On the improvement of the local boundary conditions in GFEMgl

In this work, the ZZ-BD recovered stress field is first used to enhance the data transferred from the global to the local scale models in the Generalized Finite Element Method with Global–Local enrichments (GFEM^gl). The recovered stress field is constructed by solving a block-diagonal system of equations resulting from an $L_2$ approximate function projection associated with the singular stress field in the crack tip neighboring. In GFEM^gl analysis, the global solution is imposed as Dirichlet or Cauchy-type boundary conditions in the local domain. In the former case, only displacements are considered. The main contribution of this work lies in the definition of the Cauchy boundary conditions, where the stress field is combined with the displacements. A two-dimensional plate problem with an edge crack under mixed opening mode is solved using GFEM^gl. Stress intensity factors are extracted from global and local problems using the Interaction Integral strategy. Numerical results indicate that the Cauchy boundary conditions with the ZZ-BD recovered stress field provide a more accurate solution than raw or average stress fields, as well as regular Dirichlet boundary conditions. The effects of using a buffer zone in the local problem are also examined. Finally, the Interaction Integral performance strategy is investigated, with the key parameter being the circumference radius that intersects the elements where the stress intensity factors are extracted. An investigation is performed into the local and global problems, and a range of these parameters is identified to minimize errors in the stress intensity factors.