Abordagens estáveis do MEFG/X na simulação de trincas com modelo de zona coesiva em meios parcialmente frágeis

Abstract

The Generalized Finite Element Method (GFEM), here understood as equivalent to the eXtended Finite Element Method (XFEM), has been intensively developed in the last few decades, being useful in many problems, such as fracture mechanics problems. Features as the relative mesh independence and the description's improvement on the representation of stress-field in regions close to the crack's tip may be recorded as some of the reasons behind G/XFEM good performance in aforementioned problems. Despite this, G/XFEM shortcomings yielded to the development of the Stable Generalized Finite Element Method (SGFEM). SGFEM is constructed by a simple modification of the enrichment used in G/XFEM. Regarding its potential, SGFEM has been theme of recent literature discussions. This thesis studies the simulation of cohesive crack propagation by G/XFEM and SGFEM. Different enrichment strategies are considered. Some of them carry out the simulation employing only Heaviside functions, while others consider a combination of Heaviside and trigonometric enrichment functions. The performances of the distinct enrichment strategies are compared in terms of accuracy and conditioning. To the best of the author's knowledge, a systematic study of SGFEMs application to simulate cohesive crack propagation problems with the presence of trigonometric enrichment functions has not been performed yet. A formulation of a continuous-discontinuous (C-D) model, based on a simplification of other models, is also developed. As long as it is known, this is also the first work to apply SGFEM to such a model. Numerical simulations are performed in INSANE (INteractive Structural Analysis ENviroment). In this software, it is possible to find a framework to perform simulations with G/XFEM and SGFEM. Results indicate that the different enrichment strategies are generally accurate, well-conditioned and robust, when the element's bulk is considered a linear elastic isotropic material. However, shortcomings concerning C-D model here implemented are found.