An explicit crack-tip element for stationary dynamic cracks

A crack-tip element to accurately capture dynamic response of three-dimensional (3D) cracks is proposed in the present contribution. Unlike other extended finite element methods (XFEM) which use branch functions from the analytical solution of two-dimensional cracks as the crack-tip enrichment, we construct a 3D crack-tip solution (in the form of eigen expansion) for the problem investigated. On that basis, the finite element formulation is derived strictly. It is interesting to find that the proposed crack-tip element works perfectly with an explicit precise integration method and thus gives high accuracy and efficiency. Thanks to the advantages of the precise integration method, the present method is essentially an explicit scheme and is unconditionally stable. The advantages of the combined crack-tip element and precise integration method provide a new insight of modelling 3D dynamic crack which is normally considered to be a complicated and costly task.