This project aims to develop a computational solver for applications in problems with crack propagation. For this, it will be used the multiescale method of overlapping meshes, due to the fact that the problems related to Fracture Mechanics involve localized effects within a larger domain, as it can be seen in Figure 1. To do so, we will blend a discrete and suitable local mesh over a global mesh, whose discretization is unsuitable to represent the localized effects.

Figure 1 - Basic problem of Fracture Mechanics

To solve the problem, we used the positional formulation of the finite element method, being the local mesh is formed by triangular finite elements with Lagrange polynomial shape functions. On the order hand, for the global mesh it is considered isogeometric discretization with NURBS shape functions, which will allow the exact conformity of the solid geometry.

The reconstruction of the local mesh is necessary at each crack propagation step, which will be carried out using the Delaunay triangulation technique.