74
4 Nonlinear Constitutive Relations
4.6 Summary
This chapter dealt with constitutive equations for both isotropic or orthotropic piezoelectric materials. Piezoelectricity was discussed for the deep insight of piezoelectric
materials, which is followed by fundamental theory of piezoelectricity in threedimensional space. Later, the constitutive equations for plates and shells were constructed, with the transformation law between the fiber coordinates and structural
coordinates. Two typical constitutive equations of MFC materials were developed
for multi-layered MFC structures. Finally, an electroelastic coupled nonlinear constitutive relations was presented for the simulation of structures under strong electric
filed.
References
1. H. Kawai, The piezoelectricity of poly(vinylidene) fluoride. Jpn. J. Appl. Phys. 8, 975–976
(1969)
2. R.B. Williams, B.W. Grimsley, D.J. Inman, W.K. Wilkie, Manufacturing and mechanics-based
characterization of macro fiber composite actuators, in ASME 2002 International Mechanical
Engineering Congress and Exposition (2002), pp. 79–89
3. W.K. Wilkie, R.G. Bryant, J.W. High, R.L. Fox, R.F. Hellbaum, A. Jalink, B.D. Little, P.H.
Mirick, Low-cost piezocomposite actuator for structural control applications, in SPIE - Smart
Structures and Materials 2000: Industrial and Commercial Applications of Smart Structures
Technologies, vol. 3991 (SPIE, 12 June 2000), pp. 323–334
4. R.B. Williams, W.K. Wilkie, D.J. Inman, An overview of composite actuators with piezoceramic fibers, in Proceedings of IMAC-XX: Conference & Exposition on Structural Dynamics,
vol. 4753 (Los Angeles, CA; United States, 4-7 February 2002), pp. 421–427
5. H.A. Sodano, J. Lloyd, D.J. Inman, An experimental comparison between several active composite actuators for power generation. Smart Mater. Struct. 15, 1211–1216 (2006)
6. C.R. Bowen, R. Stevens, L.J. Nelson, A.C. Dent, G. Dolman, B. Su, T.W. Button M.G. Cain,
M. Stewart, Manufacture and characterization of high activity piezoelectric fibres. Smart Mater.
Struct. 15, 295–301 (2006)
7. P. Gaudenzi, Smart Structures: Physical Behavior, Mathematical Modeling and Applications
(A John Wiley & Sons Ltd., Publication, 2009)
8. V. Piefort, Finite element modeling of piezoelectric active structures. Ph.D. Thesis, Universite
Libre de Bruxelles (2001)
9. H.F. Tiersten, Electroelastic equations for electroded thin plates subject to large driving voltages. J. Appl. Phys. 74, 3389–3393 (1993)
10. Smart Material Corp. www.smart-material.com
11. A. Deraemaeker, S. Benelechi, A. Benjeddou, A. Preumont, Analytical and numerical computation of homogenized properties of MFCs: application to a composite boom with MFC
actuators and sensors, in Proceedings of the III ECCOMAS Thematic Conference on Smart
Structures and Materials (Gdansk, Poland, 9-11 July 2007)
12. A. Deraemaeker, H. Nasser, A. Benjeddou, A. Preumont, Mixing rules for the piezoelectric
properties of macro fiber composites. J. Intell. Mater. Syst. Struct. 20(12), 1475–1482 (2009)
13. A. Deraemaeker, H. Nasser, Numerical evaluation of the equivalent properties of macro fiber
composite (MFC) transducers using periodic homogenization. Int. J. Solids Struct. 47, 3272–
3285 (2010)
4 Nonlinear Constitutive Relations
4.6 Summary
This chapter dealt with constitutive equations for both isotropic or orthotropic piezoelectric materials. Piezoelectricity was discussed for the deep insight of piezoelectric
materials, which is followed by fundamental theory of piezoelectricity in threedimensional space. Later, the constitutive equations for plates and shells were constructed, with the transformation law between the fiber coordinates and structural
coordinates. Two typical constitutive equations of MFC materials were developed
for multi-layered MFC structures. Finally, an electroelastic coupled nonlinear constitutive relations was presented for the simulation of structures under strong electric
filed.
References
1. H. Kawai, The piezoelectricity of poly(vinylidene) fluoride. Jpn. J. Appl. Phys. 8, 975–976
(1969)
2. R.B. Williams, B.W. Grimsley, D.J. Inman, W.K. Wilkie, Manufacturing and mechanics-based
characterization of macro fiber composite actuators, in ASME 2002 International Mechanical
Engineering Congress and Exposition (2002), pp. 79–89
3. W.K. Wilkie, R.G. Bryant, J.W. High, R.L. Fox, R.F. Hellbaum, A. Jalink, B.D. Little, P.H.
Mirick, Low-cost piezocomposite actuator for structural control applications, in SPIE - Smart
Structures and Materials 2000: Industrial and Commercial Applications of Smart Structures
Technologies, vol. 3991 (SPIE, 12 June 2000), pp. 323–334
4. R.B. Williams, W.K. Wilkie, D.J. Inman, An overview of composite actuators with piezoceramic fibers, in Proceedings of IMAC-XX: Conference & Exposition on Structural Dynamics,
vol. 4753 (Los Angeles, CA; United States, 4-7 February 2002), pp. 421–427
5. H.A. Sodano, J. Lloyd, D.J. Inman, An experimental comparison between several active composite actuators for power generation. Smart Mater. Struct. 15, 1211–1216 (2006)
6. C.R. Bowen, R. Stevens, L.J. Nelson, A.C. Dent, G. Dolman, B. Su, T.W. Button M.G. Cain,
M. Stewart, Manufacture and characterization of high activity piezoelectric fibres. Smart Mater.
Struct. 15, 295–301 (2006)
7. P. Gaudenzi, Smart Structures: Physical Behavior, Mathematical Modeling and Applications
(A John Wiley & Sons Ltd., Publication, 2009)
8. V. Piefort, Finite element modeling of piezoelectric active structures. Ph.D. Thesis, Universite
Libre de Bruxelles (2001)
9. H.F. Tiersten, Electroelastic equations for electroded thin plates subject to large driving voltages. J. Appl. Phys. 74, 3389–3393 (1993)
10. Smart Material Corp. www.smart-material.com
11. A. Deraemaeker, S. Benelechi, A. Benjeddou, A. Preumont, Analytical and numerical computation of homogenized properties of MFCs: application to a composite boom with MFC
actuators and sensors, in Proceedings of the III ECCOMAS Thematic Conference on Smart
Structures and Materials (Gdansk, Poland, 9-11 July 2007)
12. A. Deraemaeker, H. Nasser, A. Benjeddou, A. Preumont, Mixing rules for the piezoelectric
properties of macro fiber composites. J. Intell. Mater. Syst. Struct. 20(12), 1475–1482 (2009)
13. A. Deraemaeker, H. Nasser, Numerical evaluation of the equivalent properties of macro fiber
composite (MFC) transducers using periodic homogenization. Int. J. Solids Struct. 47, 3272–
3285 (2010)