  This study suggests a fast computational method for crack propagation, which
is based on the extended finite element method (X-FEM). It is well known that
the X-FEM might be the most popular numerical method for crack propagation.
However, with the increase of complexity of the given problem, the size of FE
model and the number of iterative steps are increased correspondingly. To
improve the efficiency of X-FEM, an efficient computational method termed
decomposed updating reanalysis (DUR) method is suggested. For most of X-FEM
simulation procedures, the change of each iterative step is small and it will
only lead a local change of stiffness matrix. Therefore, the DUR method is
proposed to predict the modified response by only calculating the changed part
of equilibrium equations. Compared with other fast computational methods, the
distinctive characteristic of the proposed method is to update the modified
stiffness matrix with a local updating strategy, which only the changed part of
stiffness matrix needs to be updated. To verify the performance of the DUR
method, several typical numerical examples have been analyzed and the results
demonstrate that this method is a highly efficient method with high accuracy.
