Energy-based limit criteria for anisotropic elastic materials with constraints

• Autorzy: Kowalczyk-Gajewska K. , Ostrowska-Maciejewska J.
• Języki publikacji: EN

Abstrakty

EN

The main aim of this paper is to investigate the influence of internal restrictions on the form of the energy-based limit condition. Some restrictions may be imposed in the elastic as well as in the limit states. Spectral decomposition of symmetric linear operators in a space with two different scalar products is applied. An algorithm for accounting for the considered restrictions in the limit condition is proposed. It was shown that as long as the energy scalar product is denned properly in the elastic range, the limit condition having the energy-based interpretation can be found. Examining the material with such an internal structure that there are stresses which do not cause any strain, the space with passive stresses and locked strains has to be introduced. The limit condition in this case has two parts, one connected with active part of stresses which has energy-based interpretation and the second one connected with passive stresses. The algorithm how to introduce this part of stresses to the limit condition has been proposed. As examples, the energy-based form of the Schmid law for single slip is derived and fiber-reinforced materials are analyzed.

Słowa kluczowe

PL

sprężystość; materiał sprężysty; naprężenia; energia w naprężeniach

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2005
• Tom: Vol. 57, nr 2-3
• Strony: 133--155
• Opis fizyczny: Bibliogr. 24 poz.

Twórcy

autor

Kowalczyk-Gajewska K.

• Institute of Fundamental Technological Research PAS Świętokrzyska 21, 00 049 Warsaw, Poland

autor

Ostrowska-Maciejewska J.

• Institute of Fundamental Technological Research PAS Świętokrzyska 21, 00 049 Warsaw, Poland

Bibliografia

• 1. Y.P. Arramon, M.M. Mehrabadi, D.W. Martin, and S.C. Cowin, A multidimensional anisotropic strength criterion based on Kelvin modes, Int. J. Solids Structures, 37, 2915–2935, 2000.
• 2. D. Banabic, H. Aretz, D.S. Comsa, and L. Paraianu, An improved analystical description of orthotropy in metallic sheets. Int. J. Plasticity, 21, 493–512, 2005.
• 3. F. Barlat, D.J. Lege, and J.C. Brem, A six-component yield function for anisotropic materials, Int. J. Plasticity, 7, 693–712, 1991.
• 4. M.W. Biegler and M.M. Mehrabadi, An energy-based failure criterion for anisotropic solids subjected to damage, Damage in Composite Materials, 34, 23–34, 1993.
• 5. W.T. Burzyński, Strength hypothesis (in Polish), Lwów, 1928, (cf. also Selected papers, vol. I, PWN, Warszawa 1982).
• 6. S.C. Cowin and M.M. Mehrabadi, Anisotropic symmetries of linear elasticity, Appl. Mech. Rev., 48, 5, 247–285, 1995.
• 7. D.E. Green, K.W. Neale, S.R. MacEwen, A. Makinde, and R. Perrin, Experimental investigation of the biaxial behaviour of an aluminum sheet, Int. J. Plasticity, 20, 1677–1706, 2004.
• 8. P. Gumbsch, Modelling brittle and semi-brittle fracture processes, Mater. Sci. Eng. A, 319-321, 1–7, 2001.
• 9. R. Hill, A user friendly theory of orthotropic plasticity in sheet metals, Int. J. Mech. Sci., 35, 1, 19–25, 1993.
• 10. K. Kowalczyk and W. Gambin, Model of plastic anisotropy evolution with texture dependent yield surface, Int. J. Plasticity, 20, 19–54, 2004.
• 11. K. Kowalczyk and J. Ostrowska-Maciejewska, Energy-based limit conditions for transversally isotropic solids, Arch. Mech., 54, 5–6, 497–523, 2002.
• 12. K. Kowalczyk, J. Ostrowska-Maciejewska, and R.B. Pęcherski, An energy-based yield criterion for solids of cubic elasticity and orthotropic limit state, Arch. Mech., 55, 5–6, 431–448, 2003.
• 13. K. Kowalczyk-Gajewska and J. Ostrowska-Maciejewska, The influence of internal restrictions on the elastic properties of anisotropic materials, Arch. Mech., 56, 205–232, 2004.
• 14. J. Li, A.H.W. Ngan and P. Gumbsch, Atomistic modeling of mechanical behavior, Acta mater., 51, 5711–5742, 2003.
• 15. W. Olszak and J. Ostrowska-Maciejewska, The plastic potential in the theory of anisotropic elastic-plastic solids, Engng. Fracture Mech., 21, 4, 625–632, 1985.
• 16. J. Ostrowska-Maciejewska and J. Rychlewski, Plane elastic and limit states in anisotropic solids, Arch. Mech., 40, 4, 379–386, 1988.
• 17. A.C. Pipkin, Constraints in linearly elastic materials, J. Elasticity, 6, 2, 179–193, 1976.
• 18. J. Rychlewski, “ceiiinosssttuv”. Mathematical structure of elastic bodies (in Russian), Technical Report 217, Inst. Mech. Probl. USSR Acad. Sci., Moskva 1983.
• 19. J. Rychlewski, Elastic energy decomposition and limit criteria, Advances in Mechanics, 7, 3, 1984. In Russian (translation see in [20]).
• 20. J. Rychlewski, On Hook’s law, Prikl. Matem. Mekhan., 48, 303–314, 1984.
• 21. J. Rychlewski, Unconventional approach to linear elasticity, Arch. Mech., 2, 149–171, 1995.
• 22. S. Sutcliffe, Spectral decomposition of the elasticity tensor, J. Appl. Mech., 59, 4, 762–773, 1992.
• 23. M. Zhang and J. He, Ab-initio calculation of elastic constants of TiN, Surface and Coating Technology, 142–144, 125–131, 2001.
• 24. Q.S. Zheng, Constitutive relations of linear elastic materials under various internal constraints, Acta Mechanica, 158, 1–2, 97–103, 2002.