On crack simulation by mixed dimensional coupling in GFEM Global- Local

Resumo

The Generalized Finite Element Method (GFEM) is a numerical method established as an alternative to
Finite Element Method (FEM). Considered as an instance of the Partition of Unity Method (PUM), the GFEM uses
enrichment functions that, multiplied by the Partition of Unity (PU) functions, expand the space of the solution
problem. These enrichment functions could be chosen according to the problem analyzed or numerically obtained
from the results of the analysis of a local problem, in the GFEM global-local strategy. Extending the field of
application of this method, the global-local Generalized Finite Element Method (GFEM) is used here to solve
mixed dimensional structural problems. Combining mixed-dimensional elements and a multi-scale analysis can be
highly effective to capture the local structure features without overburdening the global analysis of the problem.
An iterative procedure, which balances the forces between the two multi-dimensional models, was automated and
combined with the global-local analysis of GFEM. This new procedure incorporated into a computational system
made possible the simulation of quasi-static crack propagation. In the numerical example a small scale plane
stress problem, where the crack propagates, is coupled with a large-scale model described by Timoshenko beam
elements.