Derivation of Anti-Plane Dynamic Green's Function for Several Circular Inclusions with Imperfect Interfaces

Abstract

A null-field integral equation is employed to derive the two-dimensional antiplane dynamic Green's functions for a circular inclusion with an imperfect interface. We employ the linear spring model with vanishing thickness to characterize the imperfect interface. Analytical expressions of displacement and stress fields due to time-harmonic antiplane line forces located either in the unbounded matrix or in the circular inclusion are presented. To fully capture the circular geometries, degenerate- kernel expressions of fundamental solutions in the polar coordinate and Fourier series for boundary densities are adopted. Good agreement is made after comparing with the analytical solution derived by Wang and Sudak's results. Parameter study of wave number and interface constant is done. In this paper, we employ the null-field BIE to derive the analytical Green's function instead of choosing the Trefftz bases by using the Wang and Sudak's approach. Special cases of cavity and ideal bonding as well as static solutions are also examined. Besides, two-inclusions case in the matrix with a concentrated force problem is also solved.