Three-Dimensional Crack Analysis using X-FEM Considering Symmetric Conditions

Abstract

The extended finite element method (X-FEM), which can model the domain without explicitly meshing the crack surface, can be used to perform stress analyses for efficiently solving fracture mechanics problems. In the present study, the constraint condition enforcement for X-FEM analysis considering symmetry is presented. Since the interpolation functions utilized in X-FEM analysis include the enrichment basis functions, the freedoms of the node on the symmetric plane should be constrained properly in the X-FEM model with symmetric conditions. Moreover, evaluation of the energy release rate by the domain integral method should be performed considering the symmetry conditions. In the present paper, the constraint conditions for three-dimensional X-FEM analysis considering symmetric conditions are summarized, and numerical examples using symmetric X-FEM models are shown. The proposed procedure can be used to perform efficient X-FEM analyses of practical fracture problems.