids. Struct., vol. 45, no. 11–12, pp. 3313–3333, 2008. DOI: 10.1016/j.ijsolstr.2008.01.028.
   Web of Science ®Google Scholar