Dynamic interaction between an inclusion and moving crack by BEM

In this paper, the dynamic interaction between an inclusion and a nearby moving crack embedded in an elastic medium is studied by the boundary element method (BEM). To deal with this problem, the multi-region technique and two kinds of time-domain boundary integral equations (BIEs) are introduced. The system is divided into two parts along the interface between the inclusion and the matrix medium. Each part is linear, elastic, homogeneous and isotropic. The non-hypersingular traction boundary integral equation is applied on the crack surfaces; while the traditional displacement boundary integral equation is used on the interface and external boundaries. In the numerical solution procedure, square root shape functions are adopted as to describe the proper asymptotic behavior in the vicinity of the crack-tips. The crack growth is modeled by adding new elements of constant length to the moving crack tip, which is controlled by the fracture criterion based on the maximum circumferential stress. In each time step, the direction and the speed of the crack advance are evaluated. The numerical results of the crack growth path, speed, dynamic stress intensity factors (DSIFs) and dynamic interface tractions for various material combinations and geometries are presented. The effect of the inclusion on the moving crack is discussed.