Analytical expressions of effective constants for a piezoelectric composite reinforced with square cross-section fibres

• Autorzy: Otero J. , Bravo-Castillero J. , Guinovart-Diaz R. , Rodriguez-Ramos R. , Maugin G. A.
• Języki publikacji: EN

Abstrakty

EN

The purpose of this paper is to present analytical expresiion of the effective elastic, piezoelectric and dielectric constants of reinforced piezoelectric composite materials with unidirectional fibers periodically distributed in a square matrix, as obtained by means of the "double asymptotic homogenization" method. The cross-section of the fibers is square. Each periodic cell of the medium is a binary piezoelectric composite wherein both phases are homogeneous piezoelectric materials with transversely isotropic properties. Comparison between the derived theoretical predictions of characteristic parameters and the existing experimental results shows a rather good agreement. The results obtained in the present paper were verified by means of the universal relations of Schulgasser. Numerical computation of the effective properties can be realized without difficulties.

Słowa kluczowe

EN

piezocomposite; effective properties; asymptotic homogenization; fibre reinforcement; composite material

PL

własność efektywna; homogenizacja asymptotyczna; wzmocnienia włóknami; materiał kompozytowy

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2003
• Tom: Vol. 55, nr 4
• Strony: 357--371
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Otero J.

• Instituto de Cibernetica, Matematica y Fisica Calle 15 ef t C y D, C.P. 10400, Vedado, La Habana, Cuba

autor

Bravo-Castillero J.

• Facultad de Matematica y Computacion Universidad de La Habana, San Lazaro y L, Vedado, C.P. 10400, Vedado, La Habana, Cuba

autor

Guinovart-Diaz R.

• Facultad de Matematica y Computacion Universidad de La Habana, San Lazaro y L, Vedado, C.P. 10400, Vedado, La Habana, Cuba

autor

Rodriguez-Ramos R.

• Facultad de Matematica y Computacion Universidad de La Habana, San Lazaro y L, Vedado, C.P. 10400, Vedado, La Habana, Cuba

autor

Maugin G. A.

• Laboratoire de M odeLisation en M ecanique, Universite Pierre et Marie Curie. Case 162, 8 rue du Capitaine Scott. 75015 Paris, France

Bibliografia

• 1. A. A. GREKOV, S. O . KRAMAROV and A. A. KUPRIENKO, Effective properties of a transversely isotropic piezocomposite with cylindrical inclusions, Ferroelectrics, 16, 43-48, 1987.
• 2. Y. BENVENISTE and G. J. DvoRAK, Uniform fields and universal relations in piezo electric composites, J. Mech. Phys. Solids 40, 1295- 1312, 1992.
• 3. F. CRACIUN, L. SORBA, E. MOLINARI and M .PAPPALARDO, A coupled-mode theory for periodic piezoelectric composites, IEEE Trans. Ultrason. Ferroelectr. and Freq. Control, 36, 50- 56, 1989.
• 4. W. A. SMITH and B. A. AULD, Modeling 1-3 composite piezoelectrics: thickness-mode oscillations, IEEE Trans. Ultrason. Ferroelectr. and Freq. Control, 38, 40- 47, 1991.
• 5. W. A. SMITH, Modeling 1-3 composite piezoelectrics: hydrostatic response, IEEE Trans. Ultrason. Ferroelectr. and Freq. Control, 40, 41- 49, 1993.
• 6. A. GALKA, J . J. TELEGA and R . WOJNAR, Some computational aspects of homogenization of thermopiezoelectric composites, Comput. Assisted Mech. Engng. Sci. 3, 133- 154, 1996.
• 7. J . B . CASTILLERO, J . A . OTERO, R . R . RAMOS and A . BOURGEAT, Asymptotic homogenization of laminated piezocomposite materials, Int. J. Solids Struct., 35, 527- 541, 1998.
• 8. J. PASTOR, Homogenization of linear piezoelectric media, Mech. Res. Commun., 24,145-150, 1997.
• 9. IGOR V. ANDRIANOV, V. V. DANISHEVSKII and DIETER WEICHERT, Asymptotic determination of effective elastic properties of composite materials with fibrous square-shaped inclusions, Eur. J. Mech. A/Solids, 21, 1019-1036, 2002.
• 10. 1. V. ANDRIANOV, G . A. STARUSHENKO, V. V. DANISHEVSKII and S. TOKARZEWSKI, Homogenization procedure and Pade approximants for effective heat conductivity of composite materials with cylindrical inclusions having square cross section, Proc. R . Soc. Lond. A, 455, 3401-3413, 1999.
• 11. H. TAUNAUMANG, 1. L. GUY and H. L. W. CHAN, Electromechanical properties of 1-3 piezoelectric ceramic/piezoelectric polymer composites, J. Appl. Phys. 16, 484-489, 1994.
• 12. K. SCHULGASSER, Relationships between the effective properties of transversely isotropic piezoelectric composites, J. Mech. Phys. Solids 40, 473-479, 1992.
• 13. R. GUINOVART-DiAZ, J. BRAvo-CASTILLERO, R. RODRiGUEZ-RAMOS and F. J. SABINA, Closed-form expressions for the effective coefficients of fibre-reinforced composite with transversely isotropic constituents. l. Elastic and hexagonal symmetry, J. Mech. Phys. Solids, 49, 1445-1462, 200l.
• 14. F. J. SABINA, R . RODRfGUEZ-RAMOS, J . BRAVO-CASTILLERO and R. GUINOVART-DfAZ, Closed-form expressions for the effective coefficients of fibre-reinforced composite with transversely isotropic constituents. 1. Piezoelectric and hexagonal symmetry, J. Mech. Phys. Solids, 49, 1463- 1479, 2001.
• 15. R. RODRfGUEZ-RAMOS, F . J. SABINA, R . GUINOVART-DfAZ and J. BRAVO-CASTILLERO, Closed-form expressions for the effective coefficients of a fiber-reinforced composite with transversely isotropic constituents. I. Elastic and square symmetry, Mech. Mat., 33, 223-235, 2001.
• 16. J. BRAVO-CASTILLERO, R. GUINOVART-DfAZ, F . J. SABINA and R. RODRfGUEZ-RAMOS, Closed-form expressions for the effective coefficients of a fiber-reinforced composite with transversely isotropic constituents. II. Piezoelectric and square symmetry, Mech. Mat., 33, 237- 248, 2001.
• 17. R. GUINOVART-DfAZ, J . BRAVO-CASTILLERO, R . RODRfGUEZ-RAMOS and F . J. SABINA, Overall properties of piezocomposite materials 1- 3, Mat. Lett., 48, 93- 98, 2001.
• 18. D. A. BERLINCOURT, D . R. CURRAN and H. JAFFE, Piezoelectric and piezomagnetic materials and their function in transducers, Phys. of Acoust., lA, W. P . MASON [Ed.] Academic Press, New York 1964.