Effect of initial stress on the propagation of SH wave in a bi-material half space with a circular cavity

Abstract

In this paper, the dynamic problem of a circular cavity in a bi-material half space with initial stress is studied. First, the equilibrium equation for the two-dimensional elastic medium with initial stress under SH wave is obtained by tensor analysis. On the basis of image method, conformal mapping method, and substitution method, the analytical expression of scattering wave is conducted, which satisfies the boundary conditions on the boundary of the half space. Then, Green’s function method is applied, the half space is divided into two parts along the vertical interface, a pair of out-plane forces are applied on the vertical interface, and the first kind of Fredholm integral equations are set up. Finally, based on the conjunction method and theory of incremental elasticity, the expression for the total stress is derived. The integral equations are set up through boundary conditions and solved by applying orthogonal function expansion technique and effective truncation. The calculation results analyzed and discussed the dynamic stress concentration factor around the circular cavity. Besides, the analytical solutions are compared with the finite element solutions to verify the accuracy of the conclusions in this paper.