Analysis of effective properties of electroelastic composites using the self-consistent and asymptotic homogenization methods

Abstract The problem of the calculation of overall properties of a binary electroelastic fibre-reinforced composite is studied here, whose constituents are an elastic matrix and piezoelectric fibres that have transversely isotropic properties. Randomly positioned fibres as well as periodic distributed fibres are considered. The former case is dealt with by means of the self-consistent method and the latter one by asymptotic homogenization. Closed-form expressions are given for two variants of the self-consistent method, one in explicit form (effective field) and the other implicitly (effective medium). The former agree with the Mori–Tanaka equations. The equations derived using the asymptotic homogenization method are also explicit. It is shown that the three sets of effective coefficients satisfy analytically Schulgasser’s universal relations; the Milgrom–Shtrikman determinant is also explicitly satisfied by the effective field method variant. Overall properties are computed as a function of the fibre concentration. It is generally found that the properties calculated using the effective field self-consistent and homogenization methods are very close to each other for at least concentrations up to or near 0.3. In many cases the agreement is beyond that. Also the case when the constituents have either the same or opposite poling directions can be studied with the exact formulae. The antiplane strain related properties display interesting larger effects with opposite polings.

[1]  T. Ikeda.  Fundamentals of piezoelectricity , 1990 .

[2]  M. Taya,et al.  An analysis of piezoelectric composite materials containing ellipsoidal inhomogeneities , 1993, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[3]  Julián Bravo-Castillero,et al.  Closed-form expressions for the effective coefficients of fibre-reinforced composite with transversely isotropic constituents. I: Elastic and hexagonal symmetry , 2001 .

[4]  K. Schulgasser.  Relationships between the effective properties of transversely isotropic piezoelectric composites , 1992 .

[5]  A. Kelly,et al.  Smart Composite Materials Systems , 2000 .

[6]  Shtrikman,et al.  Linear response of two-phase composites with cross moduli: Exact universal relations. , 1989, Physical review. A, General physics.

[7]  R. Hill.  A self-consistent mechanics of composite materials , 1965 .

[8]  V. Levin.  THE EFFECTIVE PROPERTIES OF PIEZOACTIVE MATRIX COMPOSITE MATERIALS , 1996 .

[9]  Rodney Hill,et al.  Continuum micro-mechanics of elastoplastic polycrystals , 1965 .

[10]  Julián Bravo-Castillero,et al.  Closed-form expressions for the effective coefficients of a fiber-reinforced composite with transversely isotropic constituents – I. Elastic and square symmetry , 2001 .

[11]  Anthony Kelly,et al.  Comprehensive composite materials , 1999 .

[12]  L. E. Cross,et al.  Connectivity and piezoelectric-pyroelectric composites , 1978 .

[13]  J. Unsworth,et al.  Simple model for piezoelectric ceramic/polymer 1-3 composites used in ultrasonic transducer applications , 1989 .

[14]  Valery M. Levin,et al.  EFFECTIVE FIELD METHOD IN MECHANICS OF MATRIX COMPOSITE MATERIALS , 1994 .

[15]  Martin L. Dunn,et al.  Electroelastic Green's functions for transversely isotropic piezoelectric media and their application to the solution of inclusion and inhomogeneity problems , 1994 .

[16]  H. Banno,et al.  Recent developments of piezoelectric ceramic products and composites of synthetic rubber and piezoelectric ceramic particles , 1983 .

[17]  M. Dunn,et al.  Variational bounds for the effective moduli of heterogeneous piezoelectric solids , 2001 .

[18]  B. Budiansky.  On the elastic moduli of some heterogeneous materials , 1965 .

[19]  F. Patat,et al.  A matrix method for modeling electroelastic moduli of 0-3 piezo-composites , 1997, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[20]  M. Lethiecq,et al.  Modeling of highly loaded 0-3 piezoelectric composites using a matrix method , 1998, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[21]  S. O. Kramarov,et al.  Effective properties of a transversely isotropic piezoelectric composite with cylindrical inclusions , 1989 .

[22]  Chen Tungyang,et al.  Micromechanical estimates of the overall thermoelectroelastic moduli of multiphase fibrous composites , 1994 .

[23]  K. Tanaka,et al.  Average stress in matrix and average elastic energy of materials with misfitting inclusions , 1973 .

[24]  K. Markov.  Justification of an effective field method in elasto-statics of heterogeneous solids , 2001 .

[25]  W. Kreher,et al.  The effective thermoelectroelastic properties of microinhomogeneous materials , 1999 .

[26]  A. Safari,et al.  5.25 – Piezoelectric Composites for Transducer Applications , 2000 .

[27]  Martin L. Dunn,et al.  Micromechanics of Magnetoelectroelastic Composite Materials: Average Fields and Effective Behavior , 1998 .

[28]  Martin L. Dunn,et al.  Micromechanics predictions of the effective electroelastic moduli of piezoelectric composites , 1993 .

[29]  L. E. Cross,et al.  High frequency applications of PZT/polymer composite materials , 1981 .

[30]  M. Lethiecq,et al.  Effective electroelastic moduli of 3-3(0-3) piezocomposites , 1999, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[31]  Wang Biao,et al.  Three-dimensional analysis of an ellipsoidal inclusion in a piezoelectric material , 1992 .

[32]  R. Kar-Gupta,et al.  Electromechanical response of 1-3 piezoelectric composites: Effect of poling characteristics , 2005 .