Quasistatic Electro-Elastic Contact Modeling Using the Boundary Element Method

Article Preview

Abstract:

A three-dimensional boundary element methodology to study frictionless indentation response of piezoelectric (PE) materials is presented. The boundary element method (BEM) is used in order to compute the electro-elastic influence coeffcients of fully anisotropic piezoelectric solids. The proposed contact formulation is based on the augmented Lagrangian method presented in [33, 34, 35] and makes it possible to consider piezoelectric materials under different mechanical and electrical boundary conditions (i.e. insulating indenter and conducting indenter). The methodology is validated by comparison with theoretical solutions presented in the literature.

You might also be interested in these eBooks

Info:

Periodical:

Pages:

185-196

Citation:

Online since:

February 2016

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2016 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

[1] W.G. Cady, Piezoelectricity, Mc Graw Hill, New York, (1946).

Google Scholar

[2] T. Ikeda, Fundamentals of Piezoelectricity, Oxford Science Publications, Oxford, (1996).

Google Scholar

[3] H.J. Ding, W.Q. Chen, Three Dimensional Problems of Piezoelasticity, Nova Science Publishers, New York, (2001).

Google Scholar

[4] J. Yang, J.S. Yang, An Introduction to the Theory of Piezoelectricity, Springer, New York, (2005).

Google Scholar

[5] A. Saigal, A.E. Giannakopoulos, H.E. Pettermann, S. Suresh, Electrical response during indentation of a 1-3 piezoelectric ceramic-polymer composite, J. Appl. Phys. 86 (1999) 603-6.

DOI: 10.1063/1.370773

Google Scholar

[6] U. Ramamurty, S. Sridhar, A.E. Giannakopoulos, S. Suresh, An experimental study of spherical indentation of piezoelectric materials, Acta Mater. 47 (1999) 2417-30.

DOI: 10.1016/s1359-6454(99)00095-6

Google Scholar

[7] S.N. Kamble, D.V. Kubair, U. Ramamurty, Indentation strength of a piezoelectric ceramic: experiments and simulations, J. Mater. Res. 24 (2009) 925-934.

DOI: 10.1557/jmr.2009.0115

Google Scholar

[8] S. Matysiak, Axisymmetric problem of punch pressing into a piezoelectroelastic half space, Bull. Pol. Acad. Sci. 33 (1985) 25-34.

Google Scholar

[9] H. Fan, K.Y. Sze, W. Yang, Two-dimensional contact on a piezoelectric half-space, Int. J. Solids Struct. 33 (1996) 1305-1315.

DOI: 10.1016/0020-7683(95)00098-4

Google Scholar

[10] W.Q. Chen, H.J. Ding, Indentation of a transversely isotropic piezoelectric half-space by a rigid sphere, Acta Mech. Sol. Sin. 12 (1999) 114-120.

Google Scholar

[11] W.Q. Chen, T. Shioya, H.J. Ding, The elastoelectric field for a rigid conical punch on a transversely isotropic piezoelectric half-space, ASME J. Appl. Mech. 66 (1999) 764-771.

DOI: 10.1115/1.2791738

Google Scholar

[12] A.E. Giannakopoulos, S. Suresh, Theory of indentation of piezoelectric materials, Acta Mater. 47 (1999) 2153-2164.

DOI: 10.1016/s1359-6454(99)00076-2

Google Scholar

[13] H.J. Ding, P.F. Hou, F.L. Guo, The elastic and electric fields for three-dimensional contact for transversely isotropic piezoelectric materials, Int. J. Solids Struct. 37 (2000) 3201-3229.

DOI: 10.1016/s0020-7683(99)00027-x

Google Scholar

[14] J.G. Wang, S.S. Fang, L.F. Chen, The state vector methods for space axisymmetric problems in multilayered piezoelectric media, Int. J. Solids Struct. 38 (2002) 3959-3970.

DOI: 10.1016/s0020-7683(02)00267-6

Google Scholar

[15] G. Ramirez, P. Heyliger, Frictionless contact in a layered piezoelectric half-space, Smart Mater. Struct. 12 (2003) 612-625.

DOI: 10.1088/0964-1726/12/4/312

Google Scholar

[16] G. Ramirez, Frictionless contact in a layered piezoelectric media characterized by complex eigenvalues, Smart Mater. Struct. 15 (2006) 1287-1295.

DOI: 10.1088/0964-1726/15/5/018

Google Scholar

[17] S.V. Kalinin, E. Karapetian, M. Kachanov, Nanoelectromechanics of piezoresponse force microscopy, Phys. Rev. B. 70 (2004) 184101.

DOI: 10.1103/physrevb.70.184101

Google Scholar

[18] C.F. Gao, N. Noda, Green's functions of a half-infinite piezoelectric body: exact solutions, Acta Mech. 172 (2004) 169-179.

DOI: 10.1007/s00707-004-0153-7

Google Scholar

[19] B.L. Wang, J.C. Han, A circular indenter on a piezoelectric layer, Arch. Appl. Mech. 76 (2006) 367-379.

DOI: 10.1007/s00419-006-0029-5

Google Scholar

[20] J.H. Wang, C.Q. Chen, T.J. Lu, Indentation responses of piezoelectric films, J. Mech. Phys. Solids. 56 (2008) 3331-3351.

Google Scholar

[21] B.L. Wang, H.Y. Zhang, J.C. Han, S.Y. Du, Y.G. Sun, Electromechanical behaviour of a finite piezoelectric layer under a flat punch, Int. J. Solids Struct. 45 (2008) 6384-6398.

DOI: 10.1016/j.ijsolstr.2008.08.001

Google Scholar

[22] L.L. Ke, J. Yang, S. Kitipornchai, Y.S. Wang, Electro-mechanical frictionless contact behavior of a functionally graded piezoelectric layered half-space under a rigid punch, Int. J. Solids Struct. 45 (2008) 3313-3333.

DOI: 10.1016/j.ijsolstr.2008.01.028

Google Scholar

[23] F.Q. Yang, Analysis of the axisymmetric indentation of a semi-infinite piezoelectric material: the evaluation of the contact stiffness and the effective piezoelectric constant, J. Appl. Phys. 103 (2008) 074115.

DOI: 10.1063/1.2903568

Google Scholar

[24] W. Han, M. Sofonea, K. Kazmi, Analysis and numerical solution of a frictionless contact problem for electro-elastic-visco-plastic materials, Comput. Methods Appl. Mech. Engrg. 196 (2007) 3915-3926.

DOI: 10.1016/j.cma.2006.10.051

Google Scholar

[25] M. Barboteu, J.R. Fern´andez, Y. Ouafik, Numerical analysis of two frictionless elasticpiezoelectric contact problems, J. Math. Anal. Appl. 339 (2008) 905-917.

DOI: 10.1016/j.jmaa.2007.07.046

Google Scholar

[26] S. H¨ueber, A. Matei, B. Wohlmuth, A contact problem for electro-elastic materials, ZAMM-Z. Angew. Math. Me. 93 (2013) 789-800.

DOI: 10.1002/zamm.201200235

Google Scholar

[27] M. Liu, Y. Fuqian, Finite element analysis of the spherical indentation of transversely isotropic piezoelectric materials, Modelling Simul. Mater. Sci. Eng. 20 (2012) 045019(15pp).

DOI: 10.1088/0965-0393/20/4/045019

Google Scholar

[28] A. Blazquez, V. Mantic, F. Par´ıs, Application of BEM to generalized plane problems for anisotropic elastic materials in presence of contact. Eng. Anal. Bound. Elem. 30 (2006) 489- 502.

DOI: 10.1016/j.enganabound.2005.07.006

Google Scholar

[29] L. Rodr´ıguez-Tembleque, F.C. Buroni, R. Abascal, A. S´aez. 3D frictional contact of anisotropic solids using BEM, Eur. J. Mech. A Solids. 30 (2011) 95-104.

DOI: 10.1016/j.euromechsol.2010.09.008

Google Scholar

[30] L. Rodr´ıguez-Tembleque, F.C. Buroni, R. Abascal, A. S´aez, Analysis of FRP composites under frictional contact conditions, Int. J. Solids Struct. 50 (2013) 3947-3959.

DOI: 10.1016/j.ijsolstr.2013.08.007

Google Scholar

[31] L. Rodr´ıguez-Tembleque, A. S´aez, F.C. Buroni, Numerical study of polymer composites in contact, CMES-Computer Modeling in Engineering and Sciences. 96 (2013) 131-158.

Google Scholar

[32] L. Rodr´ıguez-Tembleque, F.C. Buroni, A. S´aez, 3D BEM for orthotropic frictional contact of piezoelectric bodies, Comput. Mech. 56 (2015) 491-502.

DOI: 10.1007/s00466-015-1183-9

Google Scholar

[33] P. Alart, A. Curnier, A mixed formulation for frictional contact problems prone to Newton like solution methods, Comput. Meth. Appl. Mech. Eng. 92 (1991) 353-375.

DOI: 10.1016/0045-7825(91)90022-x

Google Scholar

[34] N. Str¨ombeg. An augmented lagrangian method for fretting problems. European Journal of Mechanics A/Solids. 16 (1997) 573-593.

Google Scholar

[35] P.W. Christensen, A. Klarbring, J.S. Pang, N. Str¨omberg, Formulation and comparison of algorithms for frictional contact problems, Int. J. Numer. Meth. Eng. 42 (1998) 145-173.

DOI: 10.1002/(sici)1097-0207(19980515)42:1<145::aid-nme358>3.0.co;2-l

Google Scholar

[36] N. Kikuchi, J.T. Oden, Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods, SIAM, Philadelphia, (1988).

DOI: 10.1137/1.9781611970845

Google Scholar

[37] T.A. Laursen, Computational Contact and Impact Mechanics, Springer, Berlin Heidelberg, (2002).

Google Scholar

[38] P. Wriggers, Computational Contact Mechanics, J. Wiley & Sons, Chichester, (2002).

Google Scholar

[39] L.R. Hill, T.N. Farris, Three-Dimensional Piezoelectric Boundary Element Method, AIAA Journal. 36 (1998) 102-108.

DOI: 10.2514/3.13784

Google Scholar

[40] D.M. Barnett, J. Lothe, Dislocations and Line Charges in Anisotropic Piezoelectric Insulators, Phys. Stat. Sol. (b). 67 (1975) 105-111.

DOI: 10.1002/pssb.2220670108

Google Scholar

[41] F.C. Buroni, A. S´aez, Three-dimensional Green's function and its derivative for materials with general anisotropic magneto-electro-elastic coupling, Proc. R. Soc. A. 466 (2010) 515.

DOI: 10.1098/rspa.2009.0389

Google Scholar

[42] L. Rodr´ıguez-Tembleque, R. Abascal, M.H. Aliabadi, Anisotropic wear framework for 3D contact and rolling problems, Comput. Meth. Appl. Mech. Eng. 241 (2012) 1-19.

DOI: 10.1016/j.cma.2012.05.025

Google Scholar

[43] L. Rodr´ıguez-Tembleque, R. Abascal, Fast FE-BEM algorithms for orthotropic frictional contact, Int. J. Numer. Methods Eng. 94 (2013) 687-707.

DOI: 10.1002/nme.4479

Google Scholar

[44] L. Rodr´ıguez-Tembleque, R. Abascal, M.H. Aliabadi, Anisotropic contact and wear simulation using boundary elements, Key Engineering Materials. 618 (2014) 73-98.

DOI: 10.4028/www.scientific.net/kem.618.73

Google Scholar