Skip to main content
SpringerLink
Log in

Establishing the Foundations of the Mechanics of Fracture of Materials Compressed Along Cracks (Review)

  • Published:
International Applied Mechanics Aims and scope

The basic results of establishing the foundations of the mechanics of fracture of homogeneous materials compressed along cracks and inhomogeneous (composite) materials compressed along interface cracks are analyzed. These results were obtained using elastic, plastic, and viscoelastic material models. This review consists of three parts.

The first part discusses the basic concept that the start (onset) of fracture is the mechanism of local instability near the cracks located in a single plane or parallel planes. The fracture criterion and the basic problems arising in this division of fracture mechanics are also formulated. Two basic approaches to establishing the foundations of the mechanics of fracture of materials compressed along cracks are outlined. One approach, so-called beam approximation, is based on various applied theories of stability of thin-walled systems (including the Bernoulli, Kirchhoff–Love, Timoshenko-type hypotheses, etc.). This approach is essentially approximate and introduces an irreducible error into the calculated stresses. The other approach is based on the basic equations and methods of the three-dimensional linearized theory of stability of deformable bodies for finite and small subcritical strains. This approach does not introduce major errors typical for the former approach and allows obtaining results with accuracy acceptable for mechanics.

The second part offers a brief analysis of the basic results obtained with the first approach and a more detailed analysis of the basic results obtained with the second approach, including the consideration of the exact solutions for interacting cracks in a single plane and in parallel planes and results for some structural materials.

The third part reports new results for interacting cracks in very closely spaced (or coinciding, as an asymptotic case) planes. These results may be considered a transition from the second approach (three-dimensional linearized theory of elastic stability) to the first approach (beam approximation). This is how the accuracy of results produced by the first approach is evaluated and the boundary conditions near the crack tip are established in the second approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. D. Akbarov and N. Yahnioglu, “Delamination buckling of a rectangular orthotropic composite plate containing a band crack,” Mech. Comp. Mater., 46, No. 5, 493–504 (2010).

    Article  Google Scholar 

  2. L. V. Andreev, I. P. Zhelezko, and N. I. Obodan, “Bifurcation of equilibrium of spherical shells with delaminations,” Strength of Materials, 18, No. 2, 183–188 (1986).

    Article  Google Scholar 

  3. 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).

  4. V. L. Bogdanov, “Fracture of a material with a periodic array of coaxial circular cracks under prestresses acting along them,” Dop. NAN Ukrainy, No. 9, 53–59 (2008).

  5. V. L. Bogdanov and V. M. Nazarenko, “Compression of a composite material along a macrocrack near the surface,” Mech. Comp. Mater., 30, No. 3, 251–255 (1994).

    Article  Google Scholar 

  6. V. V. Bolotin, “Defects of the delamination type in composite structures,” Mech. Comp. Mater., 20, No. 2, 173–188 (1984).

    Article  Google Scholar 

  7. V. V. Bolotin, “Unified models in fracture mechanics,” Izv. AN SSSR, No. 3, 127–137 (1984).

  8. V. V. Bolotin, “Multiparameter fracture mechanics,” in: Strength Analysis [in Russian], Issue 25, Mashinostroenie, Moscow (1984), pp. 12–33.

  9. V. V. Bolotin, “Delamination fracture of composite materials,” in: Strength Analysis [in Russian], Issue 27, Mashinostroenie, Moscow (1986), pp. 8–20.

  10. V. V. Bolotin, “Interply failure of composites in combined loading,” Mech. Comp. Mater., 24, No. 3, 295–303 (1988).

    Article  MathSciNet  Google Scholar 

  11. V. V. Bolotin, K. S. Bolotina, V. P. Radin, and V. N. Shchugorev, “Fracture toughness characteristics of laminated composites,” Mech. Comp. Mater., 32, No. 1, 14–20 (1996).

    Article  Google Scholar 

  12. V. V. Bolotin, “Mechanics of dDelaminations in laminate composite structures,” Mech. Comp. Mater., 37, No. 5, 367–380 (2001).

    Article  MathSciNet  Google Scholar 

  13. V. V. Bolotin and Z. Kh. Zabel’yan, “Stability of elastic spherical shells with delaminations,” in: Strength Analysis [in Russian], Issue 22, Mashinostroenie, Moscow (1980), pp. 150–165.

  14. V. V. Bolotin, Z. Kh. Zabel’yan, and A. A. Kurzin, “Stability of compressed components with delamination-type flaws,” Strength of Materials, 12, No. 7, 813–819 (1980).

    Article  Google Scholar 

  15. V. V. Bolotin, S. V. Nefedov, V. A. Pudov, and O. V. Trifonov, “Compressive stability of multilayered delaminations in composites,” Mech. Comp. Mater., 33, No. 3, 218–224 (1997).

    Article  Google Scholar 

  16. N. N. Bugakov, “Work required to rupture laminated fiberglasses along interfaces,” Strength of Materials, 10, No. 4, 420–422 (1978).

    Article  Google Scholar 

  17. S. M. Vereshchaka, “Buckling stability of multilayer plates and shells with interfacial structural defects under axial compression,” Mech. Comp. Mater., 43, No. 4, 345–358 (2007).

    Article  Google Scholar 

  18. A. N. Vorontsov, G. Kh. Murzakhanov, and V. N. Shchugorev, “Delamination failure of composite structures,” Mech. Comp. Mater., 25, No. 6, 723–737 (1989).

    Article  Google Scholar 

  19. L. A. Galin, Contact Problems of Elasticity [in Russian], Fizmatgiz, Moscow (1953).

    Google Scholar 

  20. R. V. Gol’dshtein, “Compressive fracture,” Uspekhi Mekh., No. 2, 3–20 (2003).

  21. R. V. Gol’dshtein and N. M. Osipenko, “Local fracture of thin bodies with crack-like defects under constrained compression,” Izv. AN SSSR, Mekh. Tverd. Tela, No. 5, 158–167 (1987).

  22. E. I. Grigolyuk, A. A. Kogan, and V. I. Mamai, “Problem of deformation of layered structures with delamination,” Izv. RAN, Mekh. Tverd. Tela, No. 1, 6–32 (1994).

  23. V. I. Gulyaev, V. A. Bazhenov, and E. A. Gotsulyak, Stability of Nonlinear Mechanical Systems [in Russian], Vyshcha Shkola, Lviv (1982).

    Google Scholar 

  24. A. N. Guz, Stability of Three-Dimensional Deformable Bodies [in Russian], Naukova Dumka, Kyiv (1971).

    Google Scholar 

  25. À. N. Guz, Stability of Elastic Bodies Subject to Finite Deformations [in Russian], Naukova Dumka, Kyiv (1973).

    Google Scholar 

  26. A. N. Guz, Fundamentals of the Theory of Stability of Mine Workings [in Russian], Naukova Dumka, Kyiv (1977).

    Google Scholar 

  27. À. N. Guz, Stability of Elastic Bodies under Triaxial Compression [in Russian], Naukova Dumka, Kyiv (1979).

    Google Scholar 

  28. À. N. Guz, “Linearized theory of fracture of prestressed brittle materials,” Dokl. AN SSSR, 252, No. 5, 1085–1088(1980).

    Google Scholar 

  29. À. N. Guz, “Tensile cracks in elastic bodies with prestresses,” Dokl. AN SSSR, 254, No. 3, 571–574 (1980).

    MathSciNet  Google Scholar 

  30. À. N. Guz, “A failure criterion for solids compressed along cracks: Plane problem,” Dokl. AN SSSR, No. 259, No. 6,1315–1318 (1981).

  31. À. N. Guz, “A failure criterion for solids compressed along cracks: Three-dimensional problem,” Dokl. AN SSSR, 261, No. 1, 42–45 (1981).

    Google Scholar 

  32. A. N. Guz, Brittle Fracture Mechanics of Prestressed Materials [in Russian], Naukova Dumka, Kyiv (1983).

    Google Scholar 

  33. A. N. Guz, “The order of singularity at the crack tip in prestressed materials,” Dokl. AN SSSR, 289, No. 2, 310–313(1986).

    MathSciNet  Google Scholar 

  34. A. N. Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies [in Russian], Vyshcha Shkola, Kyiv (1986).

    Google Scholar 

  35. 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).

    Google Scholar 

  36. À. N. Guz, Fracture Mechanics of Compressed Composite Materials [in Russian], Naukova Dumka, Kyiv (1990).

    Google Scholar 

  37. A. N. Guz, Fundamentals of the Fracture Mechanics of Compressed Composites [in Russian], in 2 vols., Vol. 1:Fracture in the Structure of a Material. Vol. 2: Related Fracture Mechanisms. Litera, Kyiv (2008).

  38. 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).

    Google Scholar 

  39. 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).

    Google Scholar 

  40. 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).

    Google Scholar 

  41. 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).

    Google Scholar 

  42. 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).

    Article  Google Scholar 

  43. 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, 251–256 (1987).

    Article  MATH  Google Scholar 

  44. A. N. Guz, V. M. Nazarenko, and I. P. Starodubtsev, “Fracture of materials compressed along two parallel cracks: Plane problem,” in: V. G. Zubchaninov (ed.), Problems of Solid Mechanics [in Russian], Kalininsk. Univ., Kalinin (1986), pp. 138–151.

    Google Scholar 

  45. A. N. Guz, V. M. Nazarenko, and Yu. I. Khoma, “Fracture of a composite compressed along a cylindrical crack,” Dokl. NAN Ukrainy, No. 10, 48–52 (1995).

  46. I. A. Guz, “Stability of a composite compressed along an interface crack,” DAN SSSR, 325, No. 3, 455–458(1992).

    MathSciNet  Google Scholar 

  47. I. A. Guz, “Stability of composites with interlaminar cracks,” Mech. Comp. Mater., 28, No. 5, 414–418 (1992).

    Article  Google Scholar 

  48. I. A. Guz, “Stability of a composite compressed along two interface microcracks,” DAN SSSR, 328, No. 4, 437–439 (1993).

    Google Scholar 

  49. I. A. Guz, “Composites with interlamination cracks: Stability under compression along two microcracks between orthotropic layers,” Mech. Comp. Mater., 29, No. 6, 581–586 (1993).

    Article  Google Scholar 

  50. I. A. Guz, “Stability of composites compressed along an array of parallel interface cracks,” Dokl. NAN Ukrainy, No. 6, 44–47 (1995).

  51. M. M. Davidenkov, “Surface energy of mica,” Prikl. Mekh., 6, No. 2, 138–142 (1960).

    Google Scholar 

  52. 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).

    Article  MathSciNet  ADS  Google Scholar 

  53. M. V. Dovzhik, “Fracture of a material compressed along two closely spaced penny-shaped cracks,” Int. Appl. Mech., 48, No. 5, 563–572 (2012).

    Article  ADS  Google Scholar 

  54. 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).

  55. 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).

    Article  MathSciNet  ADS  Google Scholar 

  56. 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).

    Article  MathSciNet  ADS  Google Scholar 

  57. V. M. Enotov and R. L. Salganik, “Beam approximation in the theory of cracks,” Izv. AN SSSR, Mekh., No. 5, 95–102 (1965).

  58. I. P. Zhelezko and N. I. Obodan, “Influence of delamination on the load-bearing capacity of shells,” Izv. AN SSSR, Mekh. Tverd. Tela, No. 6, 153–158 (1986).

  59. L. M. Kachanov, “Cracks in glassfiber pipes,” Mech. Comp. Mater., 10, No. 2, 314–315 (1974).

    Google Scholar 

  60. L. M. Kachanov, “Layering in glass-fiber pipes subject to external pressure,” Mech. Comp. Mater., 11, No. 6, 947–949 (1975).

    Google Scholar 

  61. L. M. Kachanov, “Separation failure of composite materials,” Mech. Comp. Mater., 12, No. 5, 812–815 (1976).

    Google Scholar 

  62. L. M. Kachanov, “Delamination of composites revisited,” Vestn. Leningr. Univ., Mat. Mekh. Astronom., 3, No. 13, 77–81 (1976).

    Google Scholar 

  63. S. A. Kislyakov, “Stability and development of delamination in a cylindrical shell made of a composite material in compression,” Mech. Comp. Mater., 21, No. 4, 450–454 (1985).

    Article  Google Scholar 

  64. S. G. Lekhnitskii, Theory of Elasticity of an Anisotropic Body, Mir, Moscow (1981).

  65. I. A. Miklashevich, “Delamination of composites along the interface as buckling failure of the stressed layer,” Mech. Comp. Mater., 40, No. 4, 279–286 (2004).

    Article  Google Scholar 

  66. A. M. Mikhailov, “Dynamic problems of the theory of cleavages in a beam approximation,” J. Appl. Mech. Tech. Phys., 7, No. 5, 122–125 (1966).

    Article  ADS  Google Scholar 

  67. A. M. Mikhailov, “Certain problems in the theory of cracks in a beam approximation,” J. Appl. Mech. Tech. Phys., 8, No. 5, 83–86 (1967).

    Article  ADS  Google Scholar 

  68. A. M. Mikhailov, “Generalization of the beam approach to problems of crack theory,” J. Appl. Mech. Tech. Phys., 10, No. 3, 503–506 (1969).

    Article  ADS  Google Scholar 

  69. A. M. Mikhailov, “Propagation of cleavage cracks in single crystals of lithium fluoride,” J. Appl. Mech. Tech. Phys., 11, No. 4, 627–631 (1970).

    Article  ADS  Google Scholar 

  70. A. N. Guz (ed.), Mechanics of Composite Materials [in Russian], in 12 vols., Vol. 1: V. T. Golovchan (ed.), Statics of Materials (1993), Vol. 2: N. A. Shul’ga (ed.), Dynamics and Stability of Materials (1993), Vol. 3: L. P. Khoroshun, Statistical Mechanics and Effective Properties of Materials (1993), Vol. 4: A. N. Guz and S. D. Akbarova (eds.), Mechanics of Materials with Curved Structures (1995), Vol. 5: A. A. Kaminsky (ed.), Fracture Mechanics (1996), Vol. 6: N. A. Shul’ga and V. T. Tomashevskii (eds.), Process-Induced Stresses and Strains in Materials (1997), Vol. 7: A. N. Guz, A. S. Kosmodamianskii, and V. P. Shevchenko (eds.), Stress Concentration (1998), Vol. 8: Ya. M. Grigorenko (ed.), Statics of Structural Members (1999), Vol. 9: V. D. Kubenko (ed.), Dynamics of Structural Members (1999), Vol. 10: I. Yu. Babicha (ed.), Stability of Structural Members (2001), Vol. 11: Ya. M. Grigorenko and Yu. N. Shevchenko (eds.), Numerical Methods (2002), Vol. 12: A. N. Guz and L. P. Khoroshun (eds.), Applied Research (2003), Naukova Dumka (Vols. 1–4), A.S.K. (Vols. 5–12), Kyiv (1993–2003).

  71. V. I. Mossakovskiiy, N. I. Obodan, and I. P. Zhelezko, “Deformation of shells with delaminations: Nonlinear model,” Dokl. AN SSSR, 282, No. 5, 1070–1073 (1985).

    Google Scholar 

  72. N. I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen (1975).

    MATH  Google Scholar 

  73. V. M. Nazarenko, “The spatial problem of the compression of a material along a periodic system of parallel circular cracks,” J. Appl. Math. Mech., 52, No. 1, 120–125 (1988).

    Article  MathSciNet  Google Scholar 

  74. V. M. Nazarenko, “Compression of a material along a near-surface penny-shaped crack: Nonaxisymmetric problem,” Prikl. Mekh., 25, No. 1, 124–127 (1989).

    MathSciNet  Google Scholar 

  75. V. M. Nazarenko and Yu. I. Khoma, “A method for solving problems of the fracture of an unbounded material with a cylindrical crack under axial compression (case of unequal roots),” Dokl. NAN Ukrainy, No. 7, 62–67 (1994).

  76. V. M. Nazarenko and Yu. I. Khoma, “Compression of an infinite composite material along a finite cylindrical crack,” Mech. Comp. Mater., 31, No. 1, 20–25 (1995).

    Article  Google Scholar 

  77. A. N. Guz (ed.), Nonclassical Problems of Fracture Mechanics [in Russian], in four vols., five books, 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. Kaminsky and D. N. Gavrilov, Stress Rupture 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), Naukova Dumka, Kyiv (1990–1993).

  78. S. V. Nefedov, “Analysis of growth of an ellipsoidal delamination in composites at long-term quasistatic loads,” Mech. Comp. Mater., 24, No. 5, 622–628 (1988).

    Article  Google Scholar 

  79. V. V. Partsevskii, “Approximate analysis of mechanisms of fracture of laminated composites at a free edge,” Mech. Comp. Mater., 16, No. 2, 179–185 (1980).

    Article  Google Scholar 

  80. V. V. Partsevskii, “Stability of lamination in composites,” Mech. Comp. Mater., 19, No. 5, 576–581 (1983).

    Article  Google Scholar 

  81. V. V. Partsevskii, “Delamination in polymeric composites (review),” Izv. RAN, Mekh. Tverd. Tela, No. 5, 62–94 (2003).

  82. V. V. Partsevskii and S. M. Belyaev, “Stability of delaminations in composite structural members under bending,” Mech. Comp. Mater., 29, No. 6, 576–580 (1993).

    Article  Google Scholar 

  83. G. S. Pisarenko, V. P. Naumenko, O. V. Mitchenko, and G. S. Volkov, “Experimental determination of the value of KI in compression of a plate along the crack line,” Strength of Materials, 16, No. 11, 1497–1505 (1984).

    Article  Google Scholar 

  84. A. N. Polilov and Yu. N. Rabotnov, “Development of delamination in compressed composites,” Izv. AN SSSR, No. 2, 166–171 (1983).

  85. A. N. Polilov and Yu. N. Rabotnov, “Chinese lantern fracture of composite pipes,” Mekh. Komp. Mater., 19, No. 3, 548–550 (1983).

    Google Scholar 

  86. L. I. Slepyan, Crack Mechanics [in Russian], Sudostroenie, Leningrad (1990).

    Google Scholar 

  87. Yu. M. Tarnopol’skii, “Delamination of compressed rods of composites,” Mech. Comp. Mater., 15, No. 2, 225–231 (1979).

    Article  Google Scholar 

  88. Ya. S. Uflyand, Integral Transforms in the Theory of Elasticity [in Russian], Izd.ANSSSR, Moscow–Leningrad (1963).

    Google Scholar 

  89. Ya. S. Uflyand, Method of Dual Equations in Mathematical Physics [in Russian], Nauka, Leningrad (1977).

    Google Scholar 

  90. M. Adan, I. Sheinman, and E. Altus, “Buckling of multiply delaminated beams,” J. Compos. Mater., 28, No. 1, 77–80 (1994).

    Article  ADS  Google Scholar 

  91. S. D. Akbarov, “On the three dimensional stability loss problems of elements of constructions fabricated from the viscoelastic composite materials,” Mech. Compos. Mater., 34, No. 6, 537–544 (1998).

    Article  Google Scholar 

  92. S. D. Akbarov, “Three-dimensional stability loss problems of viscoelastic composite materials and structural members,” Int. Appl. Mech., 43, No. 10, 3–27 (2007).

    Article  MATH  MathSciNet  Google Scholar 

  93. S. D. Akbarov, Stability Loss and Buckling Delamination, Springer, Berlin (2012).

    Google Scholar 

  94. S. D. Akbarov, A. Celli, and A. N. Guz, “The theoretical strength limit in compression of viscoelastic layered composite materials,” Compos. Part B: Eng., 365–372 (1999).

  95. S. D. Akbarov and A. N. Guz, Mechanics of Curved Composites, Kluwer Academic Publ., Dordrecht–Boston–London (2000).

    Book  MATH  Google Scholar 

  96. S. D. Akbarov and A. N. Guz, “Mechanics of curved composites and some related problems for structural members” Mech. Advan. Mater. Struct., 11, Pt. II, No. 6, 445–515 (2004).

    Article  Google Scholar 

  97. S. D. Akbarov and O. G. Rzayev, “On the delamination of a viscoelastic composite circular plate,” Int. Appl. Mech., 39, No. 3, 368–374 (2003).

    Article  ADS  Google Scholar 

  98. S. D. Akbarov and O. G. Rzayev, “On the buckling of the elastic and viscoelastic composite circular thick plate with a penny-shaped crack,” Europ. J. Mech., A/ Solids, 21, No. 2, 269–279 (2002).

    Article  MATH  ADS  Google Scholar 

  99. S. D. Akbarov and O. G. Rzayev, “Delamination of unidirectional viscoelastic composite materials,” Mech. Comp. Mater., 39, No. 3, 368–374 (2002).

    Google Scholar 

  100. S. D. Akbarov, T. Sisman, and N. Yahnioglu, “On the fracture of the unidirectional composites in compression,” Int. J. Eng. Sci., 35, No. 12/13, 1115–1136 (1997).

    Article  MATH  Google Scholar 

  101. S. D. Akbarov and N. Yahnioglu, “The method for investigation of the general theory of stability problems of structural elements fabricated from the viscoelastic composite materials,” Compos. Part. B: Eng., 32, No. 5, 475–482 (2001).

    Article  Google Scholar 

  102. S. D. Akbarov, N. Yahnioglu, and O. H. Rzayev, “On influence of the singular type finite elements to the critical force in studying the buckling of a circular plate with a crack,” Int. Appl. Mech., 43, No. 9, 120–129 (2007).

    Article  MATH  MathSciNet  Google Scholar 

  103. C. G. Amar, “Delamination – a damage mode in composite structures,” Eng. Fract. Mech., 29, No. 5, 557–584 (1988).

    Article  Google Scholar 

  104. L. V. Andreev and N. I. Obodan, “Problem of stability of cylindrical shell with a variable rigidity under external pressure,” Int. Appl. Mech., 4, No. 12, 70–75 (1968).

    ADS  Google Scholar 

  105. D. V. Babich, “Effect of lamination of the material on the stability of orthotropic cylindrical shells,” Int. Appl. Mech., 24, No. 10, 981–984 (1988).

    MATH  ADS  Google Scholar 

  106. I. Yu. Babich, A. N. Guz, and B. N. Chekhov, “The three-dimensional theory of stability of fibrous and laminated materials,” Int. Appl. Mech., 37, No. 9, 1103–1141 (2001).

    Article  ADS  Google Scholar 

  107. V. L. Bogdanov, A. N. Guz, and B. M. Nazarenko, “Fracture of semiinfinite material with a circular surface crack in compression along the crack plane,” Int. Appl. Mech., 28, No. 11, 687–704 (1992).

    Article  ADS  Google Scholar 

  108. V. L. Bogdanov, A. N. Guz, and B. M. Nazarenko, “Nonaxisymmetric compressive failure of a circular crack parallel to a surface of halfspace,” Theor. Appl. Fract. Mech., 22, 239–247 (1995).

    Article  MathSciNet  Google Scholar 

  109. V. L. Bogdanov, A. N. Guz, and B. 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).

    Article  MathSciNet  ADS  Google Scholar 

  110. V. L. Bogdanov, A. N. Guz, and B. M. Nazarenko, “Stress-strain state of a material under forces acting along a periodic set of coaxial mode II penny-shaped cracks,” Int. Appl. Mech., 46, No. 12, 1339–1350 (2010).

    Article  MathSciNet  Google Scholar 

  111. V. L. Bogdanov and V. M. Nazarenko, “Study of the compressive failure of a semi-infinite elastic material with a harmonic potential,” Int. Appl. Mech., 30, No. 10, 760–765 (1994).

    Article  ADS  Google Scholar 

  112. V. V. Booting, “Fracture from the stand-point of non-linear stability,” J. Non-Linear Mech., 29, No. 4, 569–585 (1994).

    Article  Google Scholar 

  113. V. V. Booting, Stability Problems in Fracture Mechanics, John Wiley and Sons, New York (1994).

    Google Scholar 

  114. V. V. Booting, “Delaminations in composite structures: its origin, buckling, growth and stability,” Compos. Part B, 27, No. 2, 129–145 (1996).

    Article  Google Scholar 

  115. H. Chai, C. D. Babcock, and W. Krauss, “One dimensional modelling of failure in laminated plates by delamination buckling,” Int. J. Solids Struct., 17, No. 11, 1069–1083 (1981).

    Article  MATH  Google Scholar 

  116. H. Chai and C. D. Babcock, “Two-dimensional modelling of compressive failure in delaminated laminates,” J. Compos. Mater., 19, No. 1, 67–91 (1985).

    Article  ADS  Google Scholar 

  117. L. J. Broutman and R. H. Kroc (eds.), Composite Materials, Vols. 1–8, Academic Press, New York–London (1973–1976).

  118. A. Kelly and C. Zweden (eds.), Composite Materials, Vol. 1–6, Vol. 1: Tsu-Wei Chou (ed.), Fiber Reinforcements and General Theory of Composites, Vol. 2: R. Talreja and J.-A. E. Manson (eds.), Polymer Matrix Composites, Vol. 3: T. W. Cline (ed.), Metal Matrix Composites, Vol. 4: R. Warren (ed.), Carbon/Carbon, Cement and Ceramic Composites, Vol. 5: L. Carlsson, R. L. Crane, and K. Uchino (eds.), Test Methods, Non-destructive Evaluation and Smart Materials, Vol. 6: W. G. Bader, K. Kedsvard, and Y. Sawada (eds.), Design and Applications, Elsevier (2006).

  119. Ian Milne, R. O. Ritchie, and B. Karihaloo (eds.), Structural Integrity, Vols. 1–10, Vol. 1: Ian Milne, R. O. Ritchie, and B. Karihaloo (eds.), Structural Integrity Assessment—Examples and Case Studies, Vol. 2: B. Karihaloo and W. G. Knauss (eds.), Fundamental Theories and Mechanisms of Failure, Vol. 3: R. de Burst and H. A. Mango (eds.), Numerical and Computational Methods, Vol. 4: R. O. Ritchie and Y. Murakami (eds.), Cyclic Loading and Fatigue, Vol. 5: A. Saxena (ed.), Creep and High-Temperature Failure, Vol. 6: J. Petit and Peter Scott (eds.), Environmentally Assisted Fracture, Vol. 7: R. A. Ainsworth and K.-H. Schwable (eds.), Practical Failure Assessment Methods, Vol. 8: W. Gerberich and Wei Yang (eds.), Interfacial and Nanoscale Failure, Vol. 9: Yin-Wing Mai and Swee-Hin Tech (eds.), Bioengineering, Vol. 10: Indexes, Elsevier (2006).

  120. A. G. Evans and J. W. Hutchinson, “On the mechanics of delamination and spalling in compressed films,” Int. J. Solids Struct., 20, No. 5, 455–466 (1984).

    Article  Google Scholar 

  121. H. Liebowiz (ed.), Fracture. An Advanced Treatise, Vols. 1–7, Academic Press, New York–London (1968–1972).

  122. A. C. Garg, “Intralaminar and interlaminar fracture in graphite/epoxy laminates” Eng. Fract. Mech., 23, No. 4, 719–733 (1986).

    Article  Google Scholar 

  123. E. Yu. Gladun, A. N. Guz, and Yu. V. Kokhanenko, “An estimation of error of beam-type approximation in the plane problem of stability of the rectangular plate central crack,” Int. Appl. Mech., 40, No. 11, 117–126 (2004).

    Article  MATH  Google Scholar 

  124. A. A. Griffith, “The phenomena of rupture and flow in solids” Phil. Trans. Roy. Soc., Ser. A, 211, No. 2, 163–198 (1920).

    Google Scholar 

  125. A. N. Guz, “Fracture mechanics of solids in compression along cracks,” Int. Appl. Mech., 18, No. 3, 213– 224 (1982)

    MATH  ADS  Google Scholar 

  126. A. N. Guz, “Mechanics of fracture of solids in compression along cracks (three-dimensional problem)” Int. Appl. Mech., 18, No. 4, 283–293 (1982).

    MathSciNet  Google Scholar 

  127. A. N. Guz, “Fracture mechanics of composites in compression along cracks,” Int. Appl. Mech., 18, No. 6, 489–493 (1982).

    MATH  ADS  Google Scholar 

  128. A. N. Guz, “Foundations of mechanics of brittle fracture of materials with initial stresses,” in: Proc. 6th ICF6, India (1984), pp. 1223–1230.

  129. A. N. Guz, “General case of the plane problem of the mechanics of fracture of solids in compression along cracks,” Int. Appl. Mech., 25, No. 6, 548–552 (1989).

    MATH  MathSciNet  ADS  Google Scholar 

  130. A. N. Guz, “On construction of mechanics of fracture of materials in compression along the cracks,” in: ICF7. Advance in Fracture Research, 6, Pergamon Press (1990), pp. 3881–3892.

  131. A. N. Guz, “Construction of fracture mechanics for materials subjected to compression along cracks,” Int. Appl. Mech., 28, No. 10, 633–639 (1992).

    Article  ADS  Google Scholar 

  132. A. N. Guz, “Non-classical problems of composite failure,” in: Proc. ICF9 Advance in Fracture Research, Vol. 4, Sydney, Australia (1997), pp. 1911–1921.

  133. 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.

  134. 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).

    Google Scholar 

  135. A. N. Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies, Springer, Berlin–Hiedelberg–New York (1999).

    Book  MATH  Google Scholar 

  136. 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).

    Article  ADS  Google Scholar 

  137. A. N. Guz, “Construction of the three-dimensional theory of stability of deformable bodies,” Int. Appl. Mech., 37, No. 1, 1–37 (2001).

    Article  ADS  Google Scholar 

  138. A. N. Guz, “On study of nonclassical problems of fracture and failure mechanics and related mechanisms,” Annals of the European Academy of Sciences, 35–68 (2006–2007).

  139. A. N. Guz, “Pascal Medals lecture (written presentation),” Int. Appl. Mech., 44, No. 1, 6–11 (2008).

    Article  MATH  Google Scholar 

  140. 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).

    Article  MathSciNet  ADS  Google Scholar 

  141. A. N. Guz, “On physical incorrect results in fracture mechanics,” Int. Appl. Mech., 45, No. 10, 1041–1051 (2009).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  142. A. N. Guz, “Mechanics of crack propagation in materials with initial (residual) stresses (review),” Int. Appl. Mech., 47, No. 2, 121–168 (2011).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  143. 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).

    Article  MathSciNet  ADS  Google Scholar 

  144. A. N. Guz, “Stability of elastic bodies under uniform compression (review),” Int. Appl. Mech., 48, No. 3, 241–293 (2012).

    Article  MathSciNet  ADS  Google Scholar 

  145. 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).

    Article  ADS  Google Scholar 

  146. 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).

    Article  ADS  Google Scholar 

  147. A. N. Guz and I. A. Guz, “Analytical solution of stability problem for two composite half-plane compressed along interfacial cracks,” Compos. Part B, 31, No. 5, 405–418 (2000).

    Article  Google Scholar 

  148. 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).

    Article  ADS  Google Scholar 

  149. A. N. Guz and I. A. Guz, “The stability of the interface between two bodies compressed along interface cracks. 2. Exact solution for the case of equal roots,” Int. Appl. Mech., 36, No. 5, 615–622 (2000).

    Article  MathSciNet  ADS  Google Scholar 

  150. 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).

    Article  MathSciNet  ADS  Google Scholar 

  151. 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).

    Article  MathSciNet  ADS  Google Scholar 

  152. A. N. Guz, I. A. Guz, A. V. Men’shykov, and B. A. Men’shykov, “Three-dimensional problems in the dynamic fracture mechanics of materials with interface cracks,” Int. Appl. Mech., 49, No. 1, 1–61 (2013).

    Article  MATH  Google Scholar 

  153. 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).

    Google Scholar 

  154. 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).

    Article  Google Scholar 

  155. A. N. Guz, Yu. I. Khoma, and V. M. Nazarenko, “On fracture of an infinite elastic body in compression along a cylindrical defect,” in: Advance in Fracture Research, Proc. 9th Int. Conf. on Fracture, 4, Sydney, Australia (1999), pp. 2047–2054.

  156. 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,” Int. Appl. Mech., 20, No. 11, 1003–1012 (1984).

    MATH  ADS  Google Scholar 

  157. A. N. Guz, V. L. Knyukh, and V. M. Nazarenko, “Cleavage of composite materials in compression along internal and surface macrocracks,” Int. Appl. Mech., 22, No. 11, 1047–1051 (1986).

    ADS  Google Scholar 

  158. A. N. Guz, V. L. Knyukh, and V. M. Nazarenko, “Fracture of ductile materials in compression along two parallel disk-shaped cracks,” Int. Appl. Mech., 24, No. 2, 112–117 (1988).

    MATH  ADS  Google Scholar 

  159. A. N. Guz, V. L. Knyukh, and B. M. Nazarenko, “Compressive failure of material with two parallel cracks: small and large deformation,” Theor. Appl. Fract. Mech., 11, No. 3, 213–223 (1989).

    Article  Google Scholar 

  160. 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).

    Article  MathSciNet  Google Scholar 

  161. A. N. Guz and V. M. Nazarenko, “Fracture of a material in compression along a periodic system of parallel circular cracks,” Int. Appl. Mech., 23, No. 4, 371–377 (1987).

    ADS  Google Scholar 

  162. A. N. Guz and B. M. Nazarenko, “Fracture mechanics of material in compression along cracks. Highly elastic materials,” Int. Appl. Mech., 25, No. 9, 851–876 (1989).

    MATH  MathSciNet  ADS  Google Scholar 

  163. A. N. Guz and B. M. Nazarenko, “Fracture mechanics of materials under compression along cracks. Structural materials,” Int. Appl. Mech., 25, No. 10, 959–972 (1989).

    MATH  MathSciNet  ADS  Google Scholar 

  164. A. N. Guz, V. M. Nazarenko, and B. L. Bogdanov, “Fracture under initial stresses acting along cracks: Approach, concept and results,” Theor. Appl. Fract. Mech., 48, 285–303 (2007).

    Article  Google Scholar 

  165. A. N. Guz, V. M. Nazarenko, 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).

    Article  MATH  ADS  Google Scholar 

  166. 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).

    Article  MATH  ADS  Google Scholar 

  167. A. N. Guz, V. M. Nazarenko, and S. M. Nazarenko, “Fracture of composites under compression along periodically placed parallel circular stratifications,” Int. Appl. Mech., 25, No. 3, 215–221 (1989).

    MATH  MathSciNet  ADS  Google Scholar 

  168. A. N. Guz, V. M. Nazarenko, and I. P. Starodubtsev, “Planar problem of failure of structural materials in compression along two parallel cracks,” Int. Appl. Mech., 27, No. 4, 352 – 360 (1991).

    MATH  ADS  Google Scholar 

  169. 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).

    Article  MATH  Google Scholar 

  170. A. N. Guz and V. V. Zozulya, “Fracture dynamics with allowance for a crack edges contact interaction,” Int. J. Nonlin. Sci. Number. Simul., 2, No. 3, 173–233 (2001).

    MATH  MathSciNet  Google Scholar 

  171. A. N. Guz and V. V. Zozulya, “Elastodynamic unilateral contact problems with friction for bodies with cracks,” Int. Appl. Mech., 38, No. 8, 895–932 (2002).

    Article  MathSciNet  ADS  Google Scholar 

  172. I. A. Guz, “Computational schemes in tree-dimensional stability theory (the piecewise-homogeneous model of a medium) for composites with cracks between layers,” Int. Appl. Mech., 29, No. 4, 274–280 (1993).

    Article  ADS  Google Scholar 

  173. I. A. Guz, “The strength of a composite formed by longitudinal–transverse stacking of orthotropic layers with a crack at the boundary,” Int. Appl. Mech., 29, No. 11, 921–924 (1993).

    Article  ADS  Google Scholar 

  174. I. A. Guz, “Investigation of the stability of a composite in compression along two parallel structural cracks at the layer interface,” Int. Appl. Mech., 30, No. 11, 841–847 (1994).

    Article  MathSciNet  ADS  Google Scholar 

  175. I. A. Guz, “On one mechanism of fracture of composites in compression along interlayer cracks,” in: Proc. Int. Conf. on Design and Manufacturing Using Composites, Montreal, Canada, AuGuzt 10–12 (1994), pp. 404–412.

  176. I. A. Guz, “Problems of the stability of composite materials in compression along interlaminar cracks: periodic system of parallel macrocracks,” Int. Appl. Mech., 31, No. 7, 551–557 (1995).

    Article  ADS  Google Scholar 

  177. I. A. Guz, “Stability of composites in compression along cracks,” in: Proc. Enercomp 95 (May 8–10, 1995, Montreal, Canada), Technomic Publ., Lancaster–Basel (1995), 163–170.

  178. I. A. Guz, “Failure of layered composites with interface cracks,” in: Proc. 18th Int. Conf. Reinforced Plastics 95, Karlovy Vary, Czech. Rep., May 16–18 (1995), pp. 175–182.

  179. I. A. Guz, “Stability and failure of layered composites with interface cracks,” in: Proc. Int. Conf. on Comp. Eng. Sci. Computational Mechanics 95 (July 30–August 3, 1995, Hawaii, USA), Vols. 1–2, Springer-Verlag (1995), pp. 2317–2322.

  180. I. A. Guz, “Stability loss of composite materials with cracks between compressible elastic layers,” in: Proc. ECCM-7 (14–16 May, 1996, London, UK), Vols. 1–2, Woodhead Publ., (1996), pp. 259–264.

  181. I. A. Guz, “Composite structures in compression along parallel interfacial cracks,” in: Proc. ICCST/1, Durban, South Africa, June 18–20 (1996), pp. 167–172.

  182. I. A. Guz, “Instability in compression as a failure mechanism for layered composites with parallel interfacial cracks,” in: Proc. ICF 9 Advances in Fracture Research, Vol. 2, Sydney, Australia (1997), pp. 1053–1060.

  183. I. A. Guz, “On one fracture mechanism for composites with parallel interfacial cracks,” in: Proc. 4th Int. Conf. on Deformation and Fracture of Composites (March 24–26 March, 1997, Manchester, UK), Institute of Materials, London (1997), pp. 579–588.

  184. I. A. Guz, “On calculation of critical strains for periodical array of parallel interfacial cracks in layered materials,” in: Proc. 6th EPMESC Conf., Guang-Zhou, China, August 4–7 (1997), pp. 375–380.

  185. I. A. Guz, “On fracture of brittle matrix composites: Compression along parallel interfacial cracks,” in: Proc. 5th Int. Symp. (October 13–15, 1997, Warsaw, Poland), Woodhead Publ., Cambridge (1997), pp. 391–400.

  186. I. A. Guz, “Numerical investigation on one mechanism of fracture for rock with parallel interlaminar cracks,” in: Advances in Comp. Eng. Sci., Tech. Science Press, Forsyth, USA (1997), pp. 956–961.

  187. I. A. Guz, “On modelling of a failure mechanism for layered composites with interfacial cracks,” ZAMM, 78, No. 1, S429–S430 (1998).

    Google Scholar 

  188. I. A. Guz and H. W. Chandler, “Bifurcation problem for ceramics compressed along interlaminar microcracks,” in: R. R. Moore (ed.), Abstracts 5th Int. Congr. on Industrial and Applied Mathematics, ICIAM 2003 (July 7–11, 2003, Sydney, Australia), Univ. Techn., Sydney, Australia (2003), p. 311.

  189. I. A. Guz and A. N. Guz, “Stability of two different half-planes in compression along interfacial cracks: Analytical solutions,” Int. Appl. Mech., 37, No. 7, 906–912 (2001).

    Article  MathSciNet  ADS  Google Scholar 

  190. I. A. Guz and Yu. V. Kokhanenko, “Stability of laminated composite material in compression along microcrack,” Int. Appl. Mech., 29, No. 9, 702–708 (1993).

    Article  ADS  Google Scholar 

  191. N. J. Hoff, “Buckling and stability” J. Royal Aeronaut. Soc., 58, No. 1, 1–11 (1954).

    Google Scholar 

  192. G. R. Irwin, “Analysis of stresses and strain near the end of a crack traversing a plate,” J. Appl. Mech., 24, No. 3, 361–364 (1957).

    Google Scholar 

  193. R. M. Jones, “Buckling of stiffened two-layered shells of revolution with a circumferentially cracked unbounded layer,” AIAA J., 7, No. 8, 1511–1517 (1969).

    Article  ADS  Google Scholar 

  194. L. M. Kachanov, Delamination Buckling of Composite Materials, Kluwer Academic Publ., Boston (1988).

    Book  MATH  Google Scholar 

  195. L. M. Kerr, S. Nemat-Nasser, and A. Oranratnachai, “Surface instability and splitting in compressed brittle elastic solids containing crack arrays,” Trans. ASME, J. Appl. Mech., 49, No. 4, 761–767 (1982).

    Article  ADS  Google Scholar 

  196. R. Kienzler and G. Herrmann, Mechanics in Material Space with Applications to Defect and Fracture Mechanics, Springer, Berlin (2000).

    MATH  Google Scholar 

  197. V. L. Knyukh, “Fracture of a material with two disk-shaped cracks in the case of axisymmetric deformation in compression along the cracks,” Int. Appl. Mech., 21, No. 3, 221–225 (1985).

    ADS  Google Scholar 

  198. V. M. Nazarenko, “Mutual effect of a circular surface crack and a free boundary in an axisymmetric problem of the fracture of an incompressible half space in compression along the crack plane,” Int. Appl. Mech., 21, No. 2, 133–137 (1985).

    MATH  ADS  Google Scholar 

  199. V. M. Nazarenko, “Plastic rupture of materials during compression along near-surface fractures,” Int. Appl. Mech., 21, No. 2, 133–137 (1986).

    ADS  Google Scholar 

  200. V. M. Nazarenko, “Two-dimensional problem of the fracture of materials in compression along surface cracks,” Int. Appl. Mech., 22, No. 10, 970–977 (1986).

    MATH  ADS  Google Scholar 

  201. V. M. Nazarenko, “Theory of fracture of materials in compression along near-surface cracks under plane-strain conditions,” Int. Appl. Mech., 22, No. 12, 1192–1199 (1986).

    MathSciNet  ADS  Google Scholar 

  202. V. M. Nazarenko, “Fracture of plastic masses with translational strain-hardening in compression along near-surface cracks,” Int. Appl. Mech., 23, No. 1, 61–64 (1987).

    MathSciNet  ADS  Google Scholar 

  203. I. W. Obreimoff, “The splitting strength of mica,” Proc. Soc. London A, 127A, 290–297 (1930).

    Article  ADS  Google Scholar 

  204. O. G. Rzayev and S. D. Akbarov, “Local buckling of the elastic and viscoelastic coating around the penny-shaped interface crack” Int. J. Eng. Sci., 40, 1435–1451 (2002).

    Article  MATH  Google Scholar 

  205. R. A. Schapery, “Approximate methods of transform inversion for viscoelastic stress analyses,” Proc. US Nat. Congr. Appl. ASME, No. 4, 1075–1085 (1966).

  206. I. P. Starodubtsev, “Fracture of a body in compression along two parallel cracks under plane-strain conditions,” Int. Appl. Mech., 24, No. 6, 604–607 (1988).

    MATH  ADS  Google Scholar 

  207. A. Turin and S. D. Akbarov, “On loss of stability of a strip with two parallel macro-cracks under finite precritical deformation,” Int. Appl. Mech., 46, No. 3, 359–367 (2010).

    Article  ADS  Google Scholar 

  208. B. Winiarski and I. A. Guz, “The effect of cracks interaction on the critical strain in orthotropic heterogeneous material under compressive static loading,” in: Proc. 2006 ASME Int. Mech. Eng. Congr. & Exposition (IMECE 2006), Chicago, USA, November 5–10 (2006), p. 9.

  209. B. Winiarski and I. A. Guz, “Plane problem for layered composites with periodic array of interfacial cracks under compressive static loading,” Int. J. Fract., 144, No. 2, 113–119 (2007).

    Article  MATH  Google Scholar 

  210. B. Winiarski and I. A. Guz, “The effect of cracks interaction for transversely isotropic layered material under compressive loading,” Finite Elem. Anal. Design, 44, No. 4, 197–213 (2008).

    Article  Google Scholar 

  211. B. Winiarski and I. A. Guz, “The effect of fibre volume fraction on the onset of fracture in laminar materials with an array of coplanar interface cracks” Compos. Sci. Technol., 68, No. 12, 2367–2375 (2008).

    Article  Google Scholar 

  212. B. Winiarski and I. A. Guz, “The effect of cracks interaction in orthotropic layered materials under compressive loading” Phil. Trans. Royal Soc. A, 366, No. 1871, 1835–1839 (2008).

    Article  ADS  Google Scholar 

  213. C. H. Wu, “Plane-strain buckling of a crack in harmonic solid subjected to crack-parallel compression,” J. Appl. Mech., 46, 597–604 (1979).

    Article  MATH  ADS  Google Scholar 

  214. C. H. Wu, “Plane strain buckling of a crack in incompressible elastic solids,” J. Elasticity, 10, No. 2, 161–177 (1980).

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterova St., Kyiv, Ukraine, 03057

    A. N. Guz

Authors
  1. A. N. Guz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. N. Guz.

Additional information

Translated from Prikladnaya Mekhanika, Vol. 50, No. 1, pp. 5–88, January–February 2014.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Guz, A.N. Establishing the Foundations of the Mechanics of Fracture of Materials Compressed Along Cracks (Review). Int Appl Mech 50, 1–57 (2014). https://doi.org/10.1007/s10778-014-0609-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10778-014-0609-y

Keywords

Search

Navigation