Analysis of three-dimensional fracture mechanics problems: A two-scale approach using coarse-generalized FEM meshes

This paper presents a generalized finite element method (GFEM) based on the solution of interdependent global (structural) and local (crack)-scale problems. The local problems focus on the resolution of fine-scale features of the solution in the vicinity of three-dimensional cracks, while the global problem addresses the macro-scale structural behavior. The local solutions are embedded into the solution space for the global problem using the partition of unity method. The local problems are accurately solved using an hp-GFEM and thus the proposed method does not rely on analytical solutions. The proposed methodology enables accurate modeling of three-dimensional cracks on meshes with elements that are orders of magnitude larger than the process zone along crack fronts. The boundary conditions for the local problems are provided by the coarse global mesh solution and can be of Dirichlet, Neumann or Cauchy type. The effect of the type of local boundary conditions on the performance of the proposed GFEM is analyzed. Several three-dimensional fracture mechanics problems aimed at investigating the accuracy of the method and its computational performance, both in terms of problem size and CPU time, are presented.