Universal bounds for effective piezoelectric moduli

Mechanics of Materials

Volumn 30, Issue 1, 1998, Pages 1-19

  Hori, Muneo ^a   Nemat Nasser, Sia ^b  

^a UNIVERSITY OF TOKYO   (Japan)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; FOURIER TRANSFORMS; GREEN'S FUNCTION; PROBLEM SOLVING; TENSORS; THEOREM PROVING; VARIATIONAL TECHNIQUES;

ESHELBY'S TENSOR; HASHIN-SHTRIKMAN VARIATIONAL PRINCIPLE; PIEZOELECTRIC MODULI;

PIEZOELECTRIC MATERIALS;

EID: 0032166650     PISSN: 01676636     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6636(98)00029-5     Document Type: Article

References (23)

1. Balendran, B., Nemat-Nasser, S., 1995. Bounds on elastic moduli of composites. J. Mech. Phys. Solids 43 (11), 1825-1853.
2. Benveniste, Y., 1992. The determination of the elastic and electric fields in a piezoelectric inhomogeneity. J. Appl. Phys. 72 (3), 1086-1095.
3. Benveniste, Y., 1997. Piezoelectric inhomogeneity problems in anti-plane shear and in-plane electric fields-how to obtain the coupled fields from the uncoupled dielectric solution. Mech. Mater. 25 (1), 59-65.
4. Dunn, M.L., Taya, M., 1994. Electroelastic field concentrations in and around inhomogeneities in piezoelectric solids. Trans. ASME, J. Appl. Mech. 61 (2), 474-475.
5. Dunn, M.L., Wienecke, H.A., 1996. Green's functions for transversely isotropic piezoelectric solids. Int. J. Solids Struct. 33 (30), 4571-4581.
6. Eshelby, J.D., 1957. The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. Roy. Soc. A 241, 376-396.
7. Francfort, G.A., Murat, F., 1986. Homogenization and optimal bounds in linear elasticity. Arch. Rat. Mech. Anal. 94, 307-334.
8. Hashin, Z., Shtrikman, S., 1962. On some variational principles in anisotropic and nonhomogeneous elasticity. J. Mech. Phys. Solids 10, 335-342.
9. Hill, R., 1963. Elastic properties of reinforced solids: Some theoretical principles. J. Mech. Phys. Solids 11, 357-372.
10. Iwakuma, T., Nemat-Nasser, S., 1983. Composites with periodic microstructure. Comput. Struct. 16 (1-4), 13-19.
11. Kröner, E., 1977. Bounds for effective elastic moduli of disordered materials. J. Mech. Phys. Solids 25, 137-155.
12. Lothe, J., Barnett, D.M., 1976. Integral formation for surface waves in piezoelectric crystals: Extensive considerations. J. Appl. Phys. 47, 1799-1807.
13. Lothe, J., Barnett, D.M., 1977. Further development of the theory for surface waves in piezoelectric crystals. Phys. Norvegica 8 (4), 239-254.
14. Milton, G.W., 1990. On characterizing the set of possible effective tensors of composite: The variational method and the translation method. Comm. Pure Appl. Math. 43, 53-125.
15. Milton, G.W., Kohn, R., 1988. Variational bounds on the effective moduli of anisotropic composites. J. Mech. Phys. Solids 43, 63-125.
16. Munashinghe, H.M.S, Hori, M., Enoki, Y., 1996. Application of Hashin-Shtrikman variational principle for computing upper and lower approximate solutions of elasto-plastic problems. In: Proceedings of International Conference on Urban Eng. in Asian Cities, pp. 1-6.
17. Mura, T., 1987. Micromechanics of Defects in Solids. Martinus Nijhoff, Dordrecht.
18. Nemat-Nasser, S., Hori, M., 1993. Micromechanics: Overall Properties of Heterogeneous Materials. North-Holland, London.
19. Nemat-Nasser, S., Hori, M., 1995. Universal bounds for overall properties of linear and nonlinear heterogeneous solids. Trans. ASME 117, 412-422.
20. Torquato, S., 1991. Random heterogeneous media: Microstructure and improved bounds on effective properties. Appl. Mech. Rev. 42 (2), 37-76.
21. Torquato, S., 1992. Improved bounds on the effective elastic moduli of random arrays of cylinders. J. Appl. Mech. 42 (2), 37-76.
22. Walpole, L.J., 1966. On bounds for the overall elastic moduli of inhomogeneous systems - I. J. Mech. Phys. Solids 14, 151-162.
23. Willis, J.R., 1977. Bounds and self-consistent estimates for the overall properties of anisotropic composites. J. Mech. Phys. Solids 25, 185-202.