ADAPTIVE MULTISCALE EXTENDED FINITE ELEMENT METHOD FOR MODELING THREE-DIMENSIONAL CRACK PROBLEMS

To consider small cracks in the analysis of large structures or to improve the accuracy of modeling around the cracks at a low cost, an adaptive multiscale extended finite element method (XFEM) for modeling three-dimensional crack problems is proposed. The posteriori error estimation for three dimensional XFEM is evaluated using the recovery method, and the elements with relative errors greater than a specified value are refined accordingly. An eight-node hexahedron element is used for any scale element, and an arbitrary-node hexahedron element is used to link differently scaled elements. The three-dimensional stress intensity factors are evaluated using the interaction integral method. Numerical examples including a three-dimensional mode I crack problem and a three-dimensional mixed mode I-II crack problem are given to illustrate the correctness and efficiency of the proposed method.