Some computational aspects of homogenization of thermopiezoelectric composites

Computer Assisted Mechanics and Engineering Sciences

Volumn 3, Issue 2, 1996, Pages 133-154

  Galka, Andrzej ^a   Telega, Józef Joachim ^a   Wojnar, Ryszard ^a  

^a INSTITUTE OF FUNDAMENTAL TECHNOLOGICAL RESEARCH   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; NUMERICAL METHODS; PIEZOELECTRIC MATERIALS; PROBLEM SOLVING;

HOMOGENIZATION; RITZ METHOD; THERMOPIEZOELECTRIC COMPOSITES;

COMPOSITE MATERIALS;

EID: 0029709201     PISSN: 1232308X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (36)

1. A. Galka, J.J. Telega and R. Wojnar. Homogenization and thermopiezoelectricity. Mech. Res. Comm., 19: 315-324, 1992.
2. J.J. Telega. Piezoelectricity and homogenization. Application to biomechanics. In: G.A. Maugin, ed. Continuum Models and Discrete Systems, Vol. 2, 220-229, Longman, Essex, 1991.
3. N. Turbé and G.A. Maugin. On the linear piezoelectricity of composite materials. Math. Meth. in the Appl. Sci., 14: 403-412, 1991.
4. Y. Benveniste. The determination of the elastic and electric fields in a piezoelectric inhomogeneity. J. Appl. Phys., 72: 1086-1095, 1992.
5. Y. Benveniste. Universal relations in piezoelectric composites with eigenstress and polarization fields, Part I: Binary media - local fields and effective behavior. J. Appl. Mech., 60: 265-269, 1993; Part II: Multiphase media - effective behavior, ibid., 270-275
6. Y. Benveniste. Universal relations in piezoelectric composites with eigenstress and polarization fields, Part I: Binary media - local fields and effective behavior. J. Appl. Mech., 60: 265-269, 1993; Part II: Multiphase media - effective behavior, ibid., 270-275
7. T. Chen. Piezoelectric properties of multiphase fibrous composites: some theoretical results. J. Mech. Phys. Solids, 41: 1781-1794, 1993.
8. M.L. Dunn and M. Taya. Micromechanics predictions of the effective electrostatic moduli of piezoelectric composites. Int. J. Solids Structures, 30: 161-175, 1993.
9. M.L. Dunn and M. Taya. Electromechanical properties of porous piezoelectric ceramics, (to appear)
10. B. Gambin and A. Galka. Boundary layer problem in a piezoelectric composite. In: D.F. Parker, A.H. England, eds. Proc. IUTAM Symp. on Anisotropy, Inhomogeneity and Nonlinearity in Solid Mechanics, 327-332, Kluwer, Netherlands, 1995.
11. I.P. Getman, A.P. Ryabov and Yu.A. Ustinov. On possibilities of the avaraging method in the problem of wave propagation in an electroelastic layer with periodic nonhomogeneity across the thickness (in Russian). Mekhanika TV. Tela, No. 3, 118-124, 1987.
12. K. Schulgasser. Relationships between the effective properties of transversely isotropic piezoelectric composites. J. Mech. Phys. Solids, 40: 473-479, 1992.
13. C.-W. Nan. Comments on "Relationships between the effective properties of transversely isotropic piezoelectric composites". J. Mech. Phys. Solids, 41: 1567-1570, 1993.
14. B. Wang. Effective behavior of piezoelectric composites. Appl. Mech. Reviews, 47: No. 1, Part 2, 112-121, 1994.
15. G.A. Francfort. Two variational problems in thermoelasticity. Ph. D. Thesis, Stanford University, April 1982.
16. G.A. Francfort. Homogenization and linear thermoelasticity. SIAM J. Math. Anal., 14: 696-708, 1984.
17. S. Brahim-Otsmane, G.A. Francfort and F. Murat. Homogenization in thermoelasticity. In: R.V. Kohn and G.W.Milton, eds. Random Media and Composites, 13-45, SIAM, Philadelphia, 1988.
18. A. Galka, J.J. Telega and R. Wojnar. Thermodiffusion in heterogeneous elastic solids and homogenization. Arch. Mech., 46: 267-314, 1994.
19. Y. Benveniste. Exact results in the micromechanics of fibrous piezoelectric composites exhibiting pyroelectricity. Proc. Roy. Soc. London, A441, 59-81, 1993.
20. M.L. Dunn. Exact relations between the thermal and electroelastic moduli of composite materials with emphasis on two-phase laminates. Proc. of the 1993 SPIE North American Conference on Smart Structures and Materials, (to appear).
21. Zh. Arbash and G.M. Kobel'kov. Numerical methods for solving elasticity theory problems with strongly varying coefficients. Russ. J. Numer. Anal. Math. Modelling, 8: 371-383, 1993.
22. J.-F. Bourgat. Numerical experiments of the homogenization method for operators with periodic coefficients, IRIA Laboria, Rapport de Recherche No. 277, 1978.
23. J. Dvořák. A reliable numerical method for computing homogenized coefficients, Mat-Report No. 1994-31, Mathematical Institute, Technical University of Denmark.
24. R.Z. Dautov. On one variant of the finite element method for elliptic equations in domains with periodic structure (in Russian). Diff. Uravnenya, 21: 1155-1164, 1985.
25. J.M. Guedes and N. Kikuchi. Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods. Comp. Meth. in Appl. Mech. Eng., 83: 143-198, 1990.
26. L.D. Marini. Estimates from above and from below for the homogenized coefficients. Numer. Math., 50: 533-545, 1987.
27. W. Nowacki. Electromagnetic Effects in Deformable Solids (in Polish). PWN, Warszawa 1983.
28. W. Solucha, ed. Introduction to Piezoelectronics (in Polish). WKiL, Warszawa, 1980.
29. G. Dal Maso. Introduction to Γ-convergence. Birkhäuser, Boston, 1993.
30. E. Sanchez-Palencia. Non-Homogeneous Media and Vibration Theory. Springer- Verlag, Berlin, 1980.
31. J. Sanchez-Hubert and E. Sanchez-Palencia. Introduction aux Méthodes Asymptotiques et à L'Homogénéisation. Masson, Paris, 1992.
32. O.A. Oleinik, G.A. Yosifian, A.S. Shamaev. Mathematical Problems of Strongly Nonhomogeneous Elastic Media (in Russian). Izd. Moskovskogo Universiteta, Moskva, 1990.
33. K.-H. Hellwege, ed. Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology. Springer, Berlin, Vol. 1, 1966; Vol. 2, 1969; Vol. 11, 1979.
34. K.-H. Hellwege, ed. Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology. Springer, Berlin, Vol. 1, 1966; Vol. 2, 1969; Vol. 11, 1979.
35. K.-H. Hellwege, ed. Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology. Springer, Berlin, Vol. 1, 1966; Vol. 2, 1969; Vol. 11, 1979.
36. R.A. Heising. Quartz Crystals for Electrical Circuits: Their Design and Manufacturing. D. Van Nostrand Co, New York, 1946.