The dynamic stresses induced by moving interfacial cracks

Elastodynamic problems involving moving mixed boundary conditions are considered. In particular, uniform and nonuniform propagation in Mode I, II and III types of motion of semi-infinite cracks along the interface of two dissimilar half-spaces are treated. The equations of motion are transformed to a new coordinate system in which the moving tip of the crack appears always at the origin of the coordinates. An implicit three-level numerical method of solution is given which is proved to be more efficient than a previous explicit one. Furthermore, an implicit method for the numerical formulation of the boundary conditions is presented and is shown to yield better results than a previous formulation. The stability analysis of the proposed finite difference approximation is given, and stability criteria are presented as well as a proof of the convergence of the iterative process involved in the numerical formulation of the boundary and interface conditions. The reliability of the present method of solution is examined in several situations where analytical results are known.