| ||Mechanics of Solids|
A Journal of Russian Academy of Sciences
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936
Archive of Issues
|Total articles in the database:|| ||3985|
|In Russian (Èçâ. ÐÀÍ. ÌÒÒ):|| ||2236|
|In English (Mech. Solids):|| ||1749|
|V. N. Kukudzhanov, "Coupled models of elastoplasticity and damage and their integration," Mech. Solids. 41 (6), 83-109 (2006)|
||Coupled models of elastoplasticity and damage and their integration|
||V. N. Kukudzhanov (Moscow)|
||We present a survey of the modern state of art in coupled models of
elastoplasticity and damage. We discuss different approaches (physical and
thermodynamical) to the construction of damage models. We consider the
relation between damage, softening, and rheological instability of
nonelastic materials. We investigate the scale effect, present a well-posed
statement of the problem and methods for regularizing ill-posed models, and
consider elastoplastic models independent of the strain rate as well as
elastoviscoplastic models depending on the strain rate. The focus is on
theoretically constructed models taking into account void nucleation and
growth in elastoplastic and elastoviscoplastic materials.|
We suggest a new efficient numerical method for integrating coupled
constitutive equations of plasticity with damage based on the splitting of
elastoplastic equations. We implement this approach in modeling quasistatic
and dynamic damage problems and compare this approach with the most perfect
existing methods (used in modern FEM software) for integrating such
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Fracture Mechanics [in Russian], Izd-vo Samarsk. Un-ta, Samara, 2001.|
|2. ||G. I. Barenblatt,
"On equilibrium cracks formed in brittle fracture.
General concepts and hypotheses,"
PMM [Applied Mathematics and Mechanics], Vol. 23, No. 3,
pp. 434-444, 1959.|
|3. ||N. G. Burago and V. N. Kukudzhanov, Numerical Solution of Continual
Fracture Problems. Preprint No. 746 [in Russian], In-t Problem Mekhaniki
RAN, Moscow, 2004.|
|4. ||A. A. Vakulenko and L. M. Kachanov,
"Continual theory of a medium with cracks,"
Izv. AN SSSR MTT [Mechanics of Solids], No. 4, pp. 156-166, 1971.|
|5. ||J. J. Gilman, "Microdynamical theory of plasticity," in
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|7. ||G. P. Ezhov, "On fracture waves in an initially stressed layer of
a porous material," PMM [Applied Mathematics and Mechanics], Vol. 70,
No. 3, pp. 515-530, 2006.|
|8. ||S. N. Zhurkov,
"Kinetic concept of strength of solids,"
Vestnik AN SSSR, No. 11, pp. 78-85, 1957.|
|9. ||A. Seger, "Mechanism of slip and strengthening in cubic
face-centered and hexagonal densely packed metals," in Dislocations and
Mechanical Properties of Crystals [Russian translation], pp. 179-268,
Izd-vo Inostr. Lit-ry, Moscow, 1960.|
|10. ||A. A. Il'yushin,
"On a theory of long-term strength,"
Inzh. Zh. MTT [Mechanics of Solids], No. 3, pp. 21-35, 1967.|
|11. ||A. A. Il'yushin and B. E. Pobedrya, Foundations of Mathematical
Theory of Thermoviscoelasticity [in Russian], Nauka, Moscow, 1970.|
|12. ||A. A. Il'yushin, Continuum Mechanics [in Russian], Izd-vo MGU, Moscow, 1978.|
|13. ||G. I. Kannel, S. V. Razorenov, A. V. Utkin, and V. E. Fortov,
Impact-Wave Phenomena in Condensed Media [in Russian],
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|14. ||L. M. Kachanov, "On the fracture time under creeping
conditions," Izv. AN SSSR OTN, No. 8, pp. 26-31, 1958.|
|15. ||L. M. Kachanov, Foundations of Plasticity [in Russian], Nauka,
|16. ||L. M. Kachanov,
Foundations of Fracture Mechanics [in Russian], Nauka, Moscow, 1974.|
|17. ||V. Yu. Kibardin and V. N. Kukudzhanov, "Simulation of continual
fracture in elastoviscoplastic material," Izv. RAN. MTT [Mechanics of
Solids], No. 1, pp. 113-123, 2001.|
|18. ||V. I. Kondaurov,
"Energy approach to the problem of continual fracture of solids,"
Izv. AN SSSR Fizika Zemli [Physica of Earth], No. 6, pp. 17-22, 1986.|
|19. ||V. I. Kondaurov,
"Continual fracture of nonlinearly elastic bodies,"
PMM [Applied Mathematics and Mechanics], Vol. 52, No. 2,
pp. 302-310, 1988.|
|20. ||V. I. Kondaurov and L. V. Nikitin,
Theoretical Foundations of Rheology of Geomaterials [in Russian],
Nauka, Moscow, 1990.|
|21. ||V. I. Kondaurov and V. E. Fortov,
Foundations of Thermomechanics of Condensed Medium [in Russian],
Idz-vo MFTI, Moscow, 2002.|
|22. ||A. H. Cottrell,
Dislocations and Plastic Flow in Crystals [Russian translation],
Metallurgizdat, Moscow, 1958.|
|23. ||V. N. Kukudzhanov,
"Propagation of spherical waves in elastoviscoplastic media,"
Izv. VUZov. Mashinostroenie, No. 2, pp. 14-20, 1958.|
|24. ||V. N. Kukudzhanov, "Numerical simulation of dynamic processes of
deformation and fracture in elastoplastic media," Uspekhi Mekhaniki,
Vol. 8, No. 4, pp. 21-65, 1985.|
|25. ||V. N. Kukudzhanov, "Numerical simulation of unsteady processes of
deformation and fracture of elastoplastic bodies under large strains," in
Mathematical Methods in Mechanics of Deformed Solids [in Russian],
pp. 75-84, Nauka, Moscow, 1986.|
|26. ||V. N. Kukudzhanov, Difference Methods for Solving Problems of
Solid Mechanics [in Russian], Izd-vo MFTI, Moscow, 1992.|
|27. ||V. N. Kukudzhanov, V. L. Ivanov, A. N. Kovshov, and D. N. Shneiderman,
Study of Plastic Strain Localization in the Loss of Stability of Banks.
Preprint No. 538 [in Russian], In-t Problem Mekhaniki RAN, Moscow, 1994.|
|28. ||V. N. Kukudzhanov, "Micromechanical model of inelastic medium for describing
localizations of strains," in Proc. 9th Conf. in Strength and Plasticity. Volume 2.
Strength and Plasticity, pp. 118-125, In-t Problem Mekhaniki RAN, Moscow, 1996.|
|29. ||V. N. Kukudzhanov, "Micromechanical model of fracture of an inelastic material and
its application to the investigation of strain localization," Izv. RAN. MTT [Mechanics of
Solids], No. 5, pp. 72-87, 1999.|
|30. ||V. N. Kukudzhanov, "Decomposition method for elastoplastic equations," Izv. RAN.
MTT [Mechanics of Solids], No. 1, pp. 98-108, 2004.|
|31. ||V. N. Kukudzhanov, A. L. Levitin, and V. S. Sinyuk, Numerical
Simulation of Damaged Elastoplastic Materials. Preprint No. 807 [in
Russian], In-t Problem Mekhaniki RAN, Moscow, 2006.|
|32. ||L. V. Nikitin and S. L. Yunga,
"Methods for theoretical determining of tectonic strains and stresses in
seismically active regions,"
Izv. RAN. Fizika Zemli [Physics of Earth], No. 11, pp. 54-67.|
|33. ||V. N. Nikolaevskii, Mechanics of Porous and Fissured Media [in
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|34. ||V. E. Panin, V. A. Likhachev, and Yu. V. Grinyaev, Structural
Levels of Deformations of Solids [in Russian], Nauka, Novosibirsk, 1985.|
|35. ||P. Perzyna, Fundamental Problems in Viscoplasticity [Russian
translation], Mir, Moscow, 1968.|
|36. ||Yu. N. Rabotnov,
"Mechanism of long-term fracture,"
in Problems of Strength of Materials and Constructions [in Russian],
pp. 5-7, Izd-vo AN SSSR, Moscow, 1959.|
|37. ||Yu. N. Rabotnov, Mechanics of Solids [in Russian], Nauka, Moscow, 1979.|
|38. ||V. V. Sokolovskii,
Theory of Plasticity [in Russian],
Vysshaya Shkola, Moscow, 1969.|
|39. ||T. Suzuki, S. Takeuchi, and H. Yoshinaga, Dislocation Dynamics and
Plasticity [Russian translation], Mir, Moscow, 1989.|
|40. ||V. I. Revnivtsev (Editor), Selective Fracture of Minerals [in Russian], Nedra,
|41. ||T. Thomas,
Plastic Flow and Fracture in Solids [Russian translation],
Mir, Moscow, 1964.|
|42. ||C. Trusdell, A First Course of Rational Continuum Mechanics
[Russian translation], Mir, Moscow, 1975.|
|43. ||G. P. Cherepanov,
Mechanics of Brittle Fracture [in Russian],
Nauka, Moscow, 1974.|
|44. ||M. Wilkins,
"Computation of elastoplastic flows,"
in Computational Methods in Hydrodynamics [Russian translation],
pp. 212-263, Mir, Moscow, 1967.|
|45. ||ABAQUS Theory Manual.|
|46. ||N. Aravas,
"On the numerical integration of a class of pressure-dependent plasticity models,"
Intern. J. Numer. Methods in Eng-ng, Vol. 24, No. 7, pp. 1395-1416, 1987.|
|47. ||T. W. Barbee, L. Seaman, R. Crewdson, and R. Curran,
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Mater., Vol. 7, No. 3, pp. 393-401, 1972.|
|48. ||R. De Borst,
"Computation of post-bifurcation and post-failure behavior of
Computers and Structures, Vol. 25, No. 2, pp. 211-224, 1987.|
|49. ||B. Budiansky and R. J. O'Connel,
"Elastic moduli of a cracked solid,"
Intern. J. Solids and Structures, Vol. 12, No. 2, pp. 81-97, 1976.|
|50. ||K. Cho, Y. C. Chi, and L. Duffy,
Microscopic Observation of Adiabatic Shear Bands in Three Different Steels,
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|51. ||C. C. Chu and A. Needleman,
"Void nucleation effects in biaxially stretched sheets,"
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Phys. Today, Vol. 30, No. 1, pp. 46-55, 1977.|
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|55. ||J. D. Eshelby,
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|57. ||A. A. Griffith,
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|59. ||R. Hill,
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|60. ||D. Krajcinovic,
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