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

## Palavras-chave:

Generalized Finite Element Method, Global-Local Enrichment, Constraint Equations, Mixed-dimensional Coupling, Multi-scale modeling## 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.