The main results of research on some nonclassical problems of fracture/failure mechanics are analyzed. These results have been obtained by the author and his followers at the Department of Dynamics and Stability of Continua of the S. P. Timoshenko Institute of Mechanics of the National Academy of Sciences of Ukraine (the NAS of Ukraine) during the last 50 years. The nonclassical problems of fracture/failure mechanics are problems to which the approaches and criteria of classical fracture mechanics are not applicable. A distinguishing feature of the results obtained by the author and his followers is application of three-dimensional theories of stability, dynamics, and statics of solid mechanics to study the nonclassical problems of fracture/failure mechanics. The majority of other researchers have been using various approximate theories of shells, plates, and rods as well as other approaches to studying the nonclassical problems of fracture/failure mechanics. The main scientific results of solving the eight nonclassical problems of fracture\failure mechanics obtained in the framework of the above mentioned approach (three-dimensional theories of solid mechanics) have been presented very briefly, with focus on the statement of problems, the analysis of corresponding experiments, the development of methods for their solution within the framework of approach under consideration, and the discussion of final results. The mathematical aspects of the methods for solving the mentioned problems and their computer-aided implementation have not been discussed in this review, with information on this subject briefly presented as annotation. The following eight nonclassical problems of fracture\failure mechanics (results by the author and his followers) are considered in this review:
– first problem is fracture of composites compressed along the reinforcement;
– second problem is short-fiber model in stability and fracture of composites under compression;
– third problem is end-crush fracture of composites under compression along the reinforcement;
– fourth problem is brittle fracture of cracked materials with initial (residual) stresses acting along the cracks;
– fifth problem is shredding fracture of composites stretched or compressed along the reinforcement;
– sixth problem is fracture of materials under compression along parallel cracks;
– seventh problem is brittle fracture of cracked materials under dynamic loads (with contact interaction of the crack faces);
– eighth problem is fracture of thin-walled cracked bodies under tension with prebuckling.
About 523 monographs and papers published by the author and his followers on the eight nonclassical problems of fracture mechanics have been included in the references to this review.
This review consists of three parts. The first part is General Problems; it is published in Prikladnaya Mekhanika (55, No. 2, 2019). The second part is Compressive Failure of Composite Materials; it is published in Prikladnaya Mekhanika (55, No. 3, 2019). The third part is Other Nonclassical Problems of Fracture/Failure Mechanics; it is published in Prikladnaya Mekhanika (55, No. 4, 2019).
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References
S. D. Akbarov, “Effect of rheologic parameters of the matrix material on the distribution of self-balanced stresses in a multilayer composite with curved structures,” Mech. Comp. Mater., 22, No. 4, 421–427 (1987).
S. D. Akbarov, “Revisiting the mechanics of composites with local curvings in structure,” Prikl. Mekh., 23, No. 1, 119–122 (1987).
S. D. Akbarov, “Distribution of self-balanced stresses in a multilayer composite with curved structure,” Mat. Met. Fiz.-Mekh. Polya, No. 26, 83–89 (1987).
S. D. Akbarov and A. N. Guz, “Stressed state in a composite material with curved layers having a low filler concentration,” Mech. Comp. Mater., 20, No. 6, 688–993 (1984).
S. D. Akbarov and A. N. Guz, ”Revisiting the mechanics of composites with curved structure,” DAN SSSR, 281, No. 1, 37–41 (1985).
S. D. Akbarov and A. N. Guz, “On some effect in the fracture mechanics of composites,” DAN SSSR, 290, No. 1, 23–26 (1986).
S. D. Akbarov and A. N. Guz, “Stress distribution in multilayered composite material with curved structures (model of a piecewise homogeneous body),” Mech. Comp. Mater., 23, No. 4, 396–403 (1988).
I. Yu. Babich, “Unstable small-strain deformation of composites,” Dokl. AN USSR, Ser. A, No. 10, 909–913 (1973).
I. Yu. Babich and A. N. Guz, “Applicability of the Euler approach to the stability analysis of the deformation of anisotropic nonlinear elastic bodies at finite subcritical strains,” DAN SSSR, 202, No. 4, 795–796 (1972).
I. Yu. Babich and A. N. Guz, “Theory of the elastic stability of compressible and incompressible composite media,” Polym. Mech., 8, No. 2, 237–244 (1972).
I. Yu. Babich and A. N. Guz, “Three-dimensional problem of the stability of a fiber in a matrix subject to hyperelastic deformation,” Izv. AN SSSR, No. 3, 44–48 (1973).
V. L. Bogdanov, “Nonaxisymmetric problem of the fracture of a half-space compressed along a near-surface penny-shaped crack,” Dokl. AN USSR, Ser. B, No. 5, 42–47 (1991).
V. L. Bogdanov, “Axisymmetric problem for a near-surface mode I crack in a composite material withy residual stresses,” Mat. Met. Fiz.-Mekh. Polya, 50, No. 2, 45–54 (2007).
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V. L. Bogdanov, “Torsion of a prestressed material with two parallel coaxial cracks,” Dop. NAN Ukrainy, No. 11, 59–66 (2008).
V. L. Bogdanov, “Nonaxisymmetric problem for two parallel coaxial mode I cracks in a prestressed material,” Dop. NAN Ukrainy, No. 8, 49–59 (2010).
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L. A. Galin, Contact Problems of Elasticity [in Russian], Fizmatgiz, Moscow (1953).
I. N. Garashchuk, “Stability of a fiber in a matrix subject to inhomogeneous subcritical deformation,” Dokl. AN USSR, Ser. A, No. 8, 24–27 (1983).
A. Ya. Gol’dman, N. F. Savel’eva, and V. I. Smirnov, “Mechanical properties of glass fabric-reinforced plastics in tension and compression normal to the plane of reinforcement,” Mech. Comp. Mater., 4, No. 4, 643–648 (1968).
A. N. Guz, “On the accuracy of Kirchhoff–Love hypothesis in determining the critical forces in the theory of elastic stability,” DAN SSSR, 179, No. 3, 552–554 (1968).
A. N. Guz, “On the stability of three-dimensional elastic bodies,” J. Appl. Math. Mech., 32, No. 5, 950–955 (1968).
A. N. Guz, “On the stability of a strip,” Izv. AN SSSR, Mekh. Tverd. Tela, No. 6, 111–113 (1969).
A. N. Guz, “On setting up a stability theory of unidirectional fibrous materials,” Int. Appl. Mech., 5, No. 2, 156–162 (1969).
O. M. Guz, “Determining the theoretical ultimate compressive strength of reinforced materials,” Dop. AN URSR, Ser. A, No. 3, 236–238 (1969).
A. N. Guz, “The application condition for the Euler method of stability analysis of the deformation of nonlinear elastic bodies at finite subcritical strains,” DAN SSSR, 194, No. 3, 38–40 (1970).
A. N. Guz, “The three-dimensional theory of stability of deformation of materials with rheological properties,” Izv. AN SSSR, Mekh. Tverd. Tela, No. 6, 104–107 (1970).
A. N. Guz, “Constructing a theory for the strength of unidirectionally reinforced materials in compression,” Strength of Materials, 3, No. 3, 278–280 (1971).
A. N. Guz, Stability of Three-Dimensional Deformable Bodies [in Russian], Naukova Dumka, Kyiv (1971).
À. N. Guz, Stability of Elastic Bodies Subject to Finite Deformations [in Russian], Naukova Dumka, Kyiv (1973).
À. N. Guz, “Analogies between linearized and linear problems of elasticity,” Dokl. AN SSSR, 212, No. 5, 1089–1091 (1973).
O. M. Guz, “Variational principles of three-dimensional problems of the stability of incompressible bodies,” Dop. AN URSR, Ser. A, No. 11, 1008–1012 (1973).
A. N. Guz, Fundamentals of the Theory of Stability of Mine Workings [in Russian], Naukova Dumka, Kyiv (1977).
À. N. Guz, Stability of Elastic Bodies under Triaxial Compression [in Russian], Naukova Dumka, Kyiv (1979).
A. N. Guz, “Variational principles in the three-dimensional theory of stability of deformable bodies under follower loads,” DAN SSSR, 246, No. 6, 1314–1316 (1979).
À. N. Guz, “Linearized theory of fracture of prestressed brittle materials,” Dokl. AN SSSR, 252, No. 5, 1085–1088 (1980).
À. N. Guz, “Tensile cracks in elastic bodies with prestresses,” Dokl. AN SSSR, 254, No. 3, 571–574 (1980).
À. N. Guz, “A failure criterion for solids compressed along cracks: Plane problem,” Dokl. AN SSSR, 259, No. 6, 1315–1318 (1981).
À. N. Guz, “A failure criterion for solids compressed along cracks: Three-dimensional problem,” Dokl. AN SSSR, 261, No. 1, 42–45 (1981).
A. N. Guz, “Brittle fracture criterion for prestressed materials,” DAN SSSR, 262, No. 2, 285–288 (1982).
A. N. Guz, “Continuum theory of the fracture of a compressed composite with an elastoplastic matrix,” DAN SSSR, 262, No. 3, 556–560 (1982).
A. N. Guz, “Failure of unidirectional composite materials under axial compression,” Mech. Comp. Mater., 18, No. 3, 282–288 (1982).
A. N. Guz, Brittle Fracture Mechanics of Prestressed Materials [in Russian], Naukova Dumka, Kyiv (1983).
A. N. Guz, “Continuum theory of composites with small-scale curvature in structure,” DAN SSSR, 268, No. 2, 307–313 (1983).
A. N. Guz, “Theory of vibrations of composites with small-scale curvature in structure,” DAN SSSR, 270, No. 4, 824–827 (1983).
A. N. Guz, “A brittle-fracture criterion for materials with defects under compression,” DAN SSSR, 285, No. 4, 828–831 (1985).
A. N. Guz, “The order of singularity at the crack tip in prestressed materials,” Dokl. AN SSSR, 289, No. 2, 310–313 (1986).
A. N. Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies [in Russian], Vyshcha Shkola, Kyiv (1986).
A. N. Guz, “Continuum theory of the fracture of composites under biaxial compression,” DAN SSSR, 293, No. 4, 805–809 (1987).
A. N. Guz, “Continuum theory of the end-crushing fracture of composites,” DAN SSSR, 298, No. 3, 565–570 (1988).
A. N. Guz, “Exact solution to the plane problem of the fracture of a material compressed along cracks located in a plane,” Dokl. AN SSSR, 310, No. 3, 563–566 (1990).
A. N. Guz, “Local stability of fibrous composites,” DAN SSSR, 314, No. 4, 806–809 (1990).
À. N. Guz, Fracture Mechanics of Compressed Composite Materials [in Russian], Naukova Dumka, Kyiv (1990).
A. N. Guz, “Nonclassical problems of fracture mechanics,” Fiz.-Khim. Mekh. Mater., 29, No. 3, 86–97 (1993).
A. N. Guz, “Moving cracks in composite materials with initial stresses,” Mech. Comp. Mater., 37, No. 5/6, 449–458 (2001).
A. N. Guz, Fundamentals of the Fracture Mechanics of Compressed Composites [in Russian], in 2 vols., Litera, Kyiv (2008). Vol. 1. Fracture in the Structure of a Material. Vol. 2. Related Failure Mechanisms.
A. N. Guz, “Mechanics of crack propagation in materials with initial (residual) stresses (review),” Int. Appl. Mech., 47, No. 2, 121–168 (2011).
A. N. Guz, “Establishing the foundations of the mechanics of fracture of materials compressed along cracks (review),” Int. Appl. Mech., 50, No. 1, 1–57 (2014).
A. N. Guz, Elastic Waves in Bodies with Initial (Residual) Stresses [in Russian], in two parts, LAP LAMBERT Academic Publishing, Saarbrucken/Deutschland (2016). Part 1. General Issues. Waves in Unbounded Bodies and Surface Waves. Part 2. Waves in Semibounded Bodies.
A. N. Guz and I. A. Guz, “Continuum approximation in the theory of stability of composite laminates,” DAN SSSR, 305, No. 5, 1073–1076 (1989).
A. N. Guz and I. A. Guz, “Local instability of composite laminates,” DAN SSSR, 311, No. 4, 812–814 (1990).
A. N. Guz, I. A. Guz, A. V. Men’shikov, and V. A. Men’shikov, “Three-dimensional problems in the dynamic fracture mechanics of materials with interface cracks (review),” Int. Appl. Mech., 49, No. 1, 1–61 (2013).
A. N. Guz and V. A. Dekret, Short-Fiber Model in the Theory of the Stability of Composites [in Russian], LAP Lambert Acad. Publ., Saarbrücken/Deutschland (2015).
A. N. Guz and V. A. Dekret, “Finite-fiber model in the three-dimensional theory of stability of composites (review),” Int. Appl. Mech., 52, No. 1, 1–48 (2016).
A. N. Guz, V. A. Dekret, and Yu. V. Kokhanenko, “Plane problems of stability of composite materials with a finite-size filler,” Mech. Comp. Mater., 36, No. 1, 49–54 (2000).
A. N. Guz, V. A. Dekret, and Yu. V. Kokhanenko, “Interaction of short fibers in a matrix during loss of stability: Plane problem,” in: Problems of Mechanics [in Russian], Fizmatlit, Moscow (2003), pp. 331–341.
A. N. Guz, M. Sh. Dyshel’, G. G. Kuliev, and O. B. Milovanova, “Stability of thin plates with cracks,” Dokl. AN USSR, Ser. A, No. 5, 421–426 (1977).
A. N. Guz, M. Sh. Dyshel’, G. G. Kuliev, and O. B. Milovanova, Fracture and Stability of Thin Bodies with Cracks [in Russian], Naukova Dumka, Kyiv (1981).
A. N. Guz and V. V. Zozulya, “Dynamic problem for a plane with a cut; interaction of the banks,” Sov. Phys. Dokl., 36, No. 5, 406–409 (1991).
A. N. Guz and V. V. Zozulya, “Dynamic contact problem for a plane with two cuts,” Sov. Phys. Dokl., 36, No. 11, 804–805 (1991).
A. N. Guz and V. V. Zozulya, “Dynamic problem in elasticity with constraints in the form of inequalities,” Dokl. AN USSR, No. 5, 47–50 (1991).
A. N. Guz, V. V. Zozulya, and A. V. Men’shikov, “Contact interaction of the faces of an elliptic crack under the action of a normal harmonic load,” in: D. D. Ivlev and N. F. Morozov (eds.), Problems of Solid and Rock Mechanics [in Russian], Fizmatgiz, Moscow (2006), pp. 204–220.
A. N. Guz, V. I. Knyukh, and V. M. Nazarenko, “Delamination of a composite compressed along two parallel macrocracks,” Fiz.-Khim. Mekh. Mater., 23, No. 1, 72–78 (1987).
À. N. Guz, V. P. Korzh, and V. N. Chekhov, “Stability of a layered half-plane under distributed surface loads,” DAN SSSR, 313, No. 6, 1381–1385 (1990).
A. N. Guz and Yu. V. Kokhanenko, “Brittle end-crushing fracture of composites (piecewise-homogeneous material model),” DAN SSSR, 296, No. 4, 805–808 (1987).
A. N. Guz and G. G. Kuliev, “Problem statement for the stability of deformation of thin bodies with cracks,” Dokl. AN USSR, Ser. A, No. 12, 1085–1088 (1976).
A. N. Guz, G. G. Kuliev, and N. K. Zeinalov, “Bulging of a stretched plate with a curved hole,” Izv. AN SSSR, Mekh. Tverd. Tela, No. 2, 163–168 (1979).
A. N. Guz, G. G. Kuliev, and I. A. Tsurpal, “Concepts of stability in the theory of brittle fracture,” in: Abstracts of 4th All-Union Congress on Theory and Applied Mechanics [in Russian], Kyiv (1976).
A. N. Guz and Yu. N. Lapusta, “On a method of investigating fibre stability in an elastic semi-infinite matrix near a free surface,” J. Appl. Math. Mech., 53, No. 4, 546–550 (1989).
A. N. Guz and Yu. N. Lapusta, “Near-surface instability of a row of fibers in a composite,” DAN, 325, No. 4, 679–683 (1992).
A. N. Guz and D. A. Musaev, “Fracture of ribbon-reinforced composites under compression,” DAN SSSR, 301, No. 3, 565–568 (1988).
A. N. Guz, V. L. Bogdanov, and V. M. Nazarenko, “Fracture of a half-space with a near-surface penny-shaped crack in compression: Spatial nonaxisymmetric problem,” Dokl. AN SSSR, 319, No. 4, 835–839 (1991).
À. N. Guz and V. M. Nazarenko, “Fracture of a half-space with a surface penny-shaped crack: Axisymmetric problem,” Dokl. AN SSSR, 274, No. 1, 38–41 (1984).
A. N. Guz and V. M. Nazarenko, “Ductile near-surface fracture of a material compressed along macrocracks: Spatial problem,” Dokl. AN SSSR, 284, No. 4, 812–815 (1985).
A. N. Guz and V. M. Nazarenko, “Theory of surface delamination of composites in compression along a macrocrack,” Mech. Comp. Mater., 21, No. 5, 563–570 (1985).
A. N. Guz and V. M. Nazarenko, “Fracture of materials under compression along a periodic system of cracks under plane strain conditions,” J. Appl. Math. Mech., 51, No. 2, 261–256 (1987).
A. N. Guz, V. M. Nazarenko, and I. P. Starodubtsev, “Plane problem of the fracture of materials with two parallel cracks compressed along cracks,” in: V. G. Zubchaninov (ed.), Problems of Solid Mechanics [in Russian], Kalinin. Univ., Kalinin (1986), pp. 138–151.
A. N. Guz, V. M. Nazarenko, and Yu. I. Khoma, “Fracture of a composite compressed along a cylindrical crack,” Dokl. NANU, No. 10, 48–52 (1995).
A. N. Guz, J. J. Rushchitsky, and I. A. Guz, Introduction to the Mechanics of Nanocomposites [in Russian], Inst. Mekh. im. S. P. Timoshenko, Kyiv (2010).
A. N. Guz, E. A. Tkachenko, and V. N. Chekhov, “Calculation of stability of laminated composite coatings in tribotechnics,” Mech. Comp. Mater., 36, No. 2, 139–142 (2000).
A. N. Guz, E. A. Tkachenko, and V. N. Chekhov, “Surface instability of laminated coatings upon inelastic deformation,” Mech. Comp. Mater., 36, No. 6, 475–480 (2000).
A. N. Guz and M. A. Cherevko, “Revisiting the fracture mechanics of a fibrous composite under compression,” DAN SSSR, 268, No. 4, 806–808 (1981).
A. N. Guz and M. A. Cherevko, “Compression failure of a unidirectional fibrous composite with an elastoplastic matrix,” Mech. Comp. Mater., 18, No. 6, 656–663 (1983).
A. N. Guz, M. A. Cherevko, G. G. Margolin, and I. M. Romashko, “Failure of unidirectional boron-reinforced aluminum composites in compression,” Mech. Comp. Mater., 22, No. 2, 158–162 (1986).
A. N. Guz and V. N. Chekhov, “Surface buckling of a layered half-plane with layers subject to elastoplastic deformation,” DAN SSSR, 272, No. 3, 546–550 (1983).
A. N. Guz and V. N. Chekhov, “Surface instability of laminated materials at low and finite subcritical strains,” Mech. Comp. Mater., 20, No. 5, 590–584 (1985).
A. N. Guz and V. N. Chekhov, “Stability analysis of semi-infinite layered materials taking into account their elastic and elastoplastic properties,” Izv. AN SSSR, No. 1, 87–96 (1985).
A. N. Guz and V. N. Chekhov, “Using variational methods in stability problems for layered semibounded materials,” DAN SSSR, 283, No. 5, 1123–1126 (1985).
A. N. Guz, V. N. Chekhov, and N. A. Shul’ga, “Surface instability of a half-space of periodic structure,” DAN SSSR, 266, No. 6, 1306–1310 (1982).
I. A. Guz, “Stability of a composite compressed along an interface crack,” DAN SSSR, 325, No. 3, 455–458 (1992).
I. A. Guz, “Plane problem of the stability of composites with slipping layers,” Mech. Comp. Mater., 27, No. 5, 547–551 (1992).
I. A. Guz, “Stability of a composite compressed along two interface microcracks,” DAN SSSR, 328, No. 4, 437–439 (1993).
I. A. Guz, “Composites with interlamination cracks: Stability under compression along two microcracks between orthotropic layers,” Mech. Comp. Mater., 29, No. 6, 581–586 (1994).
I. A. Guz, “Stability of composites compressed along an array of parallel interlaminar cracks,” Dokl. NANU, No. 6, 44–47 (1995).
Yu. M. Dal’, “Local bending of a stretched plate with a crack,” Izv. AN SSSR, Mekh. Tverd. Tela, No. 4, 135–141 (1978).
V. A. Dekret, “Solving the plane buckling problem for a composite reinforced with two short fibers,” Dop. NANU, No. 8, 37–40 (2003).
V. A. Dekret, “Plane buckling problem for a composite reinforced with two parallel short fibers,” Dop. NANU, No. 12, 38–41 (2003).
V. A. Dekret, “Stability of a composite reinforced with a periodic row of inline short fibers,” Dop. NANU, No. 11, 47–50 (2004).
V. A. Dekret, “Stability of a composite reinforced with a periodic row of parallel short fibers,” Dop. NANU, No. 12, 41–44 (2004).
V. A. Dekret, “Stability of a composite under-reinforced with short fibers near the free surface,” Dop. NANU, No. 10, 49–51 (2006).
M. V. Dovzhik, “Fracture of a half-space compressed along a penny-shaped crack located at a short distance from the surface,” Int. Appl. Mech., 48, No. 3, 294–304 (2012).
M. V. Dovzhik, “Fracture of a material compressed along two closely spaced penny-shaped cracks,” Int. Appl. Mech., 49, No. 1, 563–572 (2012).
M. V. Dovzhik, “Fracture of a material compressed along a periodic array of closely spaced penny-shaped cracks,” Dop. NAN Ukrainy, No. 10, 100–105 (2013).
M. V. Dovzhik and V. M. Nazarenko, “Fracture of a material compressed along two closely spaced penny-shaped cracks,” Int. Appl. Mech., 48, No. 4, 423–429 (2012).
M. V. Dovzhik and V. M. Nazarenko, “Fracture of a material compressed along a periodic set of closely spaced cracks,” Int. Appl. Mech., 48, No. 6, 710–718 (2012).
M. Sh. Dyshel’, “Allowing for the local buckling of plates with cracks in experimental determination of the stress intensity factor,” Dokl. AN USSR, Ser. A, No. 11, 40–44 (1988).
V. M. Enotov and R. L. Salganik, “Beam approximation in the theory of cracks,” Izv. AN SSSR, Mekh., No. 5, 95–102 (1965).
V. V. Zozulya, “Dynamic problems in the theory of cracks with contact, stick, and sliding areas,” Dokl. AN USSR, Ser. A, No. 1, 47–50 (1990).
V. V. Zozulya, “Dynamic problems in the theory of cracks with contact, stick, and slip areas,” Dokl. AN USSR, Ser. A, No. 3, 53–50 (1990).
V. V. Zozulya, “Harmonic load acting on a crack with interacting edges in an unbounded body,” Dokl. AN USSR, Ser. A, No. 4, 46–49 (1990).
V. V. Zozulya, “Hadamard integrals in dynamic problems of the theory of cracks,” Dokl. AN USSR, Ser. A, No. 2, 19–22 (1991).
V. V. Zozulya, “Dynamic problem for a plane with two cracks with contacting edges,” Dokl. AN USSR, No. 8, 75–80 (1991).
V. V. Zozulya, “Solving dynamic problems for bodies with cracks by the method of boundary integral equations,” Dokl. AN USSR, Ser. A, No. 3, 38–43 (1992).
A. Yu. Ishlinskii, “Stability of the equilibrium of elastic bodies in the context of the mathematical theory of elasticity,” Ukr. Mat. J., 6, No. 2, 140–146 (1954).
M. V. Keldysh and L. I. Sedov, “Effective solution of some boundary-value problems for harmonic functions,” Dokl. AN SSSR, 16, No. 1, 7–10 (1937).
L. J. Broutman and R. H. Krock (eds.), Composite Materials, in 8 vols., Academic Press, New York–London (1974–1975).
Yu. V. Kokhanenko, “Applying the finite-difference method to problems of elastic stability,” Dop. AN URSR, Ser. A, No. 7, 537–539 (1973).
Yu. V. Kokhanenko, “One method of solving problems of the three-dimensional stability of ribbon composites,” Dokl. AN USSR, Ser. A, No. 2, 31–33 (1989).
G. G. Kuliev, “Fracture of deformable bodies with a central vertical crack in a homogeneous force field,” Dokl. AN USSR, Ser. A, No. 8, 714–717 (1978).
G. G. Kuliev, “Buckling near a crack preceding brittle fracture,” Dokl. AN USSR, Ser. A, No. 5, 355–358 (1979).
Yu. N. Lapusta, “Method of stability analysis of two fibers in an elastic semi-infinite matrix,” Dokl. AN USSR, Ser. A, No. 1, 42–45 (1989).
Yu. N. Lapusta, “Allowing for the effect of the free boundary on the stability of a periodic row of fibers in an elastic semi-infinite matrix,” Dokl. AN USSR, Ser. A, No. 5, 34–37 (1989).
Yu. N. Lapusta, “Solving the problem of the near-surface buckling of a periodic array of fibers in an elastic matrix,” Dokl. AN USSR, Ser. A, No. 7, 48–52 (1989).
Yu. N. Lapusta, “Possible buckling modes of a fiber in a semi-infinite matrix,” Dokl. AN USSR, Ser. A, No. 11, 42–45 (1989).
Yu. N. Lapusta, “Stability of a row of fibers near the free flat edge of a matrix under axial compression,” Mekh. Komp. Mater., No. 4, 739–742 (1990).
Yu. N. Lapusta, “Stability of a fiber near a cavity in an elastoplastic matrix,” Dokl. AN USSR, Ser. A, No. 9, 80–84 (1991).
Yu. N. Lapusta, “Near-surface instability of a periodic array of fibers in an elastic matrix,” Dokl. AN USSR, Ser. A, No. 8, 70–75 (1992).
L. S. Leibenzon, “Application of harmonic functions in stability analysis of spherical and cylindrical shells,” in: Collected Works [in Russian], Vol. 1, Izd. AN SSSR, Moscow (1951), pp. 110–121.
S. G. Lekhnitskii, Theory of Elasticity of an Anisotropic Body, Mir, Moscow (1981).
A. V. Men’shikov, “Spatial contact problem for two coaxial circular cracks under normal harmonic loading,” Dop. NANU, No. 6, 44–49 (2005).
A. V. Men’shikov, “Stress intensity factors for a circular crack with contacting edges under harmonic loading,” Probl. Mashinostr., 9, No. 2, 43–47 (2006).
A. V. Men’shikov and I. A. Guz, “Dependence of the shear stress intensity factors on the friction force under harmonic loading of a circular crack,” Probl. Mashinostr., 9, No. 3, 65–71 (2006).
A. V. Men’shikov and M. V. Men’shikov, “Studying the contact interaction of crack faces by the Galerkin method,” Teor. Prikl. Mekh., 41, 151–155 (2005).
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A. N. Guz (ed.), Nonclassical Problems of Fracture Mechanics [in Russian], in four vols., five books, Naukova Dumka, Kyiv (1990–1993). Vol. 1. A. A. Kaminsky, Fracture of Viscoelastic Bodies with Cracks (1990). Vol. 2. A. N. Guz, Brittle Fracture of Prestressed Materials (1991). Vol. 3. A. A. Kaminskii and D. N. Gavrilov, Delayed Fracture of Polymeric and Composite Materials with Cracks (1992). Vol. 4, Book 1. A. N. Guz, M. Sh. Dyshel’, and V. M. Nazarenko, Fracture and Stability of Materials with Cracks (1992). Vol. 4, Book 2, A. N. Guz and V. V. Zozulya, Brittle Fracture of Materials under Dynamic Loads (1993).
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S. D. Akbarov, “Normal stresses in a fiber composite with curved structures having a low concentration of filler,” Sov. Appl. Mech., 21, No. 11, 1065–1069 (1985).
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S. D. Akbarov, “Stress state in a laminar composite material with local warps in the structure,” Sov. Appl. Mech., 24, No. 5, 445–452 (1988).
S. D. Akbarov, “Distribution of self-balanced stresses in a laminated composite material with antiphase locally distorted structures,” Sov. Appl. Mech., 24, No. 6, 560–566 (1988).
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S. D. Akbarov and Z. R. Djamalov, “Influence of geometric non-linearly calculation of stress disturbation in laminar composites with curved structures,” Mech. Comp. Mater., No. 6, 799–812 (1992).
S. D. Akbarov and A. N. Guz, “Method of solving problems in mechanics of composite materials with bent layers,” Sov. Appl. Mech., 20, No. 4, 299–304 (1984).
S. D. Akbarov and A. N. Guz, “Method of solving problems in mechanics of fiber composites with curved structures,” Sov. Appl. Mech., 20, No. 9, 777–784 (1984).
S. D. Akbarov and A. N. Guz, “Model of a piecewise-homogeneous body in the mechanics of laminar composites with fine-scale curvatures,” Sov. Appl. Mech., 21, No. 4, 313–318 (1985).
S. D. Akbarov and A. N. Guz, “Stress state of a fiber composite with curved structures with a low fiber concentration,” Sov. Appl. Mech., 21, No. 6, 560–565 (1985).
S. D. Akbarov and A. N. Guz, “Continuum theory in the mechanics of composite materials with small-scale structural distorsion,” Sov. Appl. Mech., 27, No. 1, 107–117 (1991).
S. D. Akbarov and A. N. Guz, “Mechanics of composite materials with curved structures (survey). Composite laminates,” Sov. Appl. Mech., 27, No. 6, 535–550 (1991).
S. D. Akbarov and A. N. Guz, Mechanics of Curved Composites, Kluwer Academic Publisher, Dordrecht–Boston–London (2000).
S. D. Akbarov and A. N. Guz, “Mechanics of curved composites (piecewise-homogeneous body model),” Int. Appl. Mech., 38, No. 12, 1415–1439 (2002).
S. D. Akbarov and A. N. Guz, “Mechanics of curved composites and some related problems for structural members,” Mech. Adv. Mater. Struct., 11, Pt. II, No. 6, 445–515 (2004).
S. D. Akbarov, A. N. Guz, Z. R. Djamalov, and E. A. Movsumov, “Solution of problems involving the stress state of composite materials with curved layers in the geometrically nonlinear statement,” Int. Appl. Mech., 28, No. 6, 343–346 (1992).
S. D. Akbarov, A. N. Guz, and S. M. Mustafaev, “Mechanics of composite materials with anisotropic distorted layers,” Sov. Appl. Mech., 23, No. 6, 528–533 (1987).
S. D. Akbarov, A. N. Guz, and N. Yahnioglu, “Mechanics of composite materials with curved structures and elements of constructions (review),” Int. Appl. Mech., 34, No. 11, 1067–1078 (1998).
S. D. Akbarov, A. N. Guz, and A. D. Zamanov, “Natural vibrations of composite materials having structures with small-scale curvatures,” Int. Appl. Mech., 28, No. 12, 794–800 (1992).
S. D. Akbarov, A. Cilli, and A. N. Guz, “The theoretical strength limit in compression of viscoelastic layered composite materials,” Composites. Part B: Engineering, 365–372 (1999).
S. D. Akbarov, M. D. Verdiev, and A. N. Guz, “Stress and deformation in a layered composite material with distorted layers,” Sov. Appl. Mech., 24, No. 12, 1146–1153 (1988).
S. D. Akbarov, R. Kosker, and Y. Ucan, “Stress distribution in a composite material with a row of antiphase periodically curved fibers,” Int. Appl. Mech., 42, No. 4, 486–488 (2006).
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S. D. Akbarov and O. G. Rzayev, “Delamination of unidirectional viscoelastic composite materials,” Mech. Comp. Mater., 39, No. 3, 368–374 (2002).
S. D. Akbarov, T. Sisman, and N. Yahnioglu, “On the fracture of the unidirectional composites in compression,” Int. J. Eng. Sci., 35, No. 1, 1115–1136 (1997).
S. D. Akbarov and N. Yahnioglu, “Stress distribution in a strip fabricated from a composite material with small-scale curved structure,” Int. Appl. Mech., 32, No. 9, 684–690 (1996).
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V. L. Bogdanov, “Nonaxisymmetric problem of the stress-strain state of an elastic half-space with a near-surface circular crack under action of loads along it,” J. Math. Sci., 174, No. 3, 341–366 (2011).
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V. L. Bogdanov, “On the interaction of a periodic system of parallel coaxial radial-shear cracks in a prestressed composite,” J. Math. Sci., 187, No. 5, 606–618 (2012).
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V. L. Bohdanov, “Influence of initial stresses on the fracture of a composite material weakened by a subsurface mode III crack,” J. Math. Sci., 205, No. 5, 621–634 (2015).
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V. L. Bogdanov, A. N. Guz, and V. M. Nazarenko, “Fracture of a body with a periodic set of coaxial cracks under forces directed along them: an axisymmetric problem,” Int. Appl. Mech., 45, No. 2, 111–124 (2009).
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A. N. Guz, “Theory of cracks in prestressed highly elastic materials,” Sov. Appl. Mech., 17, No. 2, 11–21 (1981).
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A. N. Guz, “Theory of cracks in elastic bodies with initial stresses (cleavage problem),” Sov. Appl. Mech., 17, No. 5, 405–411 (1981).
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A. N. Guz, “General three-dimensional static problem for cracks in an elastic body with initial stress,” Sov. Appl. Mech., 17, No. 12, 1043–1050 (1981).
A. N. Guz, “Fracture mechanics of solids in compression along cracks,” Sov. Appl. Mech., 18, No. 3, 213–224 (1982).
A. N. Guz, “Mechanics of fracture of solids in compression along cracks (three-dimensional problem),” Sov. Appl. Mech., 18, No. 4, 283–293 (1982).
A. N. Guz, “Fracture mechanics of composites in compression along cracks,” Sov. Appl. Mech., 18, No. 6, 489–493 (1982).
A. N. Guz, “Mechanics of composite material failure under axial compression (brittle failure),” Sov. Appl. Mech., 18, No. 10, 863–872 (1982).
A. N. Guz, “Mechanics of composite material failure under axial compression (plastic failure),” Sov. Appl. Mech., 18, No. 11, 970–976 (1982).
A. N. Guz, “Continuum theory of fracture in the compression of composite materials with metallic matrix,” Sov. Appl. Mech., 18, No. 12, 1045–1052 (1982).
A. N. Guz, “Fracture of unidirectional composite materials under the axial compression,” in: Fracture of Composite Materials, Nijhoff (1982), pp. 173–182.
A. N. Guz, “Mechanics of the brittle failure of materials with initial stress,” Sov. Appl. Mech., 19, No. 4, 293–307 (1983).
A. N. Guz, “Mechanics of composite materials with a small-scale structural flexure,” Sov. Appl. Mech., 19, No. 5, 383–392 (1983).
A. N. Guz, “Quasiuniform states in composites with small-scale curvatures in the structure,” Sov. Appl. Mech., 19, No. 6, 479–489 (1983).
A. N. Guz, “Three-dimensional theory of stability of elastic-viscous-plastic bodies,” Sov. Appl. Mech., 20, No. 6, 512–516 (1984).
A. N. Guz, “Foundations of mechanics of brittle fracture of materials with initial stresses,” in: Proc. 6th ICF6, India (1984), pp. 1223–1230.
A. N. Guz, “Three-dimensional stability theory of deformed bodies. Internal instability,” Sov. Appl. Mech., 21, No. 11, 1023–1034 (1985).
A. N. Guz, “Three-dimensional stability theory of deformable bodies. Surface instability,” Sov. Appl. Mech., 22, No. 1, 17–26 (1986).
A. N. Guz, “Three-dimensional stability theory of deformable bodies. Stability of construction elements,” Sov. Appl. Mech., 22, No. 2, 97–107 (1986).
A. N. Guz, “Continuous theory of failure of composite materials under compression in the case of a complex stresses state,” Sov. Appl. Mech., 22, No. 4, 301–315 (1986).
A. N. Guz, “Criterion of brittle fracture near stress raisers in composites in compression,” Sov. Appl. Mech., 22, No. 12, 1148–1154 (1986).
A. N. Guz, “Continuous theory of failure of composite materials with buckling at the ends (brittle fracture),” Sov. Appl. Mech., 23, No. 1, 52–60 (1987).
A. N. Guz, “Continuous theory of failure of composite materials with buckling at the ends (plastic failure),” Sov. Appl. Mech., 23, No. 5, 411–417 (1987).
A. N. Guz, “Theory of delayed fracture of composite in compression,” Sov. Appl. Mech., 24, No. 5, 431–438 (1988).
A. N. Guz, “Construction of a theory of failure of composites in triaxial and biaxial compression,” Sov. Appl. Mech., 25, No. 1, 29–33 (1989).
A. N. Guz, “General case of the plane problem of the mechanics of fracture of solids in compression along cracks,” Sov. Appl. Mech., 25, No. 6, 548–552 (1989).
A. N. Guz, “On construction of mechanics of fracture of materials in compression along the cracks,” in: ICF7. Advance in Fracture Research, Vol. 6, Pergamon Press (1990), pp. 3881–3892.
A. N. Guz, “Principles of the continual theory of plastic fracture of unidirectional fiber composite materials with metallic matrix under compression,” Sov. Appl. Mech., 26, No. 1, 1–8 (1990).
A. N. Guz, “Plastic failure of unidirectional fibrous composite material with metal matrix in compression,” in: Mechanical Identification of Composite, Elsevier, London–New York (1991), pp. 278–286.
A. N. Guz, “Continual theory of fracture of composite materials at bearing strain of end faces in compression,” in: Proc. of Conf. on Fracture of Engineering Materials and Structures, Elsevier, Singapore (1991), pp. 838–843.
A. N. Guz, “Construction of a theory of the local instability of unidirectional fiber composites,” Int. Appl. Mech., 28, No. 1, 18–24 (1992).
A. N. Guz, “Fracture of fibrous composites at bearing strain in end faces in compression,” in: Proc. 2nd Int. Symp. on Composite Materials and Structures, Beijing, China (1992), pp. 232–236.
A. N. Guz, “Construction of fracture mechanics for materials subjected to compression along cracks,” Int. Appl. Mech., 28, No. 10, 633–639 (1992).
A. N. Guz, “Fracture of fibrous composites at bearing strain in end faces in compression,” in: Proc. ICCM/9 Composites and Applications, Vol. VI, Madrid, July 12–16 (1993), pp. 613–618.
A. N. Guz, “Continual theory of fracture of composite materials at bearing strain in end faces in compression,” in: Mechanisms and Mechanics of Composites Fracture, ASM Inter., Material Park (1993), pp. 201–207.
A. N. Guz, “The study and analysis of non-classical problems of fracture and failure mechanics,” in: Abstracts of IUTAM Symp. of Nonlinear Analysis of Fracture, Cambridge, September 3–7 (1995), pp. 19–19.
A. N. Guz, “Stability theory for unidirectional fiber reinforced composites,” Int. Appl. Mech., 32, No. 8, 577–586 (1996).
A. N. Guz, “On failure propagation in composite materials in compression (Three-dimensional continual theory),” in: Proc. ECF 11, September 3–6, Vol. III, Poitiers–Futuroscope, France (1996), pp. 1769–1774.
A. N. Guz, “Non-classical problems of composite failure,” in: Proc. ICCST/1, June 18–20, Durban, South. Africa (1996), pp. 161–166.
A. N. Guz, “On the development of brittle-fracture mechanics of materials with initial stresses,” Int. Appl. Mech., 32, No. 4, 316–323 (1996).
A. N. Guz, “Non-classical problems of composite failure,” in: Proc. ICF9 Advance in Fracture Research, Vol. 4, Sydney, Australia (1997), pp. 1911–1921.
A. N. Guz, “The fracture theory of composite at bearing strain in end faces,” in: Proc. Conf. Composite Construction and Innovation, September 16–18, Innsbruck, Austria (1997), pp. 783–788.
A. N. Guz, “Some modern problems of physical mechanics of fracture,” in: Fracture. A Topical Encyclopedia of Current Knowledge, Krieger Publ. Company, Malabar, Florida (1998), pp. 709–720.
A. N. Guz, “Conditions of hyperbolicity and mechanics of failure of composites in compression,” ZAMM., 78, Sup. 1, 427–428 (1998).
A. N. Guz, “On the singularities in problems of brittle fracture mechanics in case of initial (residual) stresses along the cracks,” in: Proc. 3rd Int. Conf. on Nonlinear Mechanics, Shanghai, China (1998), pp. 219–223.
A. N. Guz, “Order of singularity in problems of the mechanics of brittle fracture of materials with initial stresses,” Int. Appl. Mech., 34, No. 2, 103–107 (1998).
A. N. Guz, Study and Analysis of Non-classical Problems of Fracture and Failure Mechanics and Corresponding Mechanisms, Institute of Mechanics, Lecture, HANOI (1998).
A. N. Guz, “Dynamic problems of the mechanics of the brittle fracture of materials with initial stresses for moving cracks. 1. Problem statement and general relationships,” Int. Appl. Mech., 34, No. 12, 1175–1186 (1998).
A. N. Guz, “Dynamic problems of the mechanics of the brittle fracture of materials with initial stresses for moving cracks. 2. Cracks of normal separation (Mode I),” Int. Appl. Mech., 35, No. 1, 1–12 (1999).
A. N. Guz, “Dynamic problems of the mechanics of the brittle fracture of materials with initial stresses for moving cracks. 3. Transverse-shear (Mode II) and longitudinal-shear (Mode III) cracks,” Int. Appl. Mech., 35, No. 2, 109–119 (1999).
A. N. Guz, “Dynamic problems of the mechanics of the brittle fracture of materials with initial stresses for moving cracks. 4. Wedge problems,” Int. Appl. Mech., 35, No. 3, 225–232 (1999).
A. N. Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies, Springer, Berlin–Hiedelberg–New York (1999).
A. N. Guz, “On the plastic failure of unidirectional fibrous composite materials with metal matrix in compression. Continuum approximation,” in: Proc. ICCE/6, June 27–July 3, Orlando, Florida, USA (1999), pp. 279–280.
A. N. Guz, “Description and study of some nonclassical problems of fracture mechanics and related mechanisms,” Int. Appl. Mech., 36, No. 12, 1537–1564 (2000).
A. N. Guz, “Construction of the three-dimensional theory of stability of deformable bodies,” Int. Appl. Mech., 37, No. 1, 1–37 (2001).
A. N. Guz, “Elastic waves in bodies with initial (residual) stresses,” Int. Appl. Mech., 38, No. 1, 23–59 (2002).
A. N. Guz, “Critical phenomena in cracking of the interface between two prestressed materials. 1. Problem formulation and basic relations,” Int. Appl. Mech., 38, No. 4, 423–431 (2002).
A. N. Guz, “Critical phenomena in cracking of the interface between two prestressed materials. 2. Exact solution. The case of unequal roots,” Int. Appl. Mech., 38, No. 5, 548–555 (2002).
A. N. Guz, “Critical phenomena in cracking of the interface between two prestressed materials. 3. Exact solution. The case of equal roots,” Int. Appl. Mech., 38, No. 6, 693–700 (2002).
A. N. Guz, “Critical phenomena in cracking of the interface between two prestressed materials. 4. Exact solution. The combined case of unequal and equal roots,” Int. Appl. Mech., 38, No. 7, 806–814 (2002).
A. N. Guz, “Comments on ‘Effects of prestress on crack-tip fields in elastic incompressible solids’,” Int. J. Solids Struct., 40, No. 5, 1333–1334 (2003).
A. N. Guz, “Establishing the fundamentals of the theory of stability of mine working,” Int. Appl. Mech., 39, No. 1, 20–48 (2003).
A. N. Guz, “On one two-level model in the mesomechanics of compression fracture of cracked composites,” Int. Appl. Mech., 39, No. 3, 274–285 (2003).
A. N. Guz, “On some nonclassical problems of fracture mechanics taking into account the stresses along cracks,” Int. Appl. Mech., 40, No. 8, 937–942 (2004).
A. N. Guz, “On study of nonclassical problems of fracture and failure mechanics and related mechanisms,” Annals of the European Academy of Sciences, 2006, 35–68 (2007).
A. N. Guz, “Three-dimensional theory of stability of a carbon nanotube in a matrix,” Int. Appl. Mech., 42, No. 1, 19–31 (2006).
A. N. Guz, “Pascal Medals Lecture (written presentation),” Int. Appl. Mech., 44, No. 1, 6–11 (2008).
A. N. Guz, “On study of nonclassical problems of fracture and failure mechanics and related mechanisms,” Int. Appl. Mech., 45, No. 1, 1–31 (2009).
A. N. Guz, “On physical incorrect results in fracture mechanics,” Int. Appl. Mech., 45, No. 10, 1041–1051 (2009).
A. N. Guz, “On the activity of the S. P. Timoshenko Institute of Mechanics in 1991–2011,” Int. Appl. Mech., 47, No. 6, 607–626 (2011).
A. N. Guz, “Stability of elastic bodies under omnidirectional compression. Review,” Int. Appl. Mech., 48, No. 3, 241–293 (2012).
A. N. Guz and I. Yu. Babich, “Three-dimensional stability problems of composite materials and composite construction components,” Rozpr. Inz., 27, No. 4, 613–631 (1979).
A. N. Guz and V. N. Chekhov, “Linearized theory of folding in the interior of the Earth’s crust,” Sov. Appl. Mech., 11, No. 1, 1–10 (1975).
A. N. Guz and V. N. Chekhov, “Variational method of investigating the stability of laminar semiinfinite media,” Sov. Appl. Mech., 21, No. 7, 639–646 (1985).
A. N. Guz and V. N. Chekhov, “Investigation of surface instability of stratified bodies in three-dimensional formulation,” Sov. Appl. Mech., 26, No. 2, 107–125 (1990).
A. N. Guz and V. N. Chekhov, “Problems of folding in the earth’s stratified crust,” Int. Appl. Mech., 43, No. 2, 127–159 (2007).
A. N. Guz, V. N. Chekhov, and V. S. Stukotilov, “Effect of anisotropy in the physicomechanical properties of a material on the surface instability of layered semiinfinite media,” Int. Appl. Mech., 33, No. 2, 87–92 (1997).
A. N. Guz and M. A. Cherevko, “Fracture mechanics of unidirectional fibrous composites with metal matrix under compression,” Theor. Appl. Frac. Mech., 3, No. 2, 151–155 (1985).
A. N. Guz and M. A. Cherevko, “Stability of a biperiodic system of fibers in a matrix with finite deformations,” Sov. Appl. Mech., 22, No. 6, 514–518 (1986).
A. N. Guz and V. A. Dekret, “Interaction of two parallel short fibers in the matrix at loss of stability,” Comp. Model. Eng. Scie., 13, No. 3, 165–170 (2006).
A. N. Guz and V. A. Dekret, “On two models in the three-dimensional theory of stability of composites,” Int. Appl. Mech., 44, No. 8, 839–854 (2008).
A. N. Guz and V. A. Dekret, “Stability loss in nanotube reinforced composites,” Comp. Model. Eng. Sci., 49, No. 1, 69–80 (2009).
A. N. Guz and V. A. Dekret, “Stability problem of composite material reinforced by periodic row of short fibers,” Comp. Model. Eng. Sci., 42, No. 3, 179–186 (2009).
A. N. Guz, V. A. Dekret, and Yu. V. Kokhanenko, “Solution of plane problems of the three-dimensional stability of a ribbon-reinforced composite,” Int. Appl. Mech., 36, No. 10, 1317–1328 (2000).
A. N. Guz, V. A. Dekret, and Yu. V. Kokhanenko, “Two-dimensional stability problem for interacting short fibers in a composite: in-line arrangement,” Int. Appl. Mech., 40, No. 9, 994–1001 (2004).
A. N. Guz, V. A. Dekret, and Yu. V. Kokhanenko, “Planar stability problem of composite weakly reinforced by short fibers,” Mech. Adv. Mater. Struct., No. 12, 313–317 (2005).
A. N. Guz, M. V. Dovzhik, and V. M. Nazarenko, “Fracture of a material compressed along a crack located at a short distance from the free surface,” Int. Appl. Mech., 47, No. 6, 627–635 (2011).
A. N. Guz and M. Sh. Dyshel’, “Fracture of cylindrical shells with cracks in tension,” Theor. Appl. Fract. Mech., No. 4, 123–126 (1985).
A. N. Guz and M. Sh. Dyshel’, “Fracture and stability of notched thin-walled bodies in tension (Survey),” Sov. Appl. Mech., 26, No. 11, 1023–1040 (1990).
A. N. Guz, M. Sh. Dyshel’, G. G. Kuliev, and O. B. Milovanova, “Fracture and local instability of thin-walled bodies with notches,” Sov. Appl. Mech., 17, No. 8, 707–721 (1981).
A. N. Guz, M. Sh. Dyshel’, and V. M. Nazarenko, “Fracture and stability of materials and structural members with cracks: approaches and results,” Int. Appl. Mech., 40, No. 12, 1323–1359 (2004).
A. N. Guz and I. A. Guz, “Substantiation of a continuum theory of the fracture of laminated composite in compression,” Sov. Appl. Mech., 24, No. 7, 648–657 (1988).
A. N. Guz and I. A. Guz, “Foundation for the continual theory of fracture during compression of laminar composites with a metal matrix,” Sov. Appl. Mech., 24, No. 11, 1041–1047 (1988).
A. N. Guz and I. A. Guz, “On the theory of stability of laminated composites,” Int. Appl. Mech., 35, No. 4, 323–329 (1999).
A. N. Guz and I. A. Guz, “Analytical solution of stability problem for two composite half-plane compressed along interfacial cracks,” Composites. Part B., 31, No. 5, 405–418 (2000).
A. N. Guz and I. A. Guz, “The stability of the interface between two bodies compressed along interface cracks. 1. Exact solution for the case of unequal roots,” Int. Appl. Mech., 36, No. 4, 482–491 (2000).
A. N. Guz and I. A. Guz, “The stability of the interface between two bodies compressed along interface cracks. 1. Exact solution for the case of equal roots,” Int. Appl. Mech., 36, No. 5, 615–622 (2000).
A. N. Guz and I. A. Guz, “The stability of the interface between two bodies compressed along interface cracks. 3. Exact solution for the case of equal and unequal roots,” Int. Appl. Mech., 36, No. 6, 759–768 (2000).
A. N. Guz and I. A. Guz, “On publications on the brittle fracture mechanics of prestressed materials,” Int. Appl. Mech., 39, No. 7, 797–801 (2003).
A. N. Guz and I. A. Guz, “Mixed plane problems of linearized solids mechanics. Exact solutions,” Int. Appl. Mech., 40, No. 1, 1–29 (2004).
A. N. Guz and I. A. Guz, “On models in the theory of stability of multi-walled carbon nanotubes,” Int. Appl. Mech., 42, No. 6, 617–628 (2006).
A. N. Guz, I. A. Guz, A. V. Men’shikov, and V. A. Men’shikov, “Penny-shaped crack at the interface between elastic half-space under the action of a shear wave,” Int. Appl. Mech., 45, No. 5, 534–539 (2009).
A. N. Guz and Yu. I. Khoma, “Stability of an infinite solid with a circular cylindrical crack under compression using the Treloar potential,” Theor. Appl. Fract. Mech., 39, No. 3, 276–280 (2002).
A. N. Guz and Yu. I. Khoma, “Integral formulation for a circular cylindrical cavity in infinite solid and finite length coaxial cylindrical crack compressed axially,” Theor. Appl. Fract. Mech., 45, No. 2, 204–211 (2006).
A. N. Guz, Yu. I. Khoma, and V. M. Nazarenko, “On fracture of an infinite elastic body in compression along a cylindrical defect,” in: Proc. ICF 9 Advance in Fracture Research, Vol. 4, Sydney, Australia (1997), pp. 2047–2054.
A. N. Guz and Yu.V. Klyuchnikov, “Three-dimensional static problem for an elliptical crack in an elastic body with initial stress,” Sov. Appl. Mech., 20, No. 10, 898–907 (1984).
A. N. Guz, V. L. Knyukh, and V. M. Nazarenko, “Three-dimensional axisymmetric problem of fracture in material with two discoidal cracks under compression along latter,” Sov. Appl. Mech., 20, No. 11, 1003–1012 (1984).
A. N. Guz, V. L. Knyukh, and V. M. Nazarenko, “Cleavage of composite materials in compression along internal and surface macrocracks,” Sov. Appl. Mech., 22, No. 11, 1047–1051 (1986).
A. N. Guz, V. L. Knyukh, and V. M. Nazarenko, “Fracture of ductile materials in compression along two parallel disk-shaped cracks,” Sov. Appl. Mech., 24, No. 2, 112–117 (1988).
A. N. Guz, V. L. Knyukh, and V. M. Nazarenko, “Compressive failure of material with two parallel cracks: small and large deformation,” Theor. Appl. Fract. Mech., 11, No. 3, 213–223 (1989).
A. N. Guz, V. P. Korzh, and V. N. Chekhov, “Instability of layered bodies during compression taking into account the action of disturbated surface loads,” Sov. Appl. Mech., 25, No. 5, 435–442 (1989).
A. N. Guz, V. P. Korzh, and V. N. Chekhov, “Surface instability of a laminar medium connected with a homogeneous half-space under multilateral compression,” Sov. Appl. Mech., 26, No. 3, 215–222 (1990).
A. N. Guz, V. P. Korzh, and V. N. Chekhov, “Stability of a laminar half-plane of regular structure under uniform compression,” Sov. Appl. Mech., 27, No. 8, 744–749 (1991).
A. N. Guz, A. A. Kritsuk, and R. F. Emel’yanov, “Character of the failure of unidirectional glass-reinforced plastic in compression,” Sov. Appl. Mech., 5, No. 9, 997–999 (1969).
A. N. Guz, G. G. Kuliev, and I. A. Tsurpal, “Theory of the rupture of thin bodies with cracks,” Sov. Appl. Mech., 11, No. 5, 485–487 (1975).
A. N. Guz, G. G. Kuliev, and I. A. Tsurpal, “On failure of brittle materials because of grippling near cracks,” in: Abstracts 14th IUTAM Congr., Delft (1976), p. 90.
A. N. Guz, G. G. Kuliev, and I. A. Tsurpal, “On fracture of brittle materials from loss of stability near crack,” Eng. Fract. Mech., 10, No. 2, 401–408 (1978).
A. N. Guz and Yu. N. Lapusta, “Stability of a fiber near a free surface,” Sov. Appl. Mech., 22, No. 8, 711–718 (1986).
A. N. Guz and Yu. N. Lapusta, “Stability of a fiber near a free cylindrical surface,” Sov. Appl. Mech., 24, No. 10, 939–944 (1988).
A. N. Guz and Yu. N. Lapusta, “Three-dimensional problem on the stability of a row of fibers perpendicular to the free boundary of a matrix,” Int. Appl. Mech., 30, No. 12, 919–926 (1994).
A. N. Guz and Yu. N. Lapusta, “Three-dimensional problems of the near-surface instability of fiber composites in compression (Model of a piecewise-uniform medium) (Survey),” Int. Appl. Mech., 35, No. 7, 641–670 (1999).
A. N. Guz, Yu. N. Lapusta, and Yu. A. Mamzenko, “Stability of a two fibers in an elasto-plastic matrix under compression,” Int. Appl. Mech., 34, No. 5, 405–413 (1998).
A. N. Guz, Yu. N. Lapusta, and A. N. Samborskaya, “A micromechanics solution of a 3D internal instability problem for a fiber series on an infinite matrix,” Int. J. Fract., 116, No. 3, L55–L60 (2002).
A. N. Guz, Yu. N. Lapusta, and A. N. Samborskaya, “3D model and estimation of fiber interaction effects during internal instability in non-linear composites,” Int. J. Fract., 134, No. 3-4, L45–L51 (2005).
A. N. Guz, A. V. Menshikov, and V. V. Zozulya, “Surface contact of elliptical crack under normally incident tension-compression wave,” Theor. Appl. Fract. Mech., 40, No. 3, 285–291 (2003).
A. N. Guz, A. V. Menshikov, V. V. Zozulya, and I. A. Guz, “Contact problem for the plane elliptical crack under normally incident shear wave,” Comp. Model. Eng. Sci., 17, No. 3, 205–214 (2007).
A. N. Guz and D. A. Musaev, “Fracture of a unidirectional ribbon composite with elasto-plastic matrix in compression,” Sov. Appl. Mech., 26, No. 5, 425–429 (1990).
A. N. Guz, D. A. Musaev, and Ch. A. Yusubov, “Stability of two noncircular cylinder in an elastic matrix with small subcritical strains,” Sov. Appl. Mech., 25, No. 11, 1059–1064 (1989).
A. N. Guz and V. M. Nazarenko, “Symmetric failure of the halfspace with penny-shaped crack in compression,” Theor. Appl. Fract. Mech., 3, No. 3, 233–245 (1985).
A. N. Guz and V. M. Nazarenko, “Fracture of a material in compression along a periodic system of parallel circular cracks,” Sov. Appl. Mech., 23, No. 4, 371–377 (1987).
A. N. Guz and V. M. Nazarenko, “Fracture mechanics of material in compression along cracks (Review). Highly elastic materials,” Sov. Appl. Mech., 25, No. 9, 851–876 (1989).
A. N. Guz and V. M. Nazarenko, “Fracture mechanics of materials under compression along cracks (survey). Structural materials,” Sov. Appl. Mech., 25, No. 10, 959–972 (1989).
A. N. Guz, V. M. Nazarenko, and V. L. Bogdanov, “Fracture under initial stresses acting along cracks: Approach, concept and results,” Theor. Appl. Fract. Mech., 48, 285–303 (2007).
A. N. Guz, V. M. Nazarenko, and V. L. Bogdanov, “Combined analysis of fracture under stress acting along cracks,” Archive Appl. Mech., 83, No. 9, 1273–1293 (2013).
A. N. Guz, V. M. Nazarenko, and Yu. I. Khoma, “Failure of an infinite compressible composite containing a finite cylindrical crack in axial compression,” Int. Appl. Mech., 31, No. 9, 695–703 (1995).
A. N. Guz, V. M. Nazarenko, and Yu. I. Khoma, “Fracture of an infinite incompressible hyperelastic material under compression along a cylindrical crack,” Int. Appl. Mech., 32, No. 5, 325–331 (1996).
A. N. Guz, V. M. Nazarenko, and S. M. Nazarenko, “Fracture of composites under compression along periodically placed parallel circular stratifications,” Sov. Appl. Mech., 25, No. 3, 215–121 (1989).
A. N. Guz, V. M. Nazarenko, and V. A. Nikonov, “Torsion of a pre-stresses halfspace with a disc-shaped crack at the surface,” Sov. Appl. Mech., 27, No. 10, 948–954 (1991).
A. N. Guz, V. M. Nazarenko, and I. P. Starodubtsev, “Planar problem of failure of structural materials in compression along two parallel cracks,” Sov. Appl. Mech., 27, No. 4, 352–360 (1991).
A. N. Guz, V. M. Nazarenko, and I. P. Starodubtsev, “On problems of fracture of materials in compression along two internal parallel cracks,” Appl. Math. Mech., 18, No. 6, 517–528 (1997).
A. N. Guz and J. J. Rushchitskii, Short Introduction to Mechanics of Nanocomposites, Scientific&Academic Publishing Co., LTD, USA (2013).
A. N. Guz, J. J. Rushchitskii, and I. A. Guz, “Establishing fundamentals of the mechanics of nanocomposites,” Int. Appl. Mech., 43, No. 3, 247–271 (2007).
A. N. Guz and A. N. Samborskaya, “General stability problem of a series of fibers in an elastic matrix,” Sov. Appl. Mech., 27, No. 3, 223–230 (1991).
A. N. Guz and A. N. Sporykhin, “Three-dimensional theory of inelastic stability (General questions),” Sov. Appl. Mech., 18, No. 7, 581–596 (1982).
A. N. Guz and A. N. Sporykhin, “Three-dimensional theory of inelastic stability. Specific results,” Sov. Appl. Mech., 18, No. 8, 671–692 (1982).
A. N. Guz, E. A. Tkachenko, and V. N. Chekhov, “Stability of layered antifriction coating,” Int. Appl. Mech., 32, No. 9, 669–676 (1996).
A. N. Guz, E. A. Tkachenko, V. N. Chekhov, and V. S. Stukotilov, “Stability of multilayer antifriction coating for small subcritical strains,” Int. Appl. Mech., 32, No. 10, 772–779 (1996).
A. N. Guz and V. V. Zozulya, “Contact interaction between crack edges under dynamic load,” Int. Appl. Mech., 28, No. 7, 407–417 (1992).
A. N. Guz and V. V. Zozulya, “Problems of dynamic fracture mechanics without contact of the crack faces,” Int. Appl. Mech., 30, No. 10, 735–759 (1994).
A. N. Guz and V. V. Zozulya, “Problems of dynamic fracture mechanics without allowance for contact of the crack edges,” Int. Appl. Mech., 31, No. 1, 1–31 (1995).
A. N. Guz and V. V. Zozulya, “Fracture dynamic with allowance for a crack edges contact interaction,” Int. J. Nonlin. Sci. Numer. Simul., 2, No. 3, 173–233 (2001).
A. N. Guz and V. V. Zozulya, “Elastodynamic unilateral contact problem with friction for bodies with cracks,” Int. Appl. Mech., 38, No. 8, 895–932 (2002).
A. N. Guz and V. V. Zozulya, “Investigation of the effect of frictional contact in III Mode crack under action of SH-wave harmonic load,” Comp. Model. Eng. Sci., 22, No. 2, 119–128 (2007).
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Translated from Prikladnaya Mekhanika, Vol. 55, No. 4, pp. 3–100, July–August, 2019.
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Guz, A.N. Nonclassical Problems of Fracture/Failure Mechanics: On the Occasion of the 50th Anniversary of Research (Review). III. Int Appl Mech 55, 343–415 (2019). https://doi.org/10.1007/s10778-019-00960-4
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DOI: https://doi.org/10.1007/s10778-019-00960-4