Abstract
In this chapter, elastic wave scattering by cracks in inhomogeneous geological continua with quadratically or exponentially varying material parameters and under conditions of plane strain is studied. A restricted case of inhomogeneity is considered, where Poisson’s ratio is fixed at one-quarter, while both shear modulus and density profile vary along vertical direction, but proportionally to each other. Furthermore, time-harmonic conditions are assumed to hold. Although much of the basic BIEM formulation details were developed in Part I, here we discuss in more detail the in-plane wave motion phenomenon, where the governing differential equations are vectorial, in contrast to the anti-plane strain case, where they are scalar differential equations. The new factor here is the presence of a crack in the unbounded medium, and examples show how this crack modifies the elastic wave field. BIEM formulations for cracks involve hypersingular integrals, as mentioned in Sect. 3.4, where techniques for producing formulations that are amenable to numerical treatment are presented.
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Manolis, G.D., Dineva, P.S., Rangelov, T.V., Wuttke, F. (2017). In-Plane Wave Motion in Unbounded Cracked Inhomogeneous Media. In: Seismic Wave Propagation in Non-Homogeneous Elastic Media by Boundary Elements. Solid Mechanics and Its Applications, vol 240. Springer, Cham. https://doi.org/10.1007/978-3-319-45206-7_9
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