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Secant stress/strain relations of orthotropic elastic damage with dual properties

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Języki publikacji
EN
Abstrakty
EN
A constitutive framework of orthotropic elastic damage in initially-isotropic materials is presented. The constitutive equations are developed within the phenomenological approach of Continuum Damage Mechanics. Focus is made on secant stress/strain relations that can be derived by the application of the so-called damage-effect tensors, namely the fourth-order operators that define the linear transformations between nominal and effective stress and strain quantities. In the attempt to provide selected forms of anisotropic damage approaching general orthotropy, several proposals of damage-effect tensors are formulated. Such fourth-order operators are obtained from the complete orthotropic representations as particular instances that satisfy a duality requirement between compliance- and stiffness-based derivations. A complete family of solutions based on a specific non-singular tensor generator is derived in fuli invariant form.
Rocznik
Strony
133--171
Opis fizyczny
Bibliogr. 26 poz.
Twórcy
autor
autor
  • Universita degli Studi di Bergamo, Facolta di Ingegneria Dipartimento di Progettazione e Tecnologie viale G. Marconi 5, I-24044 Dalmine (BG), Italy
Bibliografia
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  • 2. J. BETTEN, Chapters 11-14, [in:] Applications of Tensor Functions in Solid Mechanics, J.P. BOEHLER [Ed.], CISM Advanced School, Springer-Verlag, Wien, 203-299, 1987.
  • 3. J. BETTEN, Recent Advances in Applications of Tensor Functions in Continuum Mechanics, [in:] Advances in Applied Mechanics, E. VAN DER GIESSEN and TH.-Y. Wu [Eds.], Vol. 37, Academic Press, New York, 277-364, 2001.
  • 4. A. BLINOWSKI and J. RYCHLEWSKI, Pure shears in the mechanics of materials, Mathe-matics and Mechanics of Solids, 3, 4, 471-503, 1998.
  • 5. J.P. BOEHLER, Chapters 1-4, [in:], Applications of Tensor Functions in Solid Mechanics, J.P. BOEHLER [Ed.], CISM Advanced School, Springer-Verlag, Wien, 3-65, 1987.
  • 6. I. CAROL, E. RIZZI and K. WILLAM, A unified theory of elastic degradation and damage based on a loading surface, Int. J. of Solids and Structures, 31, 20, 2835-2865, 1994.
  • 7. I. CAROL, E. RIZZI and K. WILLAM, On the formulation of anisotropic elastic degradation. Part I: Theory based on a pseudo-logarithmic damage tensor rate. Part II: Generalized pseudo-Rankine model for tensile damage, Int. J. of Solids and Structures, 38, 4, 491-518, 519-546, 2001.
  • 8. I. CAROL, E. RIZZI and K. WILLAM, An extended volumetric/deviatoric formulation of anisotropic damage based on a pseudolog rate, European J. of Mechanics A/Solids, 21, 5, 747-772, 2002.
  • 9. J.P. CORDEBOIS, and F. SIDOROFF, Endommagement anisotrope en elasticite et plastic-ite, J. de Mecanique Theorique et Appliquee, N. Special 1982, 45-60, 1982.
  • 10. J.W. Ju, Isotropic and anisotropic damage variables in continuum mechanics, J. of Engineering Mechanics, ASCE, 116, 12, 2764-2770, 1990.
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  • 12. D. KRAJCINOYIC, Damage Mechanics, North-Holland, Elsevier Science, Amsterdam, 1996.
  • 13. K.Y. LAM and J.M. ZHANG, On damage effect tensors o f anisotropic solids, Zeitschrift fur Angewandte Mathematik und Mechanik (ZAMM), 75, l, 51-59, 1995.
  • 14. J. LEMAITRE, A Course on Damage Mechanics, Springer-Verlag, Berlin 1992.
  • 15. T. J. Lu, and C.L. CHÓW, On constitutive equations of inelastic solids with anisotropic damage, Theoretical and Applied Fracture Mechanics, 14, 187-218, 1990.
  • 16. G. MAIER and T. HUECKEL, Nonassociated and coupled flow rules of elastoplasticity for rock-like materials, Int. J. of Rock Mechanics and Mining Science, 16, 77-92, 1979.
  • 17. S. MURAKAMI and N. OHNO, A continuum theory of creep and creep damage, [in:] Creep in Structures, A.R.S. PONTER and D.R. HAYHURST [Eds.], Third IUTAM Symposium, Sept. 8-12, Leichester, UK, Springer-Verlag, New York, 422-443, 1980.
  • 18. Y.N. RABOTNOY, Creep Problems in Structural Members, North-Holland, Amsterdam, 1969.
  • 19. E. RIZZI and I. CAROL, A formulation of anisotropic elastic damage using compact tensor formalism, J. of Elasticity, 64, 2-3, 85-109, 2001.
  • 20. E. RIZZI and I. CAROL, Dual orthotropic damage-effect tensors with complementary struc-tures, Int. J. of Engineering Science, 41, 13-14, 1445-1495, 2003.
  • 21. J. SKRZYPEK and A. GANCZARSKI, Modeling of Material Damage and Failure of Structures, Springer-Yerlag, Berlin 1999.
  • 22. K.C. YALANIS, A theory of damage in brittle materials, Engineering Fracture Mechanics, 36, 403-416, 1990.
  • 23. G.Z. YOYIADJIS and T. PARK, Anisotropic damage effect tensors for the symmetrization of the effective stress tensor, J. of Applied Mechanics, ASME, 64, 106-110, 1997.
  • 24. Q.-S. ZHENG and J. BETTEN, On damage effective stress and equivalence hypothesis, Int. J. of Damage Mechanics, 5, 219-240, 1996.
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  • 26. L. J. WALPOLE, Fourth-rank tensors of the thirty-two crystal classes: multiplication tables, Proceedings of the Royal Society of London, 391, 149-179, 1984.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT7-0005-0029
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