Análise não linear de meios parcialmente frágeis via abordagem global-local do método dos elementos finitos generalizados

Abstract

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 (PU). 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 proposed 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 in two-dimensional domain have been presented to evaluate the performance of the proposed approach and the obtained results were coherent with the experimental ones and better than the results obtained with standard GFEM.