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

Abstract

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.

Global–Local Non Intrusive Analysis with 1D to 3D Coupling: Application to Crack Propagation and Extension to Commercial Software

“…The interfaces between subdomains are connected with linear Γ interfaces. The detailed formulation and mathematical background (functional spaces, Lagrangian definition, Lagrange multipliers among others) can be found in [21]. When implementing this methodology, the mechanical problem of each domain in which it was discretized (global, auxiliary and local models) must be solved for each iteration.…”

“…In [20], the strategy is interpreted as an alternative decomposition method of optimized and non-overlapping Schwarz domains, improving the results. The non-intrusive global-local coupling is applied for complex non-linear behavior (plastic hardening, crack propagation, among others) in [21].…”

“…In [21], Robin parameters or mixed coupling [15,35,40] was studied to improve the execution times. In these studies, a Robin parameter optimization was performed in 2D and 3D problems with crack growth and plastic hardening to improve the convergence of mixed global-local non-intrusive analysis.…”

Discriminant Analysis Based on the Patch Length and Crack Depth to Determine the Convergence of Global–Local Non-Intrusive Analysis with 1D-to-3D Coupling

“…This analysis has been used to estimate crack propagation, non-linear hardening behavior, and non-linear contact, among other complex behaviors, with less computational time compared to a non-decomposed model (also known as a monolithic model) [20][21][22][23][24][25].…”

A fully non-invasive hybrid IGA/FEM scheme for the analysis of localized non-linear phenomena

“…In an iterative process, a part of the global model is replaced by the more detailed local model exactly and non-invasively: the global model is never modified; only interface displacements and reaction forces are exchanged. This strategy along with its concept of non-invasiveness have been successfully applied in FEM and are still gathering a considerable interest in the community (see [19] for local plasticity, [20,21,22,23] for crack propagation, [24,25,26] for fracture modeling with the phase-field approach, [27,28] for domain decomposition solvers, [29] for multi-contact problems, [30] for real aeronautical structures, and [31] for multiscale periodic heterogeneous materials, to name a few). In this work where we consider the coupling of a global IG model with a local FE model, the non-invasive global/local framework appears even more relevant [32]: (i) it naturally avoids costly spline re-parametrization procedures, which may have been necessary otherwise to incorporate a truly-independent local region within the initial IG model, (ii) the global IG stiffness operator can be assembled and factorized only once and the IG system to be solved remains well-conditioned regardless of the shape of the local region, and (iii) it offers the opportunity to simply couple an IG code with any existing robust FE code suitable for the modelling of complex local behaviors.…”