Constitutive laws, uniqueness theorem and Hamilton's principle in linear micropolar thermopiezoelectric/piezomagnetic continuum with relaxation time

Journal of Thermal Stresses

Volumn 30, Issue 1, 2007, Pages 59-80

  El Karamany, Ahmed S ^a  

^a Rustaq Faculty of Education   (Oman)

Author keywords

Constitutive laws; Generalized thermoelasticity; Hamilton's principle; Maxwell Cattaneo equation; Micropolar theory; Thermopiezoelectric piezomagnetic continuum; Uniqueness theorem

Indexed keywords

DIFFERENTIAL EQUATIONS; EQUATIONS OF MOTION; HAMILTONIANS; MATHEMATICAL MODELS; MAXWELL EQUATIONS; PIEZOELECTRICITY; THEOREM PROVING;

CONSTITUTIVE LAWS; HAMILTONS PRINCIPLE; HEAT EQUATION; UNIQUENESS THEOREM;

CONTINUUM MECHANICS;

EID: 33751547866     PISSN: 01495739     EISSN: 1521074X     Source Type: Journal    
DOI: 10.1080/01495730600897187     Document Type: Article

References (43)

1. I. Alshits, A. N. Darinskii, and J. Lothe, On the Existence of Surface Waves in Half-Anisotropic Elastic Media with Piezoelectric and Piezomagnetic Properties, Wave Motion, vol. 16, pp. 265-283, 1992.
2. B. L. Wang and Y.-W. Mai, Crack Tip in Piezoelectric/Piezomagnetic Media, European Journal of Mechanics A/Solids, vol. 22, pp. 591-602, 2003.
3. B.-L. Wang and Y.-W. Mai, Fracture of Piezoelectromagnetic Materials, Mechanics Research Communications, vol. 31, pp. 65-73, 2004.
4. G. C. Sih, R. Jones, and Z. F. Song, Piezoelectric Poling Effects on Mode I and II Crack Initiation Behavior of Magnetoelectroelastic Materials, Theoretical and Applied Fracture Mechanics, vol. 40, pp. 161-186, 2003.
5. E. Pan and P. R. Heyliger, Free Vibrations of Simply Supported and Multilayered Magneto-Electric-Elastic Plates, Journal of Sound and Vibration, vol. 252, no. 3, pp. 429-442, 2002.
6. Z. Chen, S. Yu, L. Meng, and Y. Lin, Effective Properties of Layered Magneto-Electro-Elastic Composites, Composite Structures, vol. 57, pp. 177-182, 2002.
7. J. Y. Li and M. L. Dunn, Micromechanics of Magnetoelectroelastic Composite Materials: Average Field and Effective Behavior, Material System & Structures, vol. 9, pp. 404-416, 1998.
8. J. Aboudi, Micromechanical Prediction of the Effective Behavior of Fully Coupled Electro-Magneto-Thermo-Elastic Multiphase Composites, Smart Mater. Struct., vol. 10, pp. 867-877, 2001.
9. A. C. Eringen and E. S. Suhubi, Non-linear Theory of Simple Microelastic Solids, Part I, Int. J. Engng. Sci., vol. 2, pp. 189-203, 1964.
10. A. C. Eringen and E. S. Suhubi, Non-linear Theory of Simple Microelastic Solids, Part II, Int. J. Engng. Sci., vol. 2, 389-404, 1964.
11. A. C. Eringen, Linear Theory of Micropolar Elasticity, J. Math. Mech., vol. 15, pp. 909-923, 1966.
12. W. Nowacki, Couple Stresses in The Theory of Thermoelasticity, I, II and III, Bull. Acad. Polon. Sci, Ser. Sci. Tech., I: vol. 14, no. 2, pp. 129-138,
13. W. Nowacki, Bull. Acad. Polon. Sci, Ser. Sci. Tech., II: vol. 14, no. 3, pp. 263-272,
14. W. Nowacki, Bull. Acad. Polon. Sci, Ser. Sci. Tech., III: vol. 14, no. 8, pp. 801-809, 1966.
15. A. C. Eringen, A Unified Theory of Thermomechanical Materials, Int. J. Engng. Sci., vol. 4, pp. 179-202, 1966.
16. T. R. Tauchert, W. D. Claus, Jr., and T. Ariman, The Linear Theory of Micropolar Thermoelasticity, Int. J. Engng. Sci., vol. 6, pp. 36-47, 1968.
17. W. Nowacki and W. Olszak, Micropolar Thermoelasticity, in W. Nowacki and W. Olszak (eds.), Micropolar Thermoelasticity, CISM Courses and Lectures, No. 151, Udine Springer-Verlag, Vienna, 1974.
18. R. S. Dhaliwal and A. Singh, Micropolar Thermoelasticity, in R. Hetnarski (ed.), Thermal Stresses II, Mechanics and Mathematical Methods, ser. 2, North-Holland, Amsterdam, 1987.
19. L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, Pergamon Press, Oxford, 1959.
20. R. D. Mindlin, On the Equations of Motion of Piezoelectric Crystals, Problem of Continuum Mechanics, N. I. Muskhelishvili 70th Birthday Volume, pp. 282-290, 1961.
21. W. Nowacki, Some General Theorems of Thermopiezoelectricity, Journal of Thermal Stresses, vol. 1, pp. 171-182, 1978.
22. A. Gałka, J. J. Telega, and R. Wojnar, Homogenization and Thermopiezoelectricity, Mech. Res. Comm., vol. 19, pp. 315-324, 1992.
23. R. Wojnar, S. Bytner, and A. Gałka, Effective Properties of Elastic Composites Subject to Thermal Fields, in R. B. Hetnarski (ed.), Mechanical and Mathematical Methods, vol. 5, Thermal Stresses, Lastran Corporation-Publishing Division, Rochester, NY, 1999.
24. A. C. Eringen, Microcontinuum Field Theories. I. Foundations and Solids, Springer-Verlag, New York, 1999.
25. W. Nowacki, Theory of Asymmetric Elasticity, Pergamon Press, Oxford, 1986.
26. M. Biot, Thermoelasticity and Irreversible Thermodynamics, J. Appl. Phys., vol. 27, pp. 240-253, 1956.
27. J. Ignaczak, Generalized Thermoelasticity and its Applications, in R. B. Hetnarski (ed.), Thermal Stresses III, pp. 279-354, Elsevier, New York, 1989.
28. R. B. Hetnarski and J. Ignaczak, Generalized Thermoelasticity, J. Thermal Stresses, vol. 22, pp. 451-476, 1999.
29. H. Lord and Y. Shulman, A Generalized Dynamical Theory of Thermo-Elasticity, J. Mech. Phys. Solids, vol. 15, pp. 299-309, 1967.
30. D. D. Joseph and L. Preziosi, Heat Waves. Revs. Mod. Physics, vol. 61, pp. 41-73, 1989.
31. D. D. Joseph and L. Preziosi, Addendum to the Paper: Heat Waves, Revs. Mod. Physics, vol. 62, pp. 375-391, 1990.
32. T. R. Tauchert, F. Ashida, N. Noda, S. Adali, and V. Verijenko, Developments in Thermopiezoelectricity with Relevance to Smart Composite Structures, Composite Structures, vol. 48, pp. 31-38, 2000.
33. D. S. Chandrasekharaiah, A generalized Linear Thermoelasticity Theory for Piezoelectric Media, Acta Mechanica, vol. 71, pp. 39-49, 1998.
34. F. Ashida, and T. R. Tauchert, Piezothermoelastic Response of a Circular Plate with Thermal Relaxation, Journal of Thermal Stresses, vol. 27, no. 6, pp. 513-536, 2004.
35. A. S. El-Karamany and M. A. Ezzat, Propagation of Discontinuities in Thermopiezoelectric Rod, Journal of Thermal Stresses, vol. 28, no. 10, pp. 997-1030, 2005.
36. A. E. Green and K A. Lindsay, Thermoelasticity, J. Elasticity, vol. 2, pp. 1-7, 1972.
37. E. S. Suhubi, Thermoelastic Solids, in A. C. Eringen (ed.), Continuum Physics, vol. 2, part 2, ch. 2, Academic Press, New York, 1975.
38. H. F. Tiersten, Linear Piezoelectric Plate Vibrations, Plenum Press, New York, 1969.
39. W. Nowacki, Dynamic Problems of Thermoelasticity, Noordhoff, Leyden, The Netherlands, 1975.
40. M. E. Gurtin, The Linear Theory of Elasticity, in C. Trucsdell (ed.), Encyclopedia of Physics, Chief Editor S. Flüge, vol. VI a /2, pp. 1-295, Springer, Berlin, 1972.
41. G. C. Sih and H. Y. Yu, Volume Fraction Effect of Magnetoelectroelastic Composite on Enhancement and Impediment of Crack Growth, Composite Structures, vol. 86, pp. 1-11, 2005.
42. E. Grimsehl, Lehrbuch der Physik. Bd. 2. Elektromagnetisches Feld, p. 342, Teubner, 1963.
43. R. B. Hetnarski and J. Ignaczak, Mathematical Theory of Elasticity, Taylor and Francis, New York, 2004.