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UDC 539.43

Bobyr M., Khalimon O., Bondarets O.
National Technical University of Ukraine «Kyiv Polytechnic Institute», Kyiv, Ukraine ( This e-mail address is being protected from spambots. You need JavaScript enabled to view it )


Бобырь Н.И. д.т.н., проф., Халимон А.П. к.т.н., доц., Бондарец А. А.
НТУУ «Киевский политехнический институт», Киев, Украина


AbstractDamage in metals is mainly the process of the initiation and growth of voids. A formulation for anisotropic damage is established in the framework of the principle of strain equivalence, principle of increment complementary energy equivalence and principle of elastic energy equivalence. This paper presents the development of an anisotropic damage theory. This work is focused on the development of evolution anisotropic damage models which is based on a Young’s modulus/Poisson’s ratio change of the initial isotropic material. Anisotropic damage account is as important as accounting of the loading history and the type of stress state. Therefore, validation of the existing damage accumulation models with anisotropy account and the development of new ones is an important and promising direction in the solid mechanics. Today more widely for engineering applications the phenomenological approach, which is based on the continuum damage mechanics (СDM) and the thermodynamics of irreversible processes are used. The main idea of all damage models consists in replacing the conventional stress with the effective stress in the constitutive equation.

Keywords: anisotropic material, damage, effective stress, strain equivalence, increment complementary energy equivalence, elastic energy equivalence.



1. Fridman Ja. B. «Mehanicheskie svojstva metallov» 2-e izd. Moscow, 1972, 368.
2. Chow C.L., Wang J. An anisotropic theory of elasticity for continuum damage mechanics. International Journal of Fracture 33: 1987, pp. 3-16.
3. Kachanov, L. M., "On Creep Rupture Time," Proc. Acad. Sci., USSR, Div. Eng. Sci., 8, 1958, pp. 26–31.
4. Rabotnov Yu. N., Creep in Structural Elements [in Russian], Nauka, Moscow, 1966.
5. Chaboche J.-L. Thermodynamically founded CDM models for creep and other conditions, in: Creep and damage in materials and structures, CISM No. 399, edited by Altenbach H., Skrzypek J.J., Springer Verlag New York, 1999, pp. 209-278.
6. Lemaitre J., Desmorat R., Sauzay M. Anisotropic damage law of evolution. Eur. J. Mech. A/Solids 19, 2000, pp. 187-208.
7. Luo A. C.J., Mou Y., Han R. P.S. A large anisotropic damage theory based on an incremental complementary energy equivalence model. International Journal of Fracture 70: 1995, pp. 19-34.
8. Strackeljan J., Bobyr M., Khalimon O. Bauteillebensdauer beim zyklischen Kriechen mit der Berücksichtigung von Schädigungsprozessen. 10. Magdeburger Maschinenbau-Tage, 2011.
9. Chaboche J.-L. Development of Continuum Damage Mechanics for Elastic Solids Sustaining Anisotropic and Unilateral Damage. Int. J. of Dam. Mech., Vol. 2 October 1993, pp. 311-329.
10. Germain P., Nguyen Q.S., Suquet P. Continuum Thermodynamics. J. of Applied Mechanics, ASME, 50: 1983, pp. 228-232.
11. Bobyr М., Grabovskii А., Khalimon О., Timoshenko O., Maslo O. Kinetics of scattered fracture in structural metals under elastoplastic deformation Strength of Materials, Vol. 39, No. 3, 2007, pp. 237-245.
12. Kracinovic D. Continuous damage mechanics revisited: Basic concepts and definitions. J. Appl. Mech. 52, 1985, pp. 829– 834.
13. Leckie F.A., Onat E.T. Tensorial nature of damage measuring internal variables. In: Hult J., Lemaitre J. (Eds.), Physical Non- Linearities in Structural Analysis, Springer, Berlin, 1981, pp. 140–155.
14. Lemaitre J., Chaboche J.L. Mécanique des matériaux solides. Dunod, Mechanics of Solid Materials, Springer-Verlag, 1985, (English translation) 1987.
15. Murakami S. Mechanical modeling of material damage. J. Appl. Mech. 55, 1988, pp. 280–286.
16. Sidoroff F. Description of anisotropic damage application to elasticity IUTAM Colloquium, Physical Nonlinearities in Structural Analysis, 1981, pp. 237-244.
17. Khalimon O.P., Bondarets O.A. “The reliability of the phenomenological damage accumulation models under complex stress state”. Research bulletin of the NTUU “KPI”. No.5, 2011, pp. 101-106.