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Numerical resolution of the boundary integral equations for elastic scattering by a plane crack. (English) Zbl 0835.73066
Summary: The problem of wave scattering by a plane crack is solved, either in the case of acoustic waves or in the case of elastic waves incidence using the boundary integral equation method. We use a variational method, first writing the problem in Fourier variables, and then writing the associated integrals in the sesquilinear form with weak singularity kernels. This representation is used in the numerical approach, made with a finite element method on the surface of the crack. Numerical tests were made with circular and elliptical cracks. Extensive results are given concerning the crack opening displacement, the scattering cross-section, the back-scattered amplitude and far-field patterns.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
74J20 Wave scattering in solid mechanics
74R99 Fracture and damage
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