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Mechanics of crack propagation in materials with initial (residual) stresses (review)

  • A. N. Guz
Article

Major results on the mechanics of crack propagation in materials with initial (residual) stresses are analyzed. The case of straight cracks of constant width that propagate at a constant speed in a material with initial (residual) stresses acting along the cracks is examined. The results were obtained, based on linearized solid mechanics, in a universal form for isotropic and orthotropic, compressible and incompressible elastic materials with an arbitrary elastic potential in the cases of finite (large) and small initial strains. The stresses and displacements in the linearized theory are expressed in terms of analytical functions of complex variables when solving dynamic plane and antiplane problems. These complex variables depend on the crack propagation rate and the material properties. The exact solutions analyzed were obtained for growing (mode I, II, III) cracks and the case of wedging by using methods of complex variable theory, such as Riemann–Hilbert problem methods and the Keldysh–Sedov formula. As the initial (residual) stresses tend to zero, these exact solutions of linearized solid mechanics transform into the respective exact solutions of classical linear solid mechanics based on the Muskhelishvili, Lekhnitskii, and Galin complex representations. New mechanical effects in the dynamic problems under consideration are analyzed. The influence of initial (residual) stresses and crack propagation rate is established. In addition, the following two related problems are briefly analyzed within the framework of linearized solid mechanics: growing cracks at the interface of two materials with initial (residual) stresses and brittle fracture under compression along cracks

Keywords

initial (residual) stresses growing cracks linearized solid mechanics complex variables exact solutions mode I, II, III cracks wedging problem 

References

  1. 1.
    L. A. Galin, Contact Problems of Elasticity [in Russian], Fizmatgiz, Moscow (1953).Google Scholar
  2. 2.
    A. N. Guz, Stability of Three-Dimensional Deformable Bodies [in Russian], Naukova Dumka, Kyiv (1971).Google Scholar
  3. 3.
    A. N. Guz, Stability of Elastic Bodies under Finite-Strain Deformation [in Russian], Naukova Dumka, Kyiv (1973).Google Scholar
  4. 4.
    A. N. Guz, Fundamentals of the Theory of Stability of Mine Workings [in Russian], Naukova Dumka, Kyiv (1977).Google Scholar
  5. 5.
    A. N. Guz, Stability of Elastic Bodies under Triaxial Compression [in Russian], Naukova Dumka, Kyiv (1979).Google Scholar
  6. 6.
    A. N. Guz, Brittle Fracture Mechanics of Prestressed Materials [in Russian], Naukova Dumka, Kyiv (1983).Google Scholar
  7. 7.
    A. N. Guz, Elastic Waves in Prestressed Bodies [in Russian], in 2 vols., Vol. 1: General Issues, Vol. 2: Propagation Laws, Naukova Dumka, Kyiv (1986).Google Scholar
  8. 8.
    A. N. Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies [in Russian], Vyshcha Shkola, Kyiv (1986).Google Scholar
  9. 9.
    A. N. Guz, Fracture Mechanics of Compressed Composite Materials [in Russian], Naukova Dumka, Kyiv (1990).Google Scholar
  10. 10.
    A. N. Guz, Brittle Fracture of Prestressed Materials, Vol. 2 of the four-volume five-book series Nonclassical Problems of Fracture Mechanics [in Russian], Naukova Dumka, Kyiv (1991).Google Scholar
  11. 11.
    A. N. Guz, Elastic Waves in Bodies with Initial (Residual) Stresses [in Russian], A.S.K., Kyiv (2004).Google Scholar
  12. 12.
    A. N. Guz, Funamentals of the Fracture Mechanics of Compressed Composites [in Russian], in 2 vols., Vol. 1: Microfracture of Material, Vol. 2: Related Fracture Mechanisms, Litera, Kyiv (2008).Google Scholar
  13. 13.
    A. N. Guz, and I. Yu. Babich, Three-Dimensional Theory of Stability of Rods, Plates, and Shells [in Russian], Vyshcha Shkola, Kyiv (1980).Google Scholar
  14. 14.
    A. N. Guz, and I. Yu. Babich, Three-Dimensional Theory of Stability of Deformable Bodies, Vol. 4 of the six-volume series Three-Dimensional Problems of Elasticity and Plasticity [in Russian], Naukova Dumka, Kyiv (1985).Google Scholar
  15. 15.
    A. N. Guz, S. Yu. Babich, and Yu. P. Glukhov, Statics and Dynamics of Elastic Foundations with Initial (Residual) Stresses [in Russian], Press-line, Kremenchug (2007).Google Scholar
  16. 16.
    A. N. Guz, M. Sh. Dyshel’, and V. M. Nazarenko, Fracture and Stability of Materials with Cracks, Vol. 4: Book 1 of the four-volume five-book series Nonclassical Problems of Fracture Mechanics [in Russian], Naukova Dumka, Kyiv (1992).Google Scholar
  17. 17.
    A. N. Guz, A. P. Zhuk, and F. G. Makhort, Waves in a Prestressed Layer [in Russian], Naukova Dumka, Kyiv (1976).Google Scholar
  18. 18.
    A. N. Guz, and F. G. Makhort, Acoustoelectromagnetoelasticity, Vol. 3 of the five-volume series Mechanics of Coupled Fields in Structural Members [in Russian], Naukova Dumka, Kyiv (1988).Google Scholar
  19. 19.
    A. N. Guz, F. G. Makhort, and O. I. Gushcha, An Introduction to Acoustoelasticity [in Russian], Naukova Dumka, Kyiv (1977).Google Scholar
  20. 20.
    A. N. Guz, F. G. Makhort, O. I. Gushcha, and V. K. Lebedev, Fundamentals of the Ultrasonic Nondestructive Stress Analysis of Solids [in Russian], Naukova Dumka, Kyiv (1974).Google Scholar
  21. 21.
    A. N. Guz, and V. B. Rudnitskii, Basic Theory of Contact of Elastic Bodies with Initial (Residual) Stresses [in Russian], Mel’nik, Khmelnitskiy (2006).Google Scholar
  22. 22.
    S. G. Lekhnitskii, Theory of Elasticity of an Anisotropic Body, Mir, Moscow (1981).zbMATHGoogle Scholar
  23. 23.
    N. I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen (1975).zbMATHGoogle Scholar
  24. 24.
    L. I. Sedov, Continuum Mechanics [in Russian], Vol. 2, Nauka, Moscow (1976).Google Scholar
  25. 25.
    G. P. Cherepanov, Mechanics of Brittle Fracture, McGraw-Hill, New York (1976).Google Scholar
  26. 26.
    N. D. Cristescu, E. M. Craciun, and E. Soos, Mechanics of Elastic Composites, CRC Press (2003).Google Scholar
  27. 27.
    A. N. Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies, Springer, Berlin–Heidelberg–New York (1999).zbMATHGoogle Scholar
  28. 28.
    A. N. Guz, Dynamics of Compressible Viscous Fluid, Cambridge Sci. Publ., Cambridge (2009).Google Scholar
  29. 29.
    G. I. Barenblatt and G. P. Cherepanov, “On the wedging of brittle bodies,” J. Appl. Math. Mech., 24, No. 4, 994–1015 (1960).CrossRefGoogle Scholar
  30. 30.
    A. N. Guz, “On the order of singularity at the leading tip of a crack propagating in materials with initial stresses,” Dokl. NAN Ukrainy, No. 1, 71–75 (1998).Google Scholar
  31. 31.
    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).zbMATHGoogle Scholar
  32. 32.
    J. Aboudi and R. Gilat, “Buckling analysis of fibers in composite materials by wave propagation analogy,” Int J. Solids Struct., 43, 5168–5181 (2006).zbMATHCrossRefGoogle Scholar
  33. 33.
    I. Yu. Babich and A. N. Guz, “Stability of composite structural members (three-dimensional formulation),” Int. Appl. Mech., 38, No. 9, 1048–1075 (2002).CrossRefGoogle Scholar
  34. 34.
    I. Yu. Babich, A. N. Guz, and V. N. Chekhov, “The three-dimensional theory of stability of fibrous and laminated materials,” Int. Appl. Mech., 37, No. 9, 1103–1141 (2001).CrossRefGoogle Scholar
  35. 35.
    S. Yu. Babich, A. N. Guz, and V. B. Rudnitskii, “Contact problems for prestressed elastic bodies and rigid and elastic punches,” Int. Appl. Mech., 40, No. 7, 744–765 (2004).ADSCrossRefGoogle Scholar
  36. 36.
    A. M. Bagno and A. N. Guz, “Elastic waves in prestressed bodies interacting with fluid (survey),” Int. Appl. Mech., 33, No. 6, 435–465 (1997).MathSciNetADSCrossRefGoogle Scholar
  37. 37.
    V. L. Bogdanov, A. N. Guz, and V. M. Nazarenko, “Nonaxisymmetric compressive failure a circular crack parallel to a surface of half-space,” Theor. Appl. Mech., 22, No. 2, 239–247 (1995).MathSciNetGoogle Scholar
  38. 38.
    V. L. Bogdanov, A. N. Guz, and V. M. Nazarenko, “Fracture of a body with periodic set of coaxial cracks under forces directed along them: An axisymmetric problem,” Int. Appl. Mech., 45, No. 2, 111–124 (2009).ADSCrossRefGoogle Scholar
  39. 39.
    I. W. Craggs, “On the propagation of a crack in an elastic-brittle materials,” J. Mech. Phys. Solids, 8, No. 1, 66–75 (1960).MathSciNetADSzbMATHCrossRefGoogle Scholar
  40. 40.
    I. D. Eshelby, “Uniformly moving dislocation,” Proc. Roy. Soc., A 62, part 5, No. 353, 131 (1949).Google Scholar
  41. 41.
    I. N. Flavin, “Surface waves in pre-stressed Mooney materials,” Quart. J. Mech. Appl. Math., 16, No. 4, 441–449 (1963).MathSciNetzbMATHCrossRefGoogle Scholar
  42. 42.
    A. A. Griffith, “The phenomenon of rupture and flow in solids,” Phil. Trans. Roy., Ser. A, 211, No. 2, 163–198 (1920).Google Scholar
  43. 43.
    A. N. Guz, On the hydroelasticity problems for a viscous liquid and elastic bodies with initial stresses // Doklady Akademii Nauk SSSR. –. – 251, N 2. – P. 305 – 308 (1980).Google Scholar
  44. 44.
    A. N. Guz, “On the linearized theory of failure of brittle bodies with initial stresses,” Dokl. AN SSSR, 252, No. 5, 42–45 (1980).Google Scholar
  45. 45.
    A. N. Guz, “On presentation of solutions to linearized Stokes–Navier equations,” Dokl. AN SSSR, 253, No. 4, 825–827 (1980).MathSciNetADSGoogle Scholar
  46. 46.
    A. N. Guz, “Breakaway cracks in elastic bodies with initial stresses,” Dokl. AN SSSR, 254, No. 3, 571–574 (1980).MathSciNetGoogle Scholar
  47. 47.
    A. N. Guz, “On presentation of solutions to linearized Stokes–Navier equations for moving fluid,” Dokl. AN SSSR, 255, No. 5, 1066–1068 (1980).MathSciNetGoogle Scholar
  48. 48.
    A. N. Guz, “Theory of cracks in elastic bodies with initial stresses. Formulation of problems, tear cracks,” Int. Appl. Mech., 16, No. 12, 1015–1023 (1980).ADSzbMATHGoogle Scholar
  49. 49.
    A. N. Guz, “A criterion of solid body destruction during compression along cracks (two-dimensional problem),” Dokl. AN SSSR, 259, No. 6, 1315–1318 (1981).Google Scholar
  50. 50.
    A. N. Guz, “A criterion of solid body destruction under compression along cracks (a 3-dimensional problem),” Dokl. AN SSSR, 261, No. 1, 42–45 (1981).Google Scholar
  51. 51.
    A. N. Guz, “On criterion of brittle fracture of materials with initial stresses,” Dokl. AN SSSR, 262, No. 2, 285–288 (1982).Google Scholar
  52. 52.
    A. N. Guz, “Moving cracks in elastic bodies with initial stresses,” Int. Appl. Mech., 18, No. 2, 132–136 (1982).ADSGoogle Scholar
  53. 53.
    A. N. Guz, “Energy criteria of the brittle fracture material with initial stresses,” Int. Appl. Mech., 18, No. 9, 771–775 (1982).ADSGoogle Scholar
  54. 54.
    A. N. Guz, “On order of singularity in cracks tip in materials with initial stresses,” Dokl. AN SSSR, 289, No. 2, 310–313 (1986).MathSciNetGoogle Scholar
  55. 55.
    A. N. Guz, “On the development of brittle-fracture mechanics of materials with initial stresses,” Int. Appl. Mech., 32, No. 4, 316–323 (1996).ADSzbMATHCrossRefGoogle Scholar
  56. 56.
    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
  57. 57.
    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).MathSciNetADSCrossRefGoogle Scholar
  58. 58.
    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).MathSciNetADSCrossRefGoogle Scholar
  59. 59.
    A. N. Guz, “Dynamic problems of the mechanics of 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).MathSciNetADSCrossRefGoogle Scholar
  60. 60.
    A. N. Guz, “Dynamic problems of the mechanics of brittle fracture of materials with initial stresses for moving cracks. 4. Wedge problems,” Int. Appl. Mech., 35, No. 3, 225–232 (1999).ADSCrossRefGoogle Scholar
  61. 61.
    A. N. Guz, “On dynamic contact problems for an elastic half-plane with initial stresses in the case of a moving rigid punch,” Int. Appl. Mech., 35, No. 5, 515–521 (1999).Google Scholar
  62. 62.
    A. N. Guz, “Compressible, viscous fluid dynamics (review). Part I,” Int. Appl. Mech., 36, No. 1, 14–39 (2000).MathSciNetADSCrossRefGoogle Scholar
  63. 63.
    A. N. Guz, “The dynamics of a compressible viscous fluid (review). Part II,” Int. Appl. Mech., 36, No. 3, 281–302 (2000).MathSciNetADSCrossRefGoogle Scholar
  64. 64.
    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).CrossRefGoogle Scholar
  65. 65.
    A. N. Guz, “Moving cracks in composite materials with initial stresses,” Mech. Comp. Mater., 37, No. 5/6, 695–708 (2001).MathSciNetCrossRefGoogle Scholar
  66. 66.
    A. N. Guz, “Constructing the three-dimensional theory of stability of deformable bodies,” Int. Appl. Mech., 37, No. 1, 1–37 (2001).CrossRefGoogle Scholar
  67. 67.
    A. N. Guz, “Elastic waves in bodies with initial (residual) stresses,” Int. Appl. Mech., 38, No. 1, 23–59 (2002).MathSciNetCrossRefGoogle Scholar
  68. 68.
    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).CrossRefGoogle Scholar
  69. 69.
    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).CrossRefGoogle Scholar
  70. 70.
    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).CrossRefGoogle Scholar
  71. 71.
    A. N. Guz, “Critical phenomena in cracking of the interface between two prestressed materials. 4. Exact solution. The case of unequal and equal roots,” Int. Appl. Mech., 38, No. 7, 806–814 (2002).CrossRefGoogle Scholar
  72. 72.
    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).CrossRefGoogle Scholar
  73. 73.
    A. N. Guz, “Establishing the fundamentals of the theory of stability of mine workings,” Int. Appl. Mech., 39, No. 1, 20–48 (2003).ADSCrossRefGoogle Scholar
  74. 74.
    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).ADSCrossRefGoogle Scholar
  75. 75.
    A. N. Guz, “Design models in linearized solid mechanics,” Int. Appl. Mech., 40, No. 5, 506–516 (2004).MathSciNetADSCrossRefGoogle Scholar
  76. 76.
    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).Google Scholar
  77. 77.
    A. N. Guz, “On study of nonclassical problems of fracture and failure mechanics and related mechanisms,” Int. Appl. Mech., 45, No. 1, 3–40 (2009).CrossRefGoogle Scholar
  78. 78.
    A. N. Guz, “Setting up a theory of stability of fibrous and laminated composites,” Int. Appl. Mech., 45, No. 6, 587–612 (2009).ADSCrossRefGoogle Scholar
  79. 79.
    A. N. Guz, “On physically incorrect results in fracture mechanics,” Int. Appl. Mech., 45, No. 10, 1041–1051 (2009).MathSciNetADSCrossRefGoogle Scholar
  80. 80.
    A. N. Guz, S. Yu. Babich, and V. B. Rudnitsky, “Contact problems for elastic bodies with initial stresses: Focus on Ukrainian research,” Appl. Mech. Reviews, 51, No. 5, 343–371 (1998).ADSCrossRefGoogle Scholar
  81. 81.
    A. N. Guz and A. M. Bagno, “Influence of initial stresses on wave velocities in prestrained compressible layer interacting with fluid half-space,” Dokl. AN, 329, No. 6, 715–717 (1993).Google Scholar
  82. 82.
    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).ADSCrossRefGoogle Scholar
  83. 83.
    A. N. Guz and V. A. Dekret, “Interaction of two parallel short fibers in the matrix at loss of stability,” CMES, 13, No. 3, 165–170 (2006).Google Scholar
  84. 84.
    A. N. Guz and V. A. Dekret, “On two models in the three-dimensional theory of stability of composite materials,” Int. Appl. Mech., 44, No. 8, 839–854 (2008).ADSCrossRefGoogle Scholar
  85. 85.
    A. N. Guz, V. A. Dekret, and Yu. V. Kokhanenko, “Plane stability problems of composite weakly reinforced by short fibers,” Mech. Adv. Mater. Struct., 12, No. 5, 313–317 (2005).CrossRefGoogle Scholar
  86. 86.
    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).ADSCrossRefGoogle Scholar
  87. 87.
    A. N. Guz and I. A. Guz, “Analytical solution of stability problem for two composite half-planes compressed along interfacial cracks,” Composites, Part B, 31, No. 5, 405–418 (2000).CrossRefGoogle Scholar
  88. 88.
    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).ADSCrossRefGoogle Scholar
  89. 89.
    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).MathSciNetADSCrossRefGoogle Scholar
  90. 90.
    A. N. Guz and I. A. Guz, “The stability of the interface between two bodies compressed along interface cracks. 4. Exact solution for the combined case of equal and unequal roots,” Int. Appl. Mech., 36, No. 6, 759–768 (2000).MathSciNetADSCrossRefGoogle Scholar
  91. 91.
    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).ADSCrossRefGoogle Scholar
  92. 92.
    A. N. Guz and I. A. Guz, “Mixed plane problem of linearized solid mechanics: Exact solutions,” Int. Appl. Mech., 40, No. 1, 1–29 (2004).MathSciNetADSCrossRefGoogle Scholar
  93. 93.
    I. A. Guz and A. N. Guz, “Stability of two-dimensional half-planes in compression along interfacial cracks: Analytical solutions,” in: Abstracts of 20th Int. Congr. of Theoretical and Applied Mechanics, Chicago, USA, August 27–September 2 (2000), p. 49.Google Scholar
  94. 94.
    A. N. Guz and Yu. V. Kokhanenko, “Numerical solution of three-dimensional stability problems for elastic bodies,” Int. Appl. Mech., 37, No. 11, 1369–1399 (2001).MathSciNetCrossRefGoogle Scholar
  95. 95.
    A. N. Guz and F. G. Makhort, “The physical fundamentals of the ultrasonic nondestructive stress analysis of solids,” Int. Appl. Mech., 36, No. 9, 1119–1149 (2000).CrossRefGoogle Scholar
  96. 96.
    A. N. Guz and V. M. Nazarenko, “Summetric failure of the half-space with penny-shaped cracks in compression,” Theor. Appl. Frac. Mech., 3, No. 3, 233–245 (1985).MathSciNetCrossRefGoogle Scholar
  97. 97.
    A. N. Guz and A. P. Zhuk, “On hydrodynamical forces acting in acoustic field in viscous fluid,” Dokl. AN SSSR, 266, No. 1, 32–35 (1982).MathSciNetGoogle Scholar
  98. 98.
    A. N. Guz and A. P. Zhuk, “Motion of solid particles in a liquid under the action of an acoustic field: The mechanism of radiation pressure,” Int. Appl. Mech., 40, No. 3, 246–265 (2004).ADSCrossRefGoogle Scholar
  99. 99.
    A. N. Guz and A. P. Zhuk, “Dynamics of a rigid cylinder near a plane boundary in the radiation field of an acoustic wave,” J. Fluids Struct., 25, 1206–1212 (2009).ADSCrossRefGoogle Scholar
  100. 100.
    M. Hayes, “On waves propagation in a deformed Mooney–Rivlin material,” Quart. Appl. Math., 34, No. 3, 319–321 (1976).MathSciNetzbMATHGoogle Scholar
  101. 101.
    M. Kurashige, “Circular crack problem for initially stressed neo-Hookean solid,” ZAMM, 49, No. 8, 671–678 (1969).zbMATHGoogle Scholar
  102. 102.
    “Micromechanics of composite materials: Focus on Ukrainian research (special issue),” Appl. Mech. Reviews, 45, No. 2, 13–101 (1992).Google Scholar
  103. 103.
    J. G. Murphy and M. Destade, “Surfave waves and surface stability for a pre-stretched, unconstrained, non-linearly elastic half-space,” Int. J. Non-Lin. Mech., 44, 545–551 (2009).CrossRefGoogle Scholar
  104. 104.
    R. W. Ogden, “Waves in isotropic elastic materials of Hadamard, Green and harmonic type,” J. Mech. Phys. Solids, 18, No. 2, 149–163 (1970).MathSciNetADSzbMATHCrossRefGoogle Scholar
  105. 105.
    E. Radi, D. Bigoni, and D. Capuati, “Effect of prestress on crack tip fields in elastic incompressible solids,” Int J. Solids Struct., 39, 3971–3996 (2002).CrossRefGoogle Scholar
  106. 106.
    S. Rajit, Dhaliwal, R. M. Singh, and I. G. Rokhe, “Axisymmetric contact and crack problems for initially stressed neo-Hookean layer,” Int. J. Eng. Sci., 18, No. 1, 169–179 (1980).CrossRefGoogle Scholar
  107. 107.
    G. A. Rogerson and K. I. Sandiford, “The effect of finite primary deformation on harmonic waves in layered elastic media,” Int. J. Solids Struct., 37, No. 14, 2059–2087 (2000).MathSciNetzbMATHCrossRefGoogle Scholar
  108. 108.
    E. Soos, “Resonance and stress concentration in a prestressed elastic solid containing a crack,” Int. J. Eng. Sci., 34, No. 3, 363–374 (1996).MathSciNetzbMATHCrossRefGoogle Scholar
  109. 109.
    D. K. Wagh, “Torsional waves in an elastic cylinder with Cauchy’s initial stress,” Gerlands Beitr. Geophys., 81, No. 6, 489–498 (1972).Google Scholar
  110. 110.
    H. M. Westergard, “Bearing pressure and cracks,” Appl. Mech., 6, No. 2, 49–53 (1939).Google Scholar
  111. 111.
    A. J. Willson, “Surface waves in uniaxially-stressed Mooney material,” Pure Appl. Geophys., 112, No. 4, 667–674 (1974).ADSCrossRefGoogle Scholar
  112. 112.
    C. H. Wu, “Plane-strain buckling of a crack in harmonic solid subjected crack parallel compression,” Appl. Mech., 46, 597–604 (1979).zbMATHCrossRefGoogle Scholar
  113. 113.
    E. Yoffe, “The moving Griffith crack,” Phil. Mag., 4, No. 330, 739–750 (1951).MathSciNetGoogle Scholar

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© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of UkraineKyivUkraine

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