A new variable-order singular boundary element for calculating stress intensity factors in three-dimensional elasticity problems

A new three-dimensional variable-order singular boundary element has been constructed for stress analysis of three-dimensional interface cracks and internal material junctions. The singular fields in the vicinity of crack front or junction have been accurately represented by the singular elements by taking account the variable order of singularities and the angular profiles of field variables. Both the singular stress fields and displacement fields are independently formulated by the element's shape functions. Different kinds of displacement formulations are investigated. The formulation combining singular and linear terms is found to be the most accurate one. The mixed-mode stress intensity factors are treated as nodal unknowns. The variation of stress intensity factors along the line of singularity can be obtained directly from the final system of equations and thus no post processing, such as three-dimensional J-integral or domain integral, is necessary. Numerical examples involving stress singularity, such as penny-shaped cracks in homogeneous and dissimilar material interface, plates with through-thickness cracks, and a dissimilar inclusion, are investigated. The analysis results are in good agreement with those reported in the literature.