Analysis of the local domain size and the number of enriched nodes in a global-local GFEM approach simulating damage propagation in an L- shaped concrete panel

Resumo

The Generalized Finite Element Method (GFEM) has been developed to overcome some limitations inherent to the FEM by using some knowledge 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 GFEM global-local approach to the nonlinear analysis of quasi-brittle media is investigated here. The kernel concern is the impact on the structural global response of expanding the local domain and the number of nodes enriched with the global-local numerically obtained functions. Such analysis has been encouraged by observations that the quality of the global solution transferred to the boundary of the local problem can indeed impact the problem solution in media with linear elastic behavior. The importance of this is grounded by the interest in having a reasonably coarse global mesh to justify a global-local analysis with the local problem discretized by a fine mesh. It is suggested, for example, the polynomial enrichment of the initial global approximation and the increase in the size of the local domain, enlarging the so-called buffer zone. Here, this strategy is evaluated to solve nonlinear problems induced by the degradation of the continuous medium. Thereby,a Smeared Crack Model of fixed direction with the stress-strain laws of Carreira and Chu is applied in the local
domain to simulate the damage propagation experimentally obtained in an L-shaped concrete panel. The resulting global-local responses are compared with experimental findings from the literature and numerical results obtained by standard GFEM.