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Review on spectral decomposition of hookes tensor for all symmetry groups of linear elastic material

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The spectral decomposition of elasticity tensor for all symmetry groups of a linearly elastic material is reviewed. In the paper it has been derived in non-standard way by imposing the symmetry conditions upon the orthogonal projectors instead of the stiffness tensor itself. The numbers of independent Kelvin moduli and stiffness distributors are provided. The corresponding representation of the elasticity tensor is specified.
Rocznik
Strony
145--183
Opis fizyczny
Bibliogr. 32 poz., wykr.
Twórcy
  • Institute of Fundamental Technological Research Polish Academy of Sciences Pawińskiego 5B. 02-106 Warszawa. Poland
Bibliografia
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  • 4. P. CHADWICK, M. VIANELLO, and S. C. COWIN, A new proof that the number of linear elastic symmetries is eight, J. Mech. Phys. Solids, 49, 2471-2492, 2001.
  • 5. R. M. CHRISTENSEN, Mechanics of Composites Materials, Dover Publications, 1979. 2005.
  • 6. S. C. COWIN and M. M. MEHRABADI, Anisotropic symmetries of linear elasticity. Appl. Mech. Hev.. 48. 5, 247-285, 1995.
  • 7. S. C. COWIN and A. M. SADEGH, Non-interacting modes for stress, strain and energii kard tissue, J. Biomechanics. 24, 859-867, 1991.
  • 8. S. FORTE and M. VIANELLO, Symmetry classes for elasticity tensors, J. Elasticity. 43,81 108, 1996.
  • 9. R. B. HETNARSKI and ,1. IGNACZAK, Methematical theory of elasticity, Taylor and Irainis.New York, 2004.
  • 10. W. THOMPSON (Lord Kelvin). Elements of Mathematical Theory of Elasticity. Chapti XV, On the Six Principal Strains of an Elastic Solid, Phil. Trans. R. Soc. London. 146, 481-498, 1856. I
  • 11. U. F. KOCKS, C. N. TOME, and H.-R. WENK, Teiture and Anisotropy, Cambridge Uni-versity Press, II edition, 2000.
  • 12. K. KOWALCZYK and J. OSTROWSKA-MACIEJEWSKA. Energy-based limit amditions transuersally isotropic solids, Arch. Mech., 54, 5-6, 497-523, 2002.
  • 13. K. KOWALCZYK-GAJEWSKA, Micromechanical modelling of metals and alloys of high -cifie strength. IFTR Reports (in preparation), 2010.
  • 14. K. KOWALCZYK-GAJEWSKA and J. OSTROWSKA MACIEJEWSKA. The influence of internat restrictions on the elastic properties of anisotropic materials, Arch. Mech.. 56. 205-232, 2004.
  • 15. K. KOWALCZYK-GAJEWSKA and J. OSTROWSKA -MACIEJEWSKA, Mechanics of the 21st Century, Proceedings of the 21 st International Congress of Theoretical and Applied Mechanics, Warsaw, Poland, 15-21 August 200Ą. Chapter "On the invariants of the elasticity tensor for orthotropic materials", Springer (e-book), 2004.
  • 16. S.G. LEKHNITSKII, Theory of elasticity of an anisotropic body, Mir Publishers, 1981.
  • 17. M. M. MEHRABADI and S. C. COWIN, Eigentensors of linear anisotropic elastic matt nah. I Quart. J. Mech. Appl. Math.. 43. 15-41, 1990.
  • 18. M. MOAKHER and N. NORRIS. The closest elastic tensor of arbitrary symmetry toaM elasticity tensor of lower symmetry, J. Elasticity, 85, 215-263, 2006.
  • 19. J. OSTROWSKA-MACIEJEWSKA and J. RYCHLEWSKI, Generalized proper states forW anisotropic elastic materials, Arch. Mech., 53. 1 ",. .")()l 518, 2001.
  • 20. J. PIEKARSKI. K. KOWALCZYK-GAJEWSKA, J. H. WAARSING, and M. MAŹDZIAHZ chanics of the 21st Century, Proceedings of the 21st International Congress of TheorettcdM and Applied Mechanics, Warsaw, Poland, 15-21 August 2004 Chapter 'Appn)xiniations of stiffness tensor of bonę determining and aceuracy", Springer (e-book), 2004.
  • 21. A. Roos, J.-L. CHABOCHE, L. GELEBART, and J. CREPIN, Multiscale modelling of tita- I nium aluminides, Int. .1. Plasticity. 20. HI 1 830. 2004.
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  • 23. J. RYCHLEWSKI, Elastic energy decomposition and limit criteria [in Russian], Advances I in Mechanics, 7, 3, 1984.
  • 24. J. RYCHLEWSKI, Zur Abschdtzung der Anisotropie, ZAMM. 65, 256-258, 1985.
  • 25. J. RYCHLEWSKI, Unconventional approach to linear elasticity, Arch. Mech., 47, 2, 149-171, 1995.
  • 26. J. RYCHLEWSKI, A qualitative approach to Hooke's tensors. Part I, Arch. Mech., 52, 737-759, 2000.
  • 27. J. RYCHLEWSKI, Elastic waves under unusual anisotropy, J. Mech. Phys. Solids, 49, 2651-2666, 2001.
  • 28. S. SUTCLIFFE, Spectral decomposition of the elasticity tensor, J. Appl. Mech., 59, 4, 762-773, 1992.
  • 29. K. TANAKA and M. KOIWA, Single-ery stal elastic constants of intermetallic compounds, Intermetallics, 4, 29-39, 1996.
  • 30. F. Xu, R. A. HOLT, and M. R. DAYMOND, Modeling lattice strain evolution during uni-axial deformation of teztured Zircaloy-2, Acta Mater., 56, 3672-3687, 2008.
  • 31. M. H. Yoo and CL. Fu, Physical constants, deformation twinning, and microcracking of titanium aluminides, Metal. Mater. Trans. A, 29A, 49-63, 1998.
  • 32. C. ZENER, Elasticite et Anelasticite des Metaux, Dunod, Paris, 1955.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPB2-0055-0002
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