Evaluation of Numerical Parameters of a global-local GFEM approach simulating damage propagation in a L-shaped concrete panel

Resumo

The nonlinear modeling of concrete structures requires strain-softening models that properly represent
the nucleation and propagation of damage. The description of those phenomena, by Finite Element Method (FEM),
is highly dependent on the quality of the mesh and the type of the approximation function adopted. The Generalized
Finite Element Method (GFEM) has been developed in order to overcome some limitations inherent to the FEM
aiming to use some knowledgment about the expected solution behavior to improve the analysis. The GFEM
enriches the space of the polynomial FEM solution with a priori known information based on the concept of
Partition of Unit. In this context, the global-local approach to the GFEM (GFEM global-local) is investigated here
as an alternative to the standard GFEM to describe the deterioration process of concrete media in the context of
Continuous Damage Mechanics. Succinctly, the global-local function used to enrich the global problem is obtained
through physically nonlinear analysis performed only in the local domain, represented by constitutive models and
discretized by a refined mesh, where in fact damage propagation occurs. In the global domain discretized by a

coarse mesh, it is performed a linear analysis considering the incorporation of local damage through the global-
local enrichment functions and damage state mapped from local problem. In this paper, the Smeared Crack Model

is the constitutive model used in the local domain to simulate the damage propagation experimentally obtained in
an L-shaped concrete panel. The numerical simulations aim to evaluate the influence of the following numerical
parameters of the GFEM global-local approach on the equilibrium paths: number of local steps added to each block
of global-local analysis and the size of the global step. The obtained results are compared with the experimental
ones, the most suitable sets of parameters can be found and then applied in other simulations that involve the
expansion of the local domain and the variation of the nodes enriched with the global-local function.