Two-scale approach to predict multi-site cracking potential in 3-D structures using the generalized finite element method

AbstractThis research utilized the novel computational framework of the generalized finite element method (GFEM) to predict the potential for crack propagation in concrete slabs. A two-scale approach, using the global–local concept within the GFEM framework (GFEMg–l), is applied to multi-site cracking problems (MSC), where different crack geometries are placed simultaneously at different positions in a three-dimensional airfield slab loaded by new generation aircraft gears. The GFEMg–l approach efficiently simulated multiple cracks without discretization in the global mesh, but only in the local domain. The GFEMg–l enrichment functions allow the displacements of the local problem to be represented in the global domain through enrichment functions from the local problems rather than explicitly modeling each crack discretely in the global domain. The main contribution of this work was extension of the GFEMg–l approach to a class of three-dimensional MSC problems involving realistic boundaries conditions and existence of multiple cracks spanning different orders of magnitude in size (scales) within the domain. For the linear elastic structure, bottom- and surface-initiated cracks with small dimensions were considered in conjunction with a larger macro-crack. Unlike traditional numerical methods, the proposed GFEMg–l made it possible to tackle this class of problems by avoiding refined crack front meshes in the global domain as well as numerical round-off errors. Furthermore, the two-scale approach significantly reduces the computational cost for large-scale 3-D MSC problems