Numerical Analysis of Scattering by Interface Flaws

  • Yonglin Xu
  • Jan D. Achenbach
Part of the Review of Progress in Quantitative Nondestructive Evaluation book series


Scattering by inhomogeneities in homogeneous media can be analyzed in an elegant manner by reducing the problem statement to the solution of a system of singular integral equations over the surface of the scatterer [1]. This system can be solved in a relatively straight forward manner by the use of the boundary element method [2]. An inhomogeneity in an interface between two solids of different mechanical properties presents some additional complications to the numerical analyst. These complications are discussed in this paper. In deriving the system of singular integral equations, it was decided to use the Green’s functions for the unbounded regions of the two materials, rather than the single Green’s function for the space of the joined half spaces. This approach introduces a considerable simplification in the integrands, but at the expense of the addition of a set of boundary integral equations over the interface between the two solids, outside of the inhomogeneity. In the boundary element approach the domain of these equations has to be truncated. Specific results are presented for backscattering by a spherical cavity in the interface of solids of different elastic moduli and mass densities.


Boundary Element Method Singular Integral Equation Critical Angle Boundary Integral Equation Spherical Cavity 
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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Yonglin Xu
    • 1
  • Jan D. Achenbach
    • 1
  1. 1.Center for Quality Engineering and Failure PreventionNorthwestern UniversityEvanstonUSA

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