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Abstrakty
In the paper a new proposition of an energy-based hypothesis of material effort is introduced. It is based on the concept of influence functions introduced by Burzyński and on the concept of decomposition of elastic energy density introduced by Rychlewski. A new proposition enables description of a wide class of linearly elastic materials of arbitrary symmetry exhibiting strength differential effect.
Czasopismo
Rocznik
Tom
Strony
125--138
Opis fizyczny
Bibliogr. 24 poz., rys.
Twórcy
autor
autor
autor
- Institute of Fundamental Technological Research Polish Academy of Sciences Pawińskiego 5B, 02-106 Warszawa, Poland, rpecher@ippt.pan.pl
Bibliografia
- 1. Bardet J.P., Lode dependences for isotropic pressure sensitive materials, J. Appl. Mech., 57, 498–506, 1990.
- 2. Bigoni D., Piccolroaz A., Yield criteria for quasibrittle and frictional materials, Int. J. Solids Structures, 41, 2855–2878, 2004.
- 3. Burzyński W., Studium nad hipotezami wytężenia, Akademia Nauk Technicznych, Lwów, 1928; see also: Selected passages from Włodzimierz Burzyński’s doctoral dissertation “Study on material effort hypotheses”, Engng. Trans., 57, 3–4, 185–215, 2009.
- 4. Drucker D.C., Plasticity Theory, Strength-Differential (SD)Phenomenon, and Volume Expansion in Metals and Plastics, Metall. Trans., 4, 667–673, 1973.
- 5. Drucker D.C., Prager W., Soil mechanics and plastic analysis for limit design, Quart. Appl. Math., 10, 2, 157-–165, 1952.
- 6. Gelfand I.M., Lectures on Linear Algebra [in Russian: Lekhtsii po linyeynoy algebre], Nauka, Moscow, 1966.
- 7. Hill R., A theory of the yielding and plastic flow of anisotropic metals, Proc. Roy. Soc. London, 193, 281–297, 1948.
- 8. Hoffman O., The brittle strength of orthotropic materials, J. Comp. Mater., 1, 200–206, 1967.
- 9. Kowalczyk K., Ostrowska-Maciejewska J., Pęcherski R.B., An energy-based yield criterion for solids of cubic elasticity and orthotropic limit state, Arch. Mech., 55, 5–6, 431–448, 2003.
- 10. Lexcellent C., Vivet A., Bouvet C., Calloch S., Blanc P., Experimental and numerical determinations of the initial surface of phase transformation under biaxial loading in some polycrystalline shape-memory alloys, J. Mech. Phys. Sol., 50, 2717–2735, 2002.
- 11. Mises R. von, Mechanik der plastischen Formanderung von Kristallen, Z. Angew. Math. u. Mech., 8, 161–185, 1928.
- 12. Ostrowska-Maciejewska J., Rychlewski J., Plane elastic and limit states in anisotropic solids, Arch. Mech., 40, 4, 379–386, 1988.
- 13. Nowak M., Ostrowska-Maciejewska J., Pęcherski R.B., Szeptyński P., Yield criterion accounting for the third invariant of stress tensor deviator. Part I. Derivation of the yield condition basing on the concepts of energy-based hypotheses of Rychlewski and Burzyński., Engng. Trans., 59, 4, 273–281, 2011.
- 14. Pęcherski R.B., Szeptyński P., Nowak M., An extension of Burzyński hypothesis of material effort accounting for the third invariant of stress tensor, Arch. Metall. Mat., 56, 2, 503–508, 2011.
- 15. Podgórski J., Limit state condition and the dissipation function for isotropic materials, Arch. Mech., 36, 3, 323–342, 1984.
- 16. Raniecki B., Mróz Z., Yield or martensitic phase transformation conditions and dissipation functions for isotropic, pressure-insensitive alloys exhibiting SD effect, Acta. Mech.,195, 81–102, 2008.
- 17. Rychlewski J., „CEIIINOSSSTTUV” Mathematical structure of elastic bodies [in Russian], Preprint 217, IPM AN SSSR, IPPT PAN, Moscow 1983.
- 18. Rychlewski J., Elastic energy decomposition and limit criteria [in Russian], Advances in Mechanics (Uspekhi mekhaniki), 7, 51–80, 1984; see also: Elastic energy decomposition and limit criteria, Engng. Trans., 59, 1, 31–63, 2011.
- 19. Rychlewski J., On Hooke’s law [in Russian], Prikl. Mat. Mekh., 48, 420–435, 1984; see also: J. Appl. Math. Mech., 48, 303–314, 1984.
- 20. Spitzig W.A., Sober R.J., Richmond O., The effect of hydrostatic pressure on the deformation behavior of maraging and HY-80 steels and its implications for plasticity theory, Metall. Trans. A, 7A, 1703–1710, 1976.
- 21. Szeptyński P., Yield criterion accounting for the influence of the third invariant of stress tensor deviator. Part II: Analysis of convexity condition of the yield surface, Engng. Trans., 59, 4, 283–297, 2011.
- 22. Szeptyński P., Pęcherski R.B., Proposition of a new yield criterion for orthotropic metal sheets accounting for asymmetry of elastic range [in Polish], Rudy i Metale Nieżelazne, 57, 4, 243–250, 2012.
- 23. Theocaris P.S., The elliptic paraboloid failure criterion for cellular solids and brittle foams, Acta Mech., 89, 93–121, 1991.
- 24. Tsai S.W., Wu E.M., A general theory of strength for anisotropic materials, J. Comp. Mater., 5, 58–80, 1971.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPB2-0071-0030