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Invariants of a Cartesian tensor of rank 3

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Języki publikacji
EN
Abstrakty
EN
General methods are applied to find complete sets of invariants of a tensor of rank 3.When the results are specialized to the piezoelectric tensor, it is found that the tensor has no linear invariant. Also under SO(2), as well as SO(3), the piezoelectric tensor has five quadratic invariants. The sets of invariants are complete.
Rocznik
Strony
383--392
Opis fizyczny
Bibliogr. 14 poz.
Twórcy
autor
  • Centre for Advanced Mathematics and Physics National University of Sciences and Technology Sector H-12, Islamabad, Pakistan, faizmath@hotmail.com
Bibliografia
  • 1. F. Ahmad, Invariants and structural invariants of the anisotropic elasticity tensor, Q. Jl. Mech. Appl. Math., 55, 597–606, 2002.
  • 2. F. Ahmad, M.A. Rashid, Linear invariants of a Cartesian tensor, Q. Jl. Mech. Appl. Math., 62, 31–38, 2009.
  • 3. V.I. Alshits, J. Lothe, Some basic properties of bulk elastic waves in anisotropic media, Wave Motion 40, 297–313, 2004.
  • 4. M. Hamermesh, Group Theory and its Applications to Physical Problems, Addison Wesley, Reading 1964.
  • 5. R.F.S. Hearmon, Crystal Physics, Benjamin, Menlo Park 1974.
  • 6. J.P. Hirth, J. Lothe, Theory of Dislocations, McGraw-Hill, New York 1968.
  • 7. J. Jerphagnon, Invariants of the third-rank Cartesian tensor: Optical nonlinear susceptibilities, Phys. Rev. B, 2, 1091–1098, 1970.
  • 8. A.N. Norris, Quadratic invariants of elastic moduli, Q. Jl. Mech. Appl. Math., 60, 367–389, 2007.
  • 9. G. Racah, Determinazione del numero dei tensori isotropi independenti di rango n, ATTI-Acad. Naz. Lincei Rend. Cl. Sci. Fis. Mat., Ser. 11, 12, 386–389, 1933.
  • 10. M.A. Rashid, F. Ahmad, N. Amir, Linear invariants of a Cartesian tensor under SO(2), SO(3) and SO(4), International Journal of Theoretical Physics, 50, 479–487, 2011.
  • 11. D. Royer and E. Dieulesaint, Elastic Waves in Solids I: Free and Guided Propagation, Springer Verlag, Berlin 2000.
  • 12. J. Schröder, D. Gross, Invariant formulation of the electromechanical enthalpy function of transversely isotropic piezoelectric materials, Archives of Applied Mechanics, 73, 533–552, 2004.
  • 13. T.C.T. Ting, Invariants of anisotropic elastic constants, Q. Jl. Mech. Appl. Math., 40, 431–448, 1987.
  • 14. P. Vannucci, The polar analysis of a third order piezoelectricity-like plane tensor, International Journal of Solids and Structures, 44, 7803–7815, 2007.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT4-0008-0046
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