Anti-plane time-harmonic Green’s functions for a coated circular inhomogeneity in a piezoelectric medium with spring- or membrane-type imperfect interfaces
Restricted accessResearch articleFirst published online September, 2017
Anti-plane time-harmonic Green’s functions for a coated circular inhomogeneity in a piezoelectric medium with spring- or membrane-type imperfect interfaces
Two-dimensional anti-plane time-harmonic dynamic Green’s functions for a coated circular inhomogeneity in an infinitely extended matrix with spring- or membrane-type imperfect interfaces are presented. The inhomogeneity, coating and matrix are all assumed to be piezoelectric and transversely isotropic. By using the Bessel function expansions, explicit solutions for the electromechanical fields induced by a time-harmonic anti-plane line force and line charge located in the unbounded matrix, the annular coating and the circular inhomogeneity are derived. The present solutions can recover the anti-plane Green’s functions for some special cases, such as the dynamic or quasi-static Green’s functions of piezoelectricity with perfect interfaces, as well as the dynamic or quasi-static Green’s functions for a two-phase composite with perfect or imperfect interfaces. By means of detailed discussions, selected calculated results are graphically shown to demonstrate the dependence of the electromechanical fields on the circular frequency and the interface properties as well as the coating and size of the inclusion.
ChanHLWUnsworthJ.Simple model for piezoelectric ceramic/polymer 1-3 composites used in ultrasonic transducer applications. IEEE Trans Ultrason Ferroelectr FrEqn Control1989; 36: 434–441.
2.
BenvenisteY.Exact results in the micromechanics of fibrous piezoelectric composites exhibiting pyroelectricity. Proc R Soc Lond (A)1993; 441: 59–81.
3.
DunnMLWieneckeHA.Inclusion and inhomogeneities in transversely isotropic piezoelectric solids. Int J Solids Struct1997; 34: 3571–3582.
4.
XiaoJHXuYLZhangFC.Size-dependent effective electroelastic moduli of piezoelectric nanocomposites with interface effect. Acta Mech2011; 222: 59–67.
5.
ShiYWanYP.Anti-plane time-harmonic Green’s functions for a circular inhomogeneity in piezoelectric medium with a spring- or membrane-type interface. Mech Res Commun2015; 70: 24–41.
6.
SudakLJ.Effect of an interphase layer on the electroelastic stresses within a three-phase elliptic inclusion. Int J Eng Sci2003; 41: 1019–1039.
7.
BreiDCannonBJ.Piezoceramic hollow fiber active composites. Compos Sci Technol2004; 64: 245–261.
8.
BeckertWKreherWBraueW.Effective properties of composites utilising fibres with a piezoelectric coating. J Eur Ceram Soc2001; 21: 1455–1458.
9.
MalakootiMHSodanoHA.Multi-inclusion modeling of multiphase piezoelectric composites. Compos Part B-Eng2013; 47: 181–189.
10.
JiangCPCheungYK.An exact solution for the three-phase piezoelectric cylinder model under antiplane shear and its applications to piezoelectric composites. Int J Solids Struct2001; 38: 4777–4796.
11.
GuSTHeQC.Interfacial discontinuity relations for coupled multifield phenomena and their application to the modeling of thin interphases as imperfect interfaces. J Mech Phys Solids2011; 59: 1413–1426.
12.
ShodjaHMTabatabaeiSMKamaliMT.A piezoelectric medium containing a cylindrical inhomogeneity: Role of electric capacitors and mechanical imperfections. Int J Solids Struct2007; 44: 6361–6381.
13.
WangZJinXYChenWQet al. Micro-scaled size-dependence of the effective properties of 0-3 PZT-cement composites: Experiments and modeling. Compos Sci Technol2014; 105: 183–189.
14.
WangZZhuJJinXYet al. Effective moduli of ellipsoidal particle reinforced piezoelectric composites with imperfect interfaces. J Mech Phys Solids2014; 65: 138–156.
15.
ShiYWanYPZhongZ.Variational bounds for the effective electroelastic moduli of piezoelectric composites with electromechanical coupling spring-type interfaces. Mech Mater2014; 72: 72–93.
16.
XiaoJHXuYLZhangFC.Evaluation of effective electroelastic properties of piezoelectric coated nano-inclusion composites with interface effect under antiplane shear. Int J Eng Sci2013; 69: 61–68.
17.
FangXQYangQLiuJXet al. Surface/interface effect around a piezoelectric nano-particle in a polymer matrix under compressional waves. Appl Phys Lett2012; 100: 151602.
18.
LiuLGaoCF. Scattering problem of the interface circular cavity in piezoelectric media. In: Proc Symp Piezoelectricity Acoust Waves and Device Appl (Spawda12), 2012. IEEE, pp.379–382. DOI: 10.1109/SPAWDA.2012. 6464113.
19.
FangXQHuangMJLiuJXet al. Dynamic effective property of piezoelectric composites with coated piezoelectric nano-fibers. Compos Sci Technol2014; 98: 79–85.
20.
DendaMArakiYYongYK.Time-harmonic BEM for 2-D piezoelectricity applied to eigenvalue problems. Int J Solids Struct2004; 41: 7241–7265.
21.
ChengZQBatraRC.Exact Eshelby tensor for a dynamic circular cylindrical inclusion. ASME J Appl Mech1999; 66: 563–565.
22.
MaHWangB.The scattering of electroelastic waves by an ellipsoidal inclusion in piezoelectric medium. Int J Solids Struct2005; 42: 4541–4554.
23.
WangXSudakLJ.Antiplane time-harmonic Green’s functions for a circular inhomogeneity with an imperfect interface. Mech Res Commun2007; 34: 352–358.
24.
WangXPanE.Two-dimensional Eshelby’s problem for two imperfectly bonded piezoelectric half-planes. Int J Solids Struct2010; 47: 148–160.
25.
BleusteinJL.A new surface wave in piezoelectric materials. Appl Phys Lett1968; 13: 412–413.
26.
ShanHZChouTW.Transverse elastic moduli of unidirectional fiber composites with fiber/matrix interfacial debonding. Compos Sci Technol1995; 53: 383–391.
27.
Rodríguez-RamosaRGuinovart-DíazaRLópez-RealpozoaJCet al. Effective properties of periodic fibrous electro-elastic composites with mechanic imperfect contact condition. Int J Mech Sci2013; 73: 1–13.
28.
HashinZ.Thin interphase/imperfect interface in elasticity with application to coated fiber composites. J Mech Phys Solids2002; 50: 2509–2537.
29.
BenvenisteY.An interface model for a three-dimensional curved thin piezoelectric interphase between two piezoelectric media. Math Mech Solids2009; 14: 102–122.
30.
HuangGYYuSW.Effect of surface piezoelectricity on the electromechanical behaviour of a piezoelectric ring. Phys Status Solidi (B)2006; 243: R22–R24.
31.
HuSLShenSP.Electric field gradient theory with surface effect for nano-dielectrics. CMC Comput Mater Contin2009; 13: 63–87.
32.
WangXZhongZ.Two-dimensional time-harmonic dynamic Green’s functions in transversely isotropic piezoelectric solids. Mech Res Commun2003; 30: 589–593.
33.
GradshteynISRyzhikIM.Table of Integrals, Series, and Products. 6th ed.San Diego: Academic Press, 2000.
34.
AkdoganEKSafariA.Electrostrictive properties of nanosize PbTiO3. IEEE Trans Ultrason Ferroelectr FrEqn Control2000; 47: 881–885.
35.
ZhangSLiHLiM.Size-dependent piezoelectric coefficient d(33) of PbTiO(3) nanoparticles. Mater Lett2008; 62: 2438–2440.
36.
YangSSHuSLShenSP.Local electroelastic field and effective electroelastic moduli of piezoelectric nanocomposites with interface effect. CMC Comput Mater Contin2012; 29: 279–298.
37.
MichalskiPJSaiNMeleEJ.Continuum theory for nanotube piezoelectricity. Phys Rev Lett2005; 95: 116803.
38.
ChenT.Exact size-dependent connections between effective moduli of fibrous piezoelectric nanocomposites with interface effects. Acta Mech2008; 196: 205–217.
