Global-Local non intrusive analysis with robin parameters: application to plastic hardening behavior and crack propagation in 2D and 3D structures

The global/local analysis allows to embed a specific local zone of interest with a different behaviour in a global coarse model. In this local model, fine meshes are usually used to model some structural details and potentially non-linear behaviours, such as plastic hardening and crack propagation. The standard global/local approach can be observed as a Dirichlet-Neumann iterative algorithm where a Dirichlet problem on the local model and a Neumann problem on the global one are solved successively. This paper proposes a new approach for the global/local framework as Robin parameters are considered on both local and global models to obtain more flexibility and improvement for convergence. Particularly, Robin parameters are obtained using a pre-defined strip of elements and the results are later improved by means of single-objective optimization, minimizing the number of iterations to achieve convergence. This improvement is illustrated for cracked domains and plastic hardening in 2D problems and 3D elements within a non-intrusive framework, allowing the usage of commercial finite element software along with open-source research finite element software.