Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
in January 1966
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IssuesArchive of Issues2010-6pp.844-855

Archive of Issues

Total articles in the database: 9198
In Russian (. . ): 6504
In English (Mech. Solids): 2694

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A.M. Lin'kov, "Loss of Stability, Characteristic Length, and Novozhilov-Neuber Criterion in Fracture Mechanics," Mech. Solids. 45 (6), 844-855 (2010)
Year 2010 Volume 45 Number 6 Pages 844-855
DOI 10.3103/S0025654410060087
Title Loss of Stability, Characteristic Length, and Novozhilov-Neuber Criterion in Fracture Mechanics
Author(s) A.M. Lin'kov (Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, Bol'shoy pr-t 61, V.O., St. Petersburg, 199178 Russia,
Abstract The present paper presents a summary of results in fracture mechanics obtained using the fundamental propositions put forward by V. V. Novozhilov in 1969. Namely, fracture is treated as loss of stability, the role of a structural parameter having the dimension of length is emphasized, and the importance of the Novozhilov-Neuber force criterion is stressed; this criterion allows obtaining simple and far-reaching generalizations. The main attention is paid to the results obtained by the author either in collaboration with Professor Novozhilov or as a result of close communication with him for almost two decades. The force treatment of the strict stability condition, which implies using a linear softening in the crack tip region, and the estimate of the maximal speed of crack propagation, based on a structural-time criterion, are performed for the first time.
Keywords fracture, crack, instability, linear softening, structure parameter
1.  A. M. Lin'kov, "Plastic Deformation of a Washer Soldered in a Plate," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 1, 80-85 (1971) [Mech. Solids (Engl. Transl.)].
2.  A. M. Lin'kov and V. V. Novozhilov, "Extremum Principles for Infinite Domains," in Progress in Mechanics of Deformable Bodies. Dedicated to Academician B. G. Galerkin on the Occasion of his 100th Anniversary (Nauka, Moscow, 1975), pp. 350-354 [in Russian].
3.  V. V. Novozhilov, "On a Necessary and Sufficient Criterion for Brittle Strength," Prikl. Mat. Mekh. 33 (2), 212-222 (1969) [J. Appl. Math. Mech. (Engl. Transl.) 33 (2), 201-210 (1969)].
4.  H. Neuber, Theory of Notch Stresses (J. W. Edwards, Ann Arbor, Michigan, 1946; Gostekhizdat, Moscow-Leningrad, 1947).
5.  M. Ya. Leonov and V. V. Panasyuk, "Propagation of Very Small Cracks in Solids," Prikl. Mekh. 5 (4), 391-401 (1959).
6.  I. M. Petukhov and A. M. Lin'kov, "The Theory of Post-Failure Deformation and the Problem of Stability in Rock Mechanics," Int. J. Rock Mech. Mining Sci. Geomech. Abstr. 16 (2), 57-76 (1979).
7.  A. M. Lin'kov and M. A. Tleuzhanov, "Calculation of Local Zones of Irreversible Deformation at the Crack Tip," Izv. AN KirgSSR. Fiz.-Tekh. Mat. Nauki, No. 1, 47-51 (1990).
8.  J. Rice, "A Path Independent Integral and Approximate Analysis of Strain Concentration by Notches and Cracks," Trans. ASME. Ser. E, J. Appl. Mech. 35 (2), 379-387 (1968).
9.  A. M. Lin'kov, "Stability Conditions in Fracture Mechanics," Dokl. Akad. Nauk SSSR 233 (1), 45-48 (1977) [Sov. Phys. Dokl. (Engl. Transl.) 22 (3), 133-137 (1977)].
10.  V. V. Novozhilov, Foundations of Nonlinear Theory of Elasticity (Gostekhizdat, Moscow-Leningrad, 1948) [in Russia].
11.  L. M. Kachanov, Foundations of Fracture Mechanics (Nauka, Moscow, 1974) [in Russian].
12.  A. M. Lin'kov and V. V. Novozhilov, "To the Question on the Theory of Crack Growth," in Strength of Materials and Constructions (Naukova Dumka, Kiev, 1975), pp. 357-363 [in Russian].
13.  A. M. Lin'kov, "Stability of Inelastic, Geometrically Nonlinear, Discrete Systems," Dokl. Akad. Nauk SSSR 294 (1), 44-47 (1987) [Sov. Phys. Dokl. (Engl. Transl.) 32 (5), 376-378 (1987)].
14.  G. Maier and D. C. Drucker, "Effects of Geometry Change on Essential Features of Inelastic Behavior," J. Engng Mech. Div. ASCE 99 (EM4), 819-834 (1973).
15.  A. M. Lin'kov, Dynamic Phenomena in Mines and the Problem of Stability (Int. Soc. Rock Mech., Lisboa, Cedex, Portugal, 1994).
16.  F. Shanley, "Inelastic Column Theory," J. Aeronaut. Sci. 14 (5), 261-268 (1947).
17.  A. M. Lin'kov and A. A. Dobroskok, "On Bifurcation and Instability due to Softening," in Proc. Int. Workshop "Bifurcation and Instabilities in Geomechanics, IWBI-2002", Ed. by J. R. Labuz and A. Drescher (Swets and Zeitlinger, Lisse, The Netherlands, 2003), pp. 17-28.
18.  A. M. Lin'kov, "Boundary Value Problem for Crack Growth in Viscoelastic Media," Int. J. Fract. 65 (3), 197-218 (1994).
19.  A. M. Lin'kov, "Key-Note Address: Equilibrium and Stability of Rock Masses," in Proc. 8th Int. Congr. on Rock Mechanics, Ed. by T. Fujji, Vol. 3 (Balkema, Rotterdam, 1995), pp. 1049-1054.
20.  A. M. Lin'kov, "Schlumberger Award Lecture: Rockbursts and Instability of Rocks Masses," Int. J. Rock Mech. Mining Sci. Geomech. Abstr. 33 (7), 727-732 (1996).
21.  A. M. Lin'kov, "Key-Note Address: New Geomechanical Approaches to Develop Quantitative Seismicity," in Proc. 4th Int. Symp. "Rockbursts and Seismicity in Mines", Ed. by S. J. Gibowicz and S. Lasocki (Balkema, Rotterdam, 1997), pp. 151-166.
22.  A. M. Lin'kov, "Key-Note Lecture: Integration of Numerical Modeling and Seismic Monitoring: General Theory and First Steps," in Proc. Int. Conf. "New Development in Rock Mechanics, Ed. by Yunmei Lim (Rinton Press, New York, 2002), pp. 259-264.
23.  A. M. Lin'kov, "Numerical Modeling of Seismic and Aseismic Events in Geomechanics," Fiz.-Tekhn. Probl. Razrab. Polez. Iskopaemykh, No. 1, 19-33 (2005).
24.  A. M. Linkov, "On Numerical Modeling of Seismic and Aseismic Events in 3D Problems of Mechanics," Fiz.-Tekhn. Probl. Razrab. Polez. Iskopaemykh, No. 1, 3-16 (2006).
25.  A. M. Linkov, Boundary Integral Equations in Elasticity Theory (Kluwer, Dordrecht etc., 2002).
26.  A. A. Dobroskok, A. Ghassemi, and A. M. Linkov, "Extended Structural Criterion for Numerical Simulation of Crack Propagation under Compressive Loads," Int. J. Fract. 133 (3), 223-246 (2005).
27.  A. A. Dobroskok, A. Ghassemi, and A. M. Linkov, "Numerical Simulation of Crack Propagation Influenced by Thermal and Porous Liquid Stresses," Int. J. Fract. 134 (2), L29-L34 (2005).
28.  A. A. Dobroskok, L. Fradkin, A. M. Linkov, and G. Mishuris, "Crack Redirection with Thermal Secondary Loading," Eng. Fract. Mech. 74 (11), 1719-1726 (2007).
29.  V. V. Zubkov, V. F. Koshelev, and A. M. Lin'kov, "Numerical Modeling of Hydraulic Fracture Initiation and Development," Fiz.-Tekh. Probl. Razrab. Polez. Iskopaemykh, No. 1, 45-63 (2007) [J. Mining Sci. (Engl. Transl.) 43 (1), 40-56 (2007)].
30.  A. M. Lin'kov and V. F. Koshelev, "Multi-Wedge Singular Points in Materials: Theory, Numerical Techniques and Applications," in Proc. 4th Int. Conf. "Mathematical Modeling and Computer Simulation of Materials Technologies, MMT-2006, Vol. 1 (The College of Judea and Samaria, Ariel, Israel, 2006), pp. I-48-I-56.
31.  N. F. Morozov, Yu. V. Petrov, and A. A. Utkin, "To Calculations of Intensity of Pulse Dynamic Loads in Crack Mechanics," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 5, 180-182 (1988) [Mech. Solids (Engl. Transl.)].
32.  V. A. Bratov, N. F. Morozov, and Yu. V. Petrov, Dynamic Strength of Continuum (St. Petersburg Univ. Press, St. Petersburg, 2009).
33.  A. M. Lin'kov, "The Size of the End Zone and the Propagation Velocity of a Displacement Jump," Prikl. Mat. Mekh. 69 (1), 144-149 (2005) [J. Appl. Math. Mech. (Engl. Transl.) 69 (1), 135-140 (2005)].
34.  A. M. Lin'kov, "A Theory of Rupture Pulse on Softening Interface with Application to the Chi-Chi Earthquake," J. Geophys. Res. 111, B09307.1-B09307.14 (2006).
Received 23 July 2010
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