Mechanics of Solids (about journal) 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

Russian  English English About Journal | Issues | Editorial Board | Contact Us

 Web hosting is provided
by the Ishlinsky Institute for
Problems in Mechanics
of the Russian
Academy of Sciences
IssuesArchive of Issues2006-6pp.83-109

Archive of Issues

Total articles in the database: 3985
In Russian (. . ): 2236
In English (Mech. Solids): 1749

<< Previous article | Volume 41, Issue 6 / 2006 | Next article >>
V. N. Kukudzhanov, "Coupled models of elastoplasticity and damage and their integration," Mech. Solids. 41 (6), 83-109 (2006)
Year 2006 Volume 41 Number 6 Pages 83-109
Title Coupled models of elastoplasticity and damage and their integration
Author(s) V. N. Kukudzhanov (Moscow)
Abstract 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 problems.
1.  V. A. Astaf'ev, Yu. N. Radaev, and L. V. Stepanova, Nonlinear 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 Microplasticity [Russian translation], pp. 18-37, Metallurgiya, Moscow, 1972.
6.  A. I. Glushko, "Study of scabbing as a process of microvoid nucleation," Izv. AN SSSR MTT [Mechanics of Solids], No. 5, pp. 132-140, 1978.
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], Yanus-K, Moscow, 1996.
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, Moscow, 1969.
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 Russian], Nedra, Moscow, 1984.
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, Moscow, 1988.
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, "Dynamic fracture criteria for ductile and brittle metals," Mater., Vol. 7, No. 3, pp. 393-401, 1972.
48.  R. De Borst, "Computation of post-bifurcation and post-failure behavior of strainsoftening solids," 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, Brown University Report, 1988.
51.  C. C. Chu and A. Needleman, "Void nucleation effects in biaxially stretched sheets," Trans ASME J. Eng-ng, Materials and Technology, Vol. 102, No. 3, pp.249-256, 1980.
52.  D. R. Curran, L. Seaman, and D. A. Shockey, "Dynamic failure in solids," Phys. Today, Vol. 30, No. 1, pp. 46-55, 1977.
53.  D. R. Curran, L. Seaman, and D. A. Shockey, "Dynamic failure of solids," Physics Reports, No. 147, pp. 253-388, 1987.
54.  W. Dornowski and P. Perzyna, "Localization and localized fracture phenomena in inelastic solids under cyclic dynamic loadings," Foundation of Civil and Environmental Eng-ng, No. 1, pp. 41-86, 2002.
55.  J. D. Eshelby, "The determination of the elastic field of an ellipsoidal inclusion and related problems," Proc. Roy. Soc. London Ser. A, Vol. 241, No. 1226, pp. 376-396, 1957.
56.  J. J. Gilliman, "Dislocation dynamics and the response of material to impact," Appl. Mech. Rev., Vol. 21, No. 8, pp. 767-783, 1968.
57.  A. A. Griffith, "The phenomena of rupture and flow in solids," Phil. Trans. Roy. Soc. London Ser. A, Vol. 221, pp. 163-198, 1920.
58.  A. L. Gurson, "Continuum theory of ductile rupture by void nucleation and growth, Pt. I, Yield criteria and flow rules for porous ductile materials, " Trans. ASME J. Eng-ng, Materials and Technology, Vol. 99, No. 1, pp. 2-15, 1977.
59.  R. Hill, "The essential structure of constitutive laws for metal composites and polycrystals," J. Mech. and Phys. of Solids, Vol. 15, No. 2, pp. 79-95, 1967.
60.  D. Krajcinovic, Damage Mechanics, Elsevier, Amsterdam, 1996.
61.  V. N. Kukudzhanov, "A new numerico-analytical method for the solution of elastoplastic equations based on the splitting of constitutive equations," in D. R. T. Owen et al. (Editors), Book Computational Plasticity VII. Volume 2, pp. 711-714, Barcelona CIMNE, 2005.
62.  V. N. Kukudzhanov, "A new splitting method for the solution of nonlinear equations of damaged elastoviscoplastic materials with complicated yield condition," in Proc. WCCM-VII, Los Angeles California USA, 2006 (CD-ROM).
63.  J. Lemaitre, A Course on Damage Materials, Springer, Berlin, London, 1992.
64.  G. A. Maugin, The Thermodynamics of Plasticity and Fracture, Cambridge University Press, Cambridge, 1992.
65.  O. Miller, L. B. Freud, and A. Needleman, "Modeling and simulation of dynamics fragmentation in brittle materials," Intern. J. Fracture, Vol. 96, pp. 101-125, 1999.
66.  M. Basista and W. K. Nowacki (Editors), Modeling of Damage and Fracture Processes in Engineering Materials. Trends in Mechanics of Materials. Volume 2, IPPT PAN, Warsaw, 1999.
67.  S. Murakami, "Mechanical modeling of material damage," Trans. ASME J. Appl. Mech., Vol. 55, No. 2, pp. 280-286, 1988.
68.  A. Needleman, "A continuum model for void nucleation by inclusion dibonding," Trans. ASME J. Appl. Mech., No. 3, pp. 525-531, 1987.
69.  W. K. Nowacki and J. R. Kiepaczko (Editors), New Experimental Methods in Material Dynamics and Impact. Trends in Mechanics of Materials. Volume 3, IPPT PAN, Warsaw, 2001.
70.  P. Perzyna and A. Drabik, "Description of micro-damage process by porosity parameter for nonlinear viscoplasticity," Arch. Mechanics, Vol. 41, No. 6, pp. 895-908, 1989.
71.  K. E. Puttick, "Ductile fracture in metals," Phil. Mag. Ser. B, Vol. 4, No. 44, pp. 964-969, 1959.
72.  Y. N. Radaev, "Thermodynamical modeling of anisotropic damage growth. Pt. I. Canonical dynamic state variable of continuum damage mechanics and thermodynamical functions of three-dimensional anisotropic damage state," I. Non-Equilib. Thermodyn., Vol. 21, No. 2, pp. 129-152, 1996.
73.  Y. N. Radaev, "Thermodynamical modeling of anisotropic damage growth. Pt. II. Canonical damage grow rate equations and theory of damage invariants," I. Non-Equilib. Thermodyn., Vol. 21, No. 3, pp. 197-222, 1996.
74.  J. W. Rudnicki and J. R. Rice, "Conditions for the localization of deformation in pressure-sensitive dilatant materials," J. Mech. and Phys. Solids, Vol. 23, No. 6, pp. 371-394, 1975.
75.  D. A. Shockey, D. R. Curran, L. Seaman, J. T. Rosenberg, and C. F. Peterson, "Fragmentation of rocks under dynamic loads," Intern. J. Rock. Mech. Min. Sci., Vol. 11, No. 8, pp. 303-317, 1974.
76.  D. Steglich, W. Brocks, and J. Heerens, Punch Test for the Simulation of Ships Hull Damage. Experiment and Simulation. FENet, NAFEMS 2003.
77.  J. W. Taylor, "Dislocation dynamics and dynamic yielding," J. Appl. Phys., Vol. 36, No. 10, pp. 3146-3150, 1965.
78.  V. Tvergaard, "Influence of voids on shear band instabilities under plane strain condition," J. Fracture Mechanics, Vol. 17, No. 4, pp. 389-407, 1981.
79.  V. Tvergaard and A. Needleman, "Analysis of the cup-cone fracture in round tensile bar," Acta Metallurgica, Vol. 32, No. 1, pp. 157-169, 1984.
80.  V. Tvergaard and A. Needleman, "Elastic-viscoplastic analysis of ductile fracture," in D. Besdo and E. Stain (Editors), Finite Inelastic Deformations - Theory of Applications, pp. 3-14, Springer, Berlin, 1991.
81.  C. H. Yew and P. A. Taylor, "A thermodynamic theory of dynamic fragmentation," Intern. J. Impact Engineering, Vol. 15, pp. 385-394, 1994.
Received 19 September 2006
<< Previous article | Volume 41, Issue 6 / 2006 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia (+7 495) 434-3538
Founders: Russian Academy of Sciences, Branch of Power Industry, Machine Building, Mechanics and Control Processes of RAS, Journals on Mechanics Ltd.
© Journals on Mechanics Ltd.
Rambler's Top100