A theory of domain switch for the nonlinear behaviour of ferro electrics

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 455, Issue 1989, 1999, Pages 3493-3511

  Li, J ^a,b   Weng, G J ^a  

^a The Cooper Union for the Advancement of Science and Art   (United States)

^b RUTGERS UNIVERSITY   (United States)

Author keywords

Domain switch; Ferroelectrics; Homogenization; Irreversible thermodynamics; Nonlinear electromechanical relations

Indexed keywords

EID: 10844285007     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.1999.0462     Document Type: Article

References (41)

1. Barnett, D. M. & Lothe, J. 1975 Dislocations and line charges in anisotropic piezoelectric insulators. Phys. Stat. Sol. B 67, 105-111.
2. Benveniste, Y. 1992 The determination of the elastic and electric fields in a piezoelectric inhomogeneity. J. Appl Phys. 72, 1086-1095.
3. Benveniste, Y. 1993 Universal relations in piezoelectric composite with eigenstress and polarization fields. I. Binary media: local fields and effective behavior. J. Appl. Mech. 60, 265-269.
4. Benveniste, Y. 1994 Exact results concerning the local-fields and effective properties in piezoelectric composites. J. Engng Mater. Tech. 116, 260-267.
5. Benveniste, Y. & Dvorak, G. J. 1992 On uniform fields and universal relations in piezoelectric composites. J. Mech. Phys. Solids 40, 1295-1312.
6. Benveniste, Y., Dvorak, G. J. & Chen, T. 1991 On diagonal symmetry of the approximate effective stiffness tensor of heterogeneous media. J. Mech. Phys. Solids 39, 927-936.
7. Berlincourt, D. 1981 Piezoelectric ceramics: characterizations and applications. J. Acoust. Soc. Am. 70, 1586-1595.
8. Cao, H. & Evans, A. G. 1993 Nonlinear deformation of ferroelectric ceramics. J. Am. Ceram. Soc. 76, 890-896.
9. Chen, T. 1993 Piezoelectric properties of multiphase fibrous composites: some theoretical results. J. Mech. Phys. Solids 41, 1781-1794.
10. Deeg, W. F. 1980 The analysis of dislocation, crack and inclusion problems in piezoelectric solids. PhD dissertation, Stanford University, CA.
11. Dünn, M. L. 1993 Exact relations between the thermoelectroelastic moduli of heterogeneous materials, Proc. R. Soc. Land. A 441, 549-557.
12. Dünn, M. L. 1994 Electroelastic Green's functions for transversely isotropic piezoelectric media and their application to the solution of inclusion and inhomogeneity problems. Int. J. Engng Sei. 32, 119-131.
13. Dünn, M. L. & Taya, M. 1993a Micromechanics predictions of the effective electroelastic moduli of piezoelectric composites. Int. J. Solids Struct. 30, 161-175.
14. Dünn, M. L. & Taya, M. 1993& An analysis of piezoelectric composite materials containing ellipsoidal inhomogeneities. Proc. R. Soc. Land. A 443, 265-287.
15. Dunn, M. L. & Wienecke, H. A. 1996 Green's function for transversely isotropic piezoelectric solids. Int. J. Solids Struct. 33, 4571-4581.
16. Dunn, M. L. & Wienecke, H. A. 1997 Inclusions and inhomogeneities in transversely isotropic piezoelectric solids. Int. J. Solids Struct. 34, 3571-3582.
17. Eshelby, J. D. 1957 The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. R. Soc. Land. A 241, 376-396.
18. Ferrari, M. 1991 Asymmetry and the high concentration limit of the Mori-Tanaka effective medium theory. Mech. Mater. 11, 251-256.
19. Hill, R. 1972 An invariant treatment of interfacial discontinuities in elastic composites. In Continuum mechanics and related problems of analysis (ed. L. I. Sedov & N. I. Muskhelishvili), 80th Anniversary volume, pp. 597-604. Moscow: USSR Academy of Sciences.
20. Hill, R. 1983 Interfacial operators in the mechanics of composite media. J. Mech. Phys. Solids 31, 347-357.
21. Hooton, J. A. & Merz, W. J. 1955 Etch pattern and ferroelectric domains in BaTiOa single crystals. Phys. Rev. 98, 409-413.
22. Huang, J. H. & Yu, J. S. 1994 Electroelastic Eshelby's tensors for an ellipsoidal piezoelectric inclusion. Comp. Engng 4, 1169-1182.
23. Hwang, S. C., Lynch, C. S. & McMeeking, R. M. 1995 Ferroelectric/ferroelastic interactions and a polarization switching model. Acta Metall. Mater. 43, 2073-2084.
24. Hwang, S. C., Huber, J. E., McMeeking, R. M. & Fleck, N. A. 1998 The simulation of switching in polycrystalline ferroelectric ceramics. J. Appl. Phys. 84, 1530-1540.
25. Ikeda, T. 1996 Fundamentals of piezoelectricity. Oxford University Press.
26. Jona, F. & Shirane, G. 1962 Ferroelectric crystals. Oxford: Pergamon.
27. Khachaturyan, A. G. 1983 Theory of structural transformation in solids. New York: Wiley.
28. Lu, Z. K. & Weng, G. J. 1997 Martensitic transformation and stress-strain relations of shapememory alloys. J. Mech. Phys. Solids 45, 1905-1928.
29. McMeeking, R. M. & Hwang, S. C. 1997 On the potential energy of a piezoelectric inclusion and the criterion for ferroelectric switching. Ferroelectrics 200, 151-173.
30. Mitsui, T., Tatsuzaki, I. & Nàkamura, E. 1976 An introduction to the physics of ferroelectrics. New York: Gordon & Breach.
31. Mori, T. & Tanaka, K. 1973 Average stress in the matrix and average elastic energy of materials with misfitting inclusions. Acta Metall. 21, 571-574.
32. Mura, T. 1987 Micromechanics of defects in solids, 2nd edn. Dordrecht: Martinus Nihoff.
33. Nye, J. F. 1979 Physical properties of crystals. Oxford University Press.
34. Qiu, Y. P. & Weng, G. J. 1990 On the application of Mori-Tanaka's theory involving transversely isotropic inclusions. Int. J. Engng Sei. 28, 1121-1137.
35. Rice, J. R. 1975 Continuum mechanics and thermodynamics of plasticity in relation to microscale deformation mechanisms. In Constitutive equations in plasticity (ed. A. S. Argon), pp. 23-75. MIT Press.
36. Shackelford, J. F. 1992 Introduction to materials science for engineers, 3rd edn. New York: Macmillan.
37. Walpole, L. J. 1969 On the overall elastic moduli of composite materials. J. Mech. Phys. Solids 17, 235-251.
38. Wang, B. 1992 Three dimensional analysis of an ellipsoidal inclusion in a piezoelectric material. Int. Jl Solids Struct. 29, 293-308.
39. Weng, G. J. 1990 The theoretical connection between Mori-Tanaka's theory and the HashinShtrikman-Walpole bounds. Int. J. Engng Sei. 28, 1111-1120.
40. Weng, G. J. 1992 Explicit evaluation of Willis' bounds with ellipsoidal inclusions. Int. J. Engng Sei. 30, 83-92.
41. Willis, J. R. 1977 Bounds and self-consistent estimates for overall properties of anisotropic composites. J. Mech. Phys. Solids 25, 185-202.