Nonlinear analysis of three-point bending notched concrete beams via global-local Generalized Finite Element Method approach

Resumo

The Generalized Finite Element Method (GFEM) was developed in order to overcome some limitations
inherent to the Finite Element Method (FEM), related to the defects propagation, presence of large deformations
or even in the description of high gradients of state variables. The GFEM enriches the space of the polynomial
FEM solution with a priori known information based on the concept of Partition of Unit (PoU). Certain obstacles of
nonlinear analysis can be mitigated with the GFEM, and damage and plasticity fronts can be accurately represented.
In this context, the global-local approach to the GFEM (GFEM global-local) was proposed. The success of its
application to problems of Linear Elastic Fracture Mechanics is already proven, but its extension to the simulation
of collapse of structures made of quasi-brittle media is still a vast field to be researched. Here, a coupling strategy
is presented based on the global-local GFEM to describe the deterioration process of quasi-brittle media, such
as concrete, in the context of Continuous Damage Mechanics. The numerical solution used to enrich the global
problem, represented by a coarse mesh, is obtained through physically nonlinear analysis performed only in the
local region where damage propagation occurs, represented by constitutive models. The linear analysis of the
global region is performed considering the incorporation of local damage through the global-local enrichment
functions and damage state mapped from local problem. Numerical examples of three-point bending notched
concrete beams have been presented to evaluate the performance of the proposed approach and the obtained results
were compared with the experimental results and with the ones obtained with standard GFEM. Two constitutive
models were applied to represent the concrete in the local region: smeared crack model and microplane model.