Comparison of Generalized/eXtended Finite Element Methods for Quasi- Brittle Media Cracking Problems

This work presents a comparative study of the application of the Generalized/eXtended Finite Element Method (GFEM) in the solution of cracking problems. Different strategies are performed: Polynomial enrichment strategy with the GFEM and numerical enrichment strategy with and without Stable Generalized Finite Element Method (SGFEM) procedure. The numerical enrichment strategy is based on global-local analysis. For this strategy, the nonlinear analysis is performed in the global problem and a local problem is solved in the end of each converged step. The local solution is used as numerical enrichment for next incremental step of the global problem. This local problem, solved with a fine mesh, is a subdomain of the global problem in the cracking region of the problem. For the application of the polynomial enrichment strategy, the same subdomain of global problem is enriched with prescribed polynomial functions. The smeared cracking model is used as elastic-degradation constitutive model to simulate the behavior of quasi-brittle media. The implementations have been performed in the INSANE (Interactive Structural Analysis Environment) system, a free software developed at Department of Structural Engineering of Federal University of Minas Gerais. Numerical example of a two-dimensional problem (2D) is presented for validation and comparison of the strategies. Besides, the results are compared with experimental data and reference solutions obtained via classical Finite Element Method (FEM).