Global Local Analysis with Robin Parameters: Applications to Crack Propagation in 2D and 3D Models

Abstract

Global local analysis is a part of the structural analysis that allows to study, with an iterative solution, a coarse global linear model with a specific zone. This zone is defined as a local model with fine mesh and a non-linear behaviour such as crack propagation. However, the current trend in Global Local analysis is to impose displacements on the fine model to later obtain the reactions that will be applied to the global model for each iteration (Primal to Dual solution algorithm). Therefore, we propose a mixed analysis in the local and global models through the application of Robin conditions on the interface, allowing a higher grade of flexibility for the case of the patch or fine model with crack propagation behaviour. As a result, the algorithm converges successfully, presenting kinematic compatibility and good results with respect to the Monolithic (non-decomposed) model. Finally, a sensitivity analysis is performed on some variables regarding the crack propagation for 2D models. Finally, the proposed methodology also allows to improve the performance of the method for cracked models or other nonlinearities when compared with the current global local analysis, presented in the state of the art.