2-D and 3-D Elastodynamic Contact Problems for Interface Cracks Under Harmonic Loading


Achievements of material science, such as with the new high-tech materials, make it possible to significantly increase the strength and stiffness of designed structures. However, the cost of an unpredictable fracture is always enormously high. Apart from the increased economic costs due to increased safety requirements, it is necessary to remember that in extreme cases the material or structural fracture can put human life at risk. Therefore, the ultimate milestone of modern fracture mechanics is fracture control, which allows the prediction of the construction behavior and the avoidance of sudden collapse.


Stress Intensity Factor Contact Force Contact Problem Interface Crack Crack Closure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [AlRo91]
    Aliabadi, M.H., Rook, D.P.: Numerical Fracture Mechanics, Computational Mechanics Publications and Kluwer Academic Publishers (1991). MATHCrossRefGoogle Scholar
  2. [BaSl89]
    Balas, S., Sladek, J., Sladek, V.: Stress Analysis by Boundary Element Methods, Elsevier, Amsterdam (1989). MATHGoogle Scholar
  3. [Ch79]
    Cherepanov, G.P.: Mechanics of Brittle Fracture, McGraw Hill, New York (1979). MATHGoogle Scholar
  4. [Ch05]
    Chen, Z.T.: Interfacial coplanar cracks in piezoelectric bi-material systems under pure mechanical impact loading. Int. J. Solids. Struct., 43, 5085–5099 (2005). CrossRefGoogle Scholar
  5. [Co77]
    Comninou, M.: The interface crack. J. Appl. Mech., 44, 631–636 (1977). MATHCrossRefGoogle Scholar
  6. [Di02]
    Dineva, P., Gross, D., Rangelov, T.: Dynamic behavior of a bi-material interface-cracked plate. Eng. Fract. Mech., 69, 1193–1218 (2002). CrossRefGoogle Scholar
  7. [Ga07]
    Garcia-Sanchez, F., Zhang, Ch.: A comparative study of three BEM for transient dynamic crack analysis of 2-D anisotropic solids. Computat. Mech., 40, 753–769 (2007). MATHCrossRefGoogle Scholar
  8. [Go76]
    Goldstein, R.W., Vainshelbaum, V.M.: Axisymmetric problem of a crack at the interface of layers in a multi-layered medium. Int. J. Eng. Sci., 14, n. 4, 335–352 (1976). MathSciNetMATHCrossRefGoogle Scholar
  9. [Guo09]
    Guo, S.: Elastic wave scattering from a penny-shaped interface crack in coated materials. Arch. Appl. Mech., 79, 709–723 (2009). CrossRefGoogle Scholar
  10. [Gu02]
    Guz, A.N., Zozulya, V.V.: Elastodynamic unilateral contact problems with friction for bodies with cracks. Int. Appl. Mech., 38, 895–932 (2002). MathSciNetCrossRefGoogle Scholar
  11. [Gu06]
    Guz, I.A., Menshykov, O.V., Menshykov, V.A.: Application of boundary integral equations to elastodynamics of an interface crack. Int. J. Fract., 140, 277–284 (2006) MATHCrossRefGoogle Scholar
  12. [Gu09a]
    Guz, A.N., Guz, I.A., Menshykov, O.V., Menshykov, V.A.: Penny-shaped interface crack under shear wave. Int. Appl. Mech., 45, n. 5, 534–539 (2009). CrossRefGoogle Scholar
  13. [Gu09b]
    Guz, A.N., Zozulya, V.V.: On dynamical fracture mechanics in the case of polyharmonic loading by P-waves. Int. Appl. Mech., 45, n. 9, 1033–1039 (2009). CrossRefGoogle Scholar
  14. [It80]
    Itou, S.: Transient analysis of stress waves around two coplanar Griffith cracks under impact load. Eng. Fr. Mech., 13, 349–356 (1980). CrossRefGoogle Scholar
  15. [Ka93]
    Kachanov, M.: Elastic solids with many cracks and related problems, in: Advances in Applied Mechanics, vol. 30 (Editors: J.W. Hutchinson, T.Y. Wu), Academic Press, 259–445 (1993). CrossRefGoogle Scholar
  16. [Ki06]
    Kilic, B., Madenci, E., Mahajan, R.: Energy release rate and contact zone in a cohesive and an interface crack by hypersingular integral equations. Int. J. Solids Struct., 43, 1159–1188 (2006). MATHCrossRefGoogle Scholar
  17. [Lo73]
    Loeber, J.F., Sih, G.C.: Transmission of anti-plane shear waves past an interface crack in dissimilar media. Eng. Fract. Mech., 5, 699–725 (1973). CrossRefGoogle Scholar
  18. [Ma06]
    Martin, P.A.: Multiple Scattering. Interaction of Time-Harmonic Waves with N Obstacles, Cambridge University Press (2006). MATHCrossRefGoogle Scholar
  19. [Me07]
    Menshykov, O.V., Menshykov, V.A., Guz, I.A.: The effect of frequency in the problem of interface crack under harmonic loading. Int. J. Fract., 146, 197–202 (2007). MATHCrossRefGoogle Scholar
  20. [Me08a]
    Menshykov, O.V., Guz, I.A.: Elastodynamic problem for two penny-shaped cracks: the effect of cracks’ closure. Int. J. Fract., 153, 69–76 (2008). CrossRefGoogle Scholar
  21. [Me08b]
    Menshykov, O.V., Guz, I.A., Menshykov, V.A.: Boundary integral equations in elastodynamics of interface crack. Phil. Trans. R. Soc. A., 366, 1835–1839 (2008). MathSciNetCrossRefGoogle Scholar
  22. [Me08c]
    Menshykov, O.V., Menshykov, V.A., Guz, I.A.: The contact problem for an open penny-shaped crack under normally incident tension–compression wave. Eng. Fract. Mech., 75, 1114–1126 (2008). CrossRefGoogle Scholar
  23. [Me08d]
    Menshykov, O.V., Menshykova, M.V., Guz, I.A.: Effect of friction of the crack faces for a linear crack under an oblique harmonic loading. Int. J. Eng. Sci., 46, 438–458 (2008). MATHCrossRefGoogle Scholar
  24. [Me09a]
    Menshykov, O.V., Menshykov, V.A., Guz, I.A.: Elastodynamics of a crack on the bimaterial interface. Eng. Anal. Bound. Elem., 33, 294–301 (2009). MathSciNetCrossRefGoogle Scholar
  25. [Me09b]
    Menshykova, M.V., Menshykov, O.V., Guz, I.A.: Linear interface crack under plane shear wave. CMES: Comput. Model. Eng. Sci., 48, n. 2, 107–120 (2009). MathSciNetGoogle Scholar
  26. [Me10]
    Menshykova, M.V., Menshykov, O.V., Guz, I.A.: Modelling crack closure for an interface crack under harmonic loading. Int. J. Fract., 165, 127–134 (2010). CrossRefGoogle Scholar
  27. [My06]
    Mykhas’kiv, V., Zhang, Ch., Sladek, J., Sladek, V.: A frequency-domain BEM for non-synchronous crack interaction analysis in elastic solids. Eng. Anal. Bound. Elem., 30, 167–175 (2006). MATHCrossRefGoogle Scholar
  28. [Qu94]
    Qu, J.: Interface crack loaded by a time-harmonic plane wave. Int. J. Solids. Struct., 31, n. 3, 329–345 (1994). MATHCrossRefGoogle Scholar
  29. [Qu95]
    Qu, J.: Scattering of plane waves from an interface crack. Int. J. Eng. Sci., 33, n. 2, 179–194 (1995). MATHCrossRefGoogle Scholar
  30. [Wa01]
    Wang, Y.S., Gross, D.: Interaction of harmonic waves with a periodic array of interface cracks in a multi-layered medium: anti-plane case. Int. J. Solids Struct., 38, 4631–4655 (2001). MATHCrossRefGoogle Scholar
  31. [Wü09]
    Wünsche, M., Zhang, Ch., Sladek, J., Sladek, V., Hirose, S., Kuna, M.: Transient dynamic analysis of interface cracks in layered anisotropic solids under impact loading. Int. J Fract., 157, n. 1–2, 131–147 (2009). MATHCrossRefGoogle Scholar
  32. [Zh89]
    Zhang, Ch., Achenbach, J.D.: Time-domain boundary element analysis of dynamic near-tip fields for impact-loaded collinear cracks. Eng. Frac. Mech., 32, n. 6, 899–909 (1989). CrossRefGoogle Scholar
  33. [Zh91]
    Zhang, Ch.: Dynamic stress intensity factors for periodically spaced collinear antiplane shear cracks between dissimilar media. Theor. Appl. Fract. Mech., 15, 219–227 (1991). CrossRefGoogle Scholar
  34. [Zo02]
    Zozulya, V.V., Men’shikova, M.V.: Study of iterative algorithms for solution of dynamic contact problems for elastic cracked bodies. Int. Appl. Mech., 38, n. 5, 573–577 (2002). CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • O. Menshykov
    • 1
  • M. Menshykova
    • 1
  • I. Guz
    • 1
  • V. Mikucka
    • 1
  1. 1.University of AberdeenAberdeenUK

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