A new tool for defining cracks in meshes: FEM equipped with continuous visibility functions

By introducing continuous “visibility functions”, we present a new strategy for using the classical finite elements in cracked media with no need for enrichment functions, mesh alignment, or adding nodes. The visibility functions (VFs) help to construct continuous displacement fields with steep gradients through shape functions having Kronecker-delta, and first order consistency, in the cracked elements. Moreover, the continuity of the overall functions helps to use the conventional integration rules with no need for splitting the elements. The cracks are defined through a set of points, here called “crack points”. Such a feature removes the necessity of defining explicit relations for the crack path. Through using the crack points and the VFs, it becomes possible to consider geometrical/material-based width for the crack. This, in turn, enables us to employ a simple damage model. Along with the introduction of VFs, in this paper we use a hybrid fracture model employing a damage model combined with the concept of Griffith’s energy release, assuming that the damaged area, with sufficiently thin width, represents the crack with strong discontinuity. Eight benchmark problems, including static and progressive cracks, are solved to show the capability of the VFs, and also the hybrid model, in the solution of crack problems.