An incremental formulation of the moving-grid finite element method for the prediction of dynamic crack propagation Original Research Article

This paper presents an incremental formulation of the moving-grid finite element method based on the Eulerian-Lagrangian Lagramatic description (ELD) to predict dynamic crack propagation in brittle materials. The variational statement of the equations of motion based on the ELD and an integral form of the energy balance criterion for crack growth are used to form the governing equations for the prediction problems of dynamic crack propagation. The resulting governing equations for the present formulation are nonlinear with respect to two unknowns, displacement and crack-tip position. An iterative solution scheme for the present formulation is proposed. The unknown crack-tip position is computed directly in the solution procedure. Numerical results of the prediction of mode I dynamic crack propagation are presented and compared with experimental results and other numerical solutions.