Theory of Generalized Piezoporo Thermoelasticity

Subject Areas : Engineering

M Jabbari ¹ , A Yooshi ²

1 - Postgraduate School of Engineering, South Tehran Branch, Islamic Azad University
2 - Postgraduate School of Engineering, South Tehran Branch, Islamic Azad University

Received: 2012-09-10 Accepted : 2012-11-05 Published : 2012-12-30

Keywords: Generalized thermoelasticity, Porous piezo materials, Biot’s theory, Two phase, Electro-dynamic Maxwell’s equation,

Abstract :

In this paper, the basic constitutive equations and equations of motion are derived to describe the behavior of thermoelastic porous piezoelectric medium by using Biot’s theory and the theory of generalized thermoelasticity with on relaxation time (Lord-Shulman). The electrical enthalpy density function is derived in the general coordinates. Also, clear definitions for the poroelastic modulus, electrical, thermal and additional mixed coefficients are embedded. The uniqueness of the solution for the complete system of equations is presented.

References:

[1] Biot M.A., 1941, General theory of three –dimensional consolidation, Journal of Applied Physics12:155-164.

[2] Biot M.A., 1955, Theory of elasticity and consolidation for a porous anisotropic solid, Journal of Applied Physics 26:182-185.

[3] Biot M.A., Willis D.G., 1954, The elastic coefficients of the theory of consolidation, Journal of Applied Physics 24:594-601.

[4] Vashishth A.K., Gupta V., 2009, Vibrations of porous piezoelectric ceramic plates, Journal of Sound and Vibration 325:781-797.

[5] Biot M.A., 1962, Mechanics of deformation and acoustic propagation in porous media, Journal of Applied Physics 33:1482-1498.

[6] Mandl G., 1964, Change in skeletal volume of a fluid-filled porous body under stress, Journal of the Mechanics and Physics of Solids 12:299–315.

[7] Brown R.J.S, Korringa J., 1975, The dependence of the elastic properties of a porous rock on the compressibility of the pore fluid, Geophysics 40:608-616.

[8] Zimmerman R.W., Somerton W.H., King M.S., 1986, Compressibility of porous rocks , Journal of Geophysical Reasearch 91:12765–12777.
[9] Zimmerman R.W., Myer L.R., Cook N.G.W., 1994, Grain and void compression in fractured and porous rock, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 31:179–184.

[10] Garg S. K., Nayfeh A. H., 1986, Compressional wave propagation in liquid and/or gas saturated elastic porous media, Journal of Applied Physics 60:3045-3055.

[11] Pride S.R., Gangi A.F., Morgan F.D., 1992, Deriving the equations of motion for porous isotropic media, Journal of the Acoustical Society of America 92:3278-3290.

[12] Thompson M., Willis J.R., 1991, A reformulation of the equations of anisotropic poroelasticity, Journal of Applied Mechanics 58:612–616.

[13] Albert D. G, 1993, A comparison between wave propagation in water‐saturated and air‐saturated porous materials, Journal of Applied Physics 73:28-36.

[14] Cowin S., 1999, Bone poroelasticity, Journal of Biomechanics 32:217-238.

[15] Tod S.R., 2003, An anisotropic fractured poroelastic effective medium theory, Geophysical Journal International 155:1006–1020.

[16] Wersing W., Lubitz K., Moliaupt J., 1986, Dielectric elastic and piezoelectric properties of porous PZT ceramics, Ferroelectrics 68:77-97.

[17] Dunn H., Taya M., 1993, Electromechanical properties of porous piezoelectric ceramics, Journal of the American Ceramic Society 76:1697-1706.

[18] Kurashige M., 1989, A thermoelastic theory of fluid-filled porous materials, International Journal of Solids and Structures 25: 1039-1052.

[19] Ciarletta M., Scarpetta E., 1996, Some results on thermoelasticity for porous piezoelectric materials, Mechanics Research Communications 23:1-10.

[20] Ghassemi A., Diek A., 2002, Porothermoelasticity for swelling shales, Journal of Petroleum Science and Engineering 34:123 –135.

[21] Batifol C., Zielinski T. G., Galland M.A., Ichchou M. N., 2006, Hybrid piezo-poroelastic sound package concept: numerical/experimental validations, Proceedings of International Symposium on Active Control of Sound and Vibration, Adelaide, Australia.

[22] Youssef H.M., 2007, Theory of generalized porothermoelasticity, International Journal of Rock Mechanics and Mining Sciences 44:222-227.

[23] Nasedkin A., 2009, New model for piezoelectric porous medium with application to analysis of ultrasonic piezoelectric transducers, Proceedings of the 7th Euromech Solid Mechanics Conference, Lisbon, Portugal.

[24] Zielinski T.G., 2010, Fundamentals of multiphysics modelling of piezo-poro-elastic structures, Archives of Mechanics 62:343-378.

[25] Sharma M.D., 2010, Piezoelectric effect on the velocities of waves in an anisotropic piezo-poroelastic medium, Proceedings the Royal of Society A Mathematical Physical and Engineering sciences 466:1977-1992.

[26] Wang H.F., 2000, Theory of Linear Poroelasticity: with Application to Geomechanics and Hydrogeology, USA, Princeton University Press.

[27] Coussy O., 2004, Poromechanics, New York, Wiley, First edition.

[28] Coussy O., 2010, Mechanics and Physics of Porous Solids, New York, Wiley, First edition.

[29] Ikeda T., 1990, Fundamentals of Piezoelectricity, Oxford University Press.

[30] Hetnarski B., Eslami M.R., 2009, Thermal Stresses: Advanced Theory and Applications, USA, Springer, First edition.

[31] Kidner M. R. F., Hansen C. H., 2008, A comparison and review of theories of the acoustics of porous materials, International Journal Acoustics and Vibration 13:112-119.

[32] Yang D., Zhang Z., 2002, Poroelastic wave equation including the Biot/squirt mechanism and the solid/fluid coupling anisotropy, Wave Motion 35:223–245.

[33] Kraus J.D., 1984, Electromagnetic, USA, McGraw-Hill Inc, Second edition.

[34] Deresiewicz H., Skalak R., 1963, On uniqueness in dynamic poroelasticity, Bulletin of the Seismological Society of America 53:783-788.