Analytical solution to Scholte’s secular equation for isotropic elastic media

In terms of a method based on Cauchy integrals, we have obtained a robust analytic expression to predict a unique physical solution for the Scholte slowness in all range of possible elastic and isotropic media. Proper analysis of the discontinuities of the secular Scholte equation allows the identification of the velocity of the evanescent wave in one of three possible regimes. When the liquid phase tends to vanish, it was observed: a) the Rayleigh wave solution or the free surface limit, and b) the rarefied fluid medium limit, where there exists a gradual extinction of the Scholte wave as both the density and velocity of the fluid decrease. In general terms, the results show that the propagation speed of a Scholte wave is less than or equal to that of a Rayleigh wave.

Generalized Cauchy integrals on the plane

The integrals with homogeneous-difference kernels are considered on a smooth contour. The boundary properties of the integrals are described in the H?lder space. An analogue of the known Sokhotski-Plemelj formula is obtained. Moreover, the differentiation formula of these integrals is also given.

Debonded arc-shaped interface anticracks

We analytically investigate a debonded arc-shaped anticrack lying on the interface between a circular elastic inhomogeneity and an infinite matrix when subjected to uniform remote in-plane stresses. One side of the anticrack is perfectly bonded to either the inhomogeneity or the matrix, whereas its other side has become fully debonded. Through the introduction of two sectionally holomorphic functions, the problem is reduced to a non-homogeneous Riemann–Hilbert problem of vector form that can be solved through a decoupling procedure and through evaluation of the Cauchy integrals. Solutions to both the non-degenerate case of distinct eigenvalues and the degenerate case of identical eigenvalues are derived.