Literature Cited
S. Yu. Babich and A. N. Guz', “Complex potentials of the plane dynamic problem for compressible bodies with initial stress,” Prikl. Mekh.,17, No. 7, 75–83 (1981).
S. Yu. Babich and A. N. Guz', “Complex potentials of plane dynamic problems for elastic incompressible bodies with initial stress,” Dokl. Akad. Nauk Ukr. SSR Ser. A, No. 11, 41–45 (1981).
S. Yu. Babich and A. N. Guz', “Plane dynamic problems for elastic incompressible bodies with initial stress,” Prikl. Mat. Mekh.,46, No. 2, 263–271 (1982).
G. I. Barenblatt and G. P. Cherepanov, “Splitting brittle bodies,” Prikl. Mat. Mekh.,24, No. 4, 666–682 (1960).
L. A. Galin, Contact Problems of Elasticity Theory [in Russian], Fizmatgiz, Moscow (1953).
A. N. Guz', Stability of Three-Dimensional Deformed Bodies [in Russian], Naukova Dumka, Kiev (1971).
A. N. Guz', Stability of Elastic Bodies with Finite Deformations [in Russian], Naukova Dumka, Kiev (1973).
A. N. Guz', “Representation of general solutions of the linearized elasticity theory of a compressible body,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 8, 700–703 (1975).
A. N. Guz', “Representation of general solutions of the linearized elasticity theory of incompressible bodies,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 12, 1092–1096 (1975).
A. N. Guz', Principles of the Theory of Mine-Working Stability [in Russian], Naukova Dumka, Kiev (1977).
A. N. Guz', Stability of Elastic Bodies with Omnidirectional Compression [in Russian], Naukova Dumka, Kiev (1979).
A. N. Guz', “Linearized theory of the failure of brittle bodies with initial stress,” Dokl. Akad. Nauk SSSR,252, No. 5, 1085–1088 (1980).
A. N. Guz', “Rupture cracks in elastic bodies with initial stress,” Dokl. Akad. Nauk SSSR,254, No. 3, 571–574 (1980).
A. N. Guz', “Complex potentials of plane linearized problems of elasticity theory (compressible bodies),” Prikl. Mekh.,16, No. 5, 72–83 (1980).
A. N. Guz', “Complex potentials of plane linearized problems of elasticity theory (incompressible bodies),” Prikl. Mekh.,16, No. 6, 64–70 (1980).
A. N. Guz', “Complex potentials of plane linearized elasticity theory,” Prikl. Mekh.,16, No. 9, 83–97 (1980).
A. N. Guz', “Theory of cracks in elastic bodies with initial stress (formulation of the problem, rupture cracks),” Prikl. Mekh.,16, No. 12, 3–14 (1980).
A. N. Guz', “Three-dimensional problem for shear cracks in elastic bodies with initial stress,” Dokl. Akad. Nauk SSSR,257, No. 3, 562–565 (1981).
A. N. Guz', “Failure criterion for solid bodies under compression along the cracks. Plane problem,” Dokl. Akad. Nauk SSSR,259, No. 6, 1315–1318 (1981).
A. N. Guz', “Failure criterion for solid bodies under compression along the cracks. Three-dimensional problem,” Dokl. Akad. Nauk SSSR,261, No. 1, 42–45 (1981).
A. N. Guz', “Theory of cracks in elastic bodies with initial stress (shear cracks, limiting case),” Prikl. Mekh.,17, No. 1, 3–13 (1981).
A. N. Guz', “Theory of cracks in elastic bodies with initial stress (highly elastic materials),” Prikl. Mekh.,17, No. 2, 11–21 (1981).
A. N. Guz', “Theory of cracks in bodies with initial stress (rigid materials),” Prikl. Mekh.,17, No. 4, 3–9 (1981).
A. N. Guz', “Theory of cracks in elastic bodies with initial stress (problem of splitting),” Prikl. Mekh.,17, No. 5, 3–12 (1981).
A. N. Guz', “Theory of cracks in elastic bodies with initial stress (three-dimensional static problems),” Prikl. Mekh.,17, No. 6, 3–20 (1981).
A. N. Guz', “Three-dimensional problem for disk-shaped cracks in an elastic body with initial stress,” Prikl. Mekh.,17, No. 11, 21–30 (1981).
A. N. Guz', “General three-dimensional problem for cracks in an elastic body with initial stress,” Prikl. Mekh.,17, No. 12, 3–12 (1981).
A. N. Guz', “Brittle-failure criterion for materials with initial stress,” Dokl. Akad. Nauk SSSR,262, No. 2, 285–288 (1982).
A. N. Guz', “Moving cracks in elastic bodies with initial stress,” Prikl. Mekh.,18, No. 2, 60–67 (1982).
A. N. Guz', “Mechanics of the failure of solids under compression along the cracks (plane problem),” Prikl. Mekh.,18, No. 3, 35–49 (1982).
A. N. Guz', “Mechanics of the failure of solids under compression along the cracks (three-dimensional problem),” Prikl. Mekh.,18, No. 4, 3–13 (1982).
A. N. Guz', “Mechanics of the failure of composite materials under compression along macrocracks,” Prikl. Mekh.,18, No. 6, 3–9 (1982).
A. N. Guz', “Energetic brittle-failure criteria for materials with initial stress,” Prikl. Mekh.,18, No. 9, 3–9 (1982).
A. N. Guz', “Energetic brittle-failure criteria for composite materials with initial stress,” Prikl. Mekh.,19, No. 1, 3–9 (1983).
A. N. Guz' and S. Yu. Babich, “Plane dynamic problems for elastic bodies with initial stress,” Dokl. Akad. Nauk SSSR,261, No. 2, 313–316 (1981).
A. N. Guz', M. Sh. Dyshel', G. G. Kuliev, and O. B. Milovanova, Failure and Stability of Thin Bodies with Cracks [in Russian], Naukova Dumka, Kiev (1981).
A. A. Kaminskii, Brittle Failure around Holes [in Russian], Naukova Dumka, Kiev (1982).
M. V. Keldysh and L. I. Sedov, “Effective solution of some boundary problems for harmonic functions,” Dokl. Akad. Nauk SSSR,16, No. 1, 7–10 (1937).
A. Ya. Krasovskii, Brittleness of Metals at Low Temperatures [in Russian], Naukova Dumka, Kiev (1980).
M. Ya. Leonov and V. V. Panasyuk, Prikl. Mekh. [in Ukrainian],5, No. 5, 391–401 (1959).
S. G. Lekhnitskii, Elasticity Theory for an Anisotropic Body [in Russian], Nauka, Moscow (1977).
A. K. Malmeister, V. P. Tamuzh, and G. A. Teters, Strength of Polymers and Composite Materials [in Russian], Zinatne, Riga (1980).
E. M. Morozov and G. P. Nikishkov, Finite-Element Method in the Mechanics of Failure [in Russian], Nauka, Moscow (1980).
N. I. Muskhelishvili, Some Fundamental Problems of the Mathematical Theory of Elasticity [in Russian], Nauka, Moscow (1966).
V. V. Panasyuk, Limiting Equilibrium of Brittle Bodies with Cracks [in Russian] Naukova Dumka, Kiev (1968).
V. V. Panasyuk, A. E. Andreikiv, and S. E. Kovchik, Methods of Estimating the Crack Resistance of Building Materials [in Russian], Naukova Dumka, Kiev (1977).
B. A. Drozdovskii (ed.), Applied Problems of Failure Viscosity [Russian translation], Mir, Moscow (1968).
G. Libovits, Failure [Russian translation], Vols. 1–7, Mir, Moscow (1973–1976).
Failure of Composite Materials [in Russian], Zinatne, Riga (1979).
M. P. Savruk, Two-Dimensional Elasticity Problems for Bodies with Cracks [in Russian], Naukova Dumka, Kiev (1981).
L. I. Sedov, Continuum Mechanics [in Russian], Vol. 2, Nauka, Moscow (1976).
L. I. Slepyan, Mechanics of Cracks [in Russian], Sudostroenie, Leningrad (1981).
G. P. Cherepanov, “Crack propagation in a continuous medium,” Prikl. Mat. Mekh.,31, No. 3, 476–488 (1967).
G. P. Cherepanov, Mechanics of Brittle Failure [in Russian], Nauka, Moscow (1974).
M. A. Biot, Mechanics of Incremental Deformations, Wiley, New York (1965).
A. E. Green, R. S. Rivlin, and R. T. Shield, “General theory of small elastic deformations superposed on finite elastic deformations,” Proc. R. Soc., Ser. A,211, No. 1104, 128–154 (1952).
A. A. Griffith, “The phenomenon of rupture and flow in solids,” Phil. Trans. R. Soc.,A221, No. 2, 163–198 (1920).
A. N. Guz, G. G. Kuliev, and J. A. Tsurpal, “On fracture of brittle materials from loss of stability near a crack,” Eng. Fract. Mech.,10, No. 2, 401–408 (1978).
G. R. Irwin, “Fracture dynamics,” in: Fracturing of Metals [in Russian], ASM, Cleveland (1948), pp. 147–166.
G. R. Irwin, “Analysis of stresses and strains near the end of crack traversing a plate,” J. Appl. Mech.,24, 361–364 (1957).
G. R. Irwin, “Fracture,” in: Handbuch der Physik, Vol. 6, Springer, Berlin (1958), pp. 551–590.
M. K. Kassir and G. C. Sih, Mechanics of Fracture, Vol. 2, Three-Dimensional Crack Problems, Noordhoff International, Leyden, The Netherlands (1975).
M. Kurashinge, “Circular crack problems for initially stressed neo-Hookean solid,” Z. Angew. Math. Mech.,49, No. 11, 671–678 (1969).
E. O. Orowan, “Fundamentals of brittle behavior of metals,” in: W. M. Murrau (ed.), Fatigue and Fracture of Metals [in Russian], Wiley, London (1950), pp. 139–167.
Rajit S. Dhaliwal, B. M. Singh, and J. G. Rokne, “Axisymmetric contact and crack problems for an initially stressed neo-Hookean elastic layer,” Int. J. Eng. Sic.,18, No. 1, 169–179 (1980).
J. R. Rice, “A path independent integral and approximate analysis of strain concentration by notches and cracks,” J. Appl. Mech.,35, No. 2, 379–386 (1968).
A. A. Wells, “Application of fracture mechanics at and beyond general yielding,” Brit. Weld. J.,10, No. 11, 563–570 (1963).
H. M. Westergaard, “Bearing pressure and cracks,” J. Appl. Mech.,6, No. 2, A49-A53 (1939).
C. H. Wu, “Plane-strain buckling of a crack in a harmonic solid subjected to crack-parallel compression,” J. Appl. Mech.,46, 597–604 (1979).
C. H. Wu, “Plane strair buckling of crack in incompressible elastic solids,” J. Elast.,10, No. 2, 161–177 (1980).
E. Joffe, “The moving Griffith crack,” Phil. Mag.,42, No. 330, 739–750 (1951).
Additional information
Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 19, No. 4, pp. 3–23, April, 1983.
Rights and permissions
About this article
Cite this article
Guz', A.N. Mechanics of the brittle failure of materials with initial stress. Soviet Applied Mechanics 19, 293–308 (1983). https://doi.org/10.1007/BF00884855
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00884855