Asymptotic Analysis of a “Crack” in a Layer of Finite Thickness

  • J. P. Bercial-Velez
Conference paper
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 113)


Rice et al. [1] studied a perturbation problem for the wave equation in a space containing a moving discontinuity surface. We analyse the solutions of the wave equation in a 3D layer, which contains a “crack” propagating dynamically, using the singular perturbation technique developed by Willis and Movchan [3]. The dynamic weight function is discussed for time-dependent Neumann boundary conditions on a semi-infinite “crack” extending at a constant speed V in a 3D layer. The Fourier transform of the weight function is constructed by solving a scalar Wiener-Hopf problem. In this case the weight function is no longer homogeneous (due to the geometry considered). Within the first order perturbation theory framework, a relationship between the intensity factor and a small time-dependent perturbation of the “crack” front is found; we also analyse the transfer function which relates the “crack” front position and the energy release rate.


Wave equation dynamic weight function 


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  1. [1]
    Rice, J.R., Ben-Zion, Y. and Kim, K.S., (1994) “Three-dimensional perturbation solution for a dynamic crack moving unsteadily in a model elastic solid”, J. Mech. Phys. Solids, Vol. 42, No. 5, 814–843.MathSciNetGoogle Scholar
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    Willis, J. R. and Movchan, A. B., (1995) “Dynamic weight functions for a moving crack. I. Mode I loading”, J. Mech. Phys. Solids, Vol. 43, No. 3, 319–341.CrossRefMathSciNetGoogle Scholar
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    Woolfries, S., Movchan, A. B., Willis, J. R., (2002) “Perturbation of a dynamic planar crack moving in a model viscoelastic solid” Int. J. Solids Struct., Vol. 39, Nos. 21–22, 5409–5426.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • J. P. Bercial-Velez
    • 1
  1. 1.Dept. of Mathematical SciencesUniversity of LiverpoolUK

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