3-D local mesh refinement XFEM with variable-node hexahedron elements for extraction of stress intensity factors of straight and curved planar cracks

Abstract

A novel local mesh refinement approach for fracture analysis of three-dimensional (3-D) linear elastic solids is developed, considering both 3-D straight and curved planar cracks. The present local mesh refinement formulation is a combination of the extended finite element method (XFEM), variable-node hexahedron elements, and a posteriori error indicator. Our 3-D formulation using hexahedron elements rigorously embraces a posteriori error estimation scheme, a structural coupling scale-meshes strategy and an enrichment technique. Local mesh refinement is only performed where it is needed, e.g., a vicinity of crack, through an error estimator based on the recovery stress procedure. To treat the mismatching problem induced by different scale-meshes in the domain, a structural coupling scheme employing variable-node transition hexahedron elements based on the generic point interpolation with an arbitrary number of nodes on each of their faces is presented. The 3-D finite element approximations of field variables are enhanced by enrichments so that the mesh is fully independent of the crack geometry. The displacement extrapolation method is taken for the evaluation of linear elastic fracture parameters (e.g., stress intensity factors—SIFs). To show the accuracy and performance of our proposed 3-D formulation, six numerical examples of planar 3-D straight and curved shaped cracks with single and mixed-mode fractures and different configurations are considered and analyzed. The SIFs computed by the developed method are validated with respect to analytical solutions and the ones derived from the conventional XFEM. Associated with an adaptive process, the present 3-D formulation allows the analysts to gain a desirable accuracy with a few trials, which is suited for practices purpose.