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

TL;DR

This paper introduces a fully non-invasive hybrid IGA/FEM scheme that combines the geometric accuracy of IGA with FEM's ability to model complex local non-linear phenomena, using a coupling method compatible with standard FE software.

Contribution

The work presents a novel non-invasive coupling scheme between IGA and FEM that requires no modification of the global spline model and leverages conventional FE packages for local non-linear analysis.

Findings

Successfully couples IGA with FEM using Bézier extraction

Enables accurate simulation of local non-linear phenomena like cracks and delamination

Compatible with existing FE software such as Code Aster

Abstract

This work undertakes to combine the interests of IsoGeometric Analysis (IGA) and standard Finite Element Methods (FEM) for the global/local simulation of structures. The idea is to adopt a hybrid global-IGA/local-FEM modeling, thereby benefiting from: (i) the superior geometric description and per-Degree-Of-Freedom accuracy of IGA for capturing global, regular responses, and (ii) the ability of FEM to compute local, strongly non-linear or even singular behaviors. For the sake of minimizing the implementation effort, we develop a coupling scheme that is fully non-invasive in the sense that the initial global spline model to be enriched is never modified and the construction of the coupling operators can be performed using conventional FE packages. The key ingredient is to express the FEM-to-IGA bridge, based on B{\'e}zier extraction, to transform the initial global spline interface into a FE one on which the local FE mesh can be constructed. This allows to resort to classic FE trace operators to implement the coupling. It results in a strategy that offers the opportunity to simply couple an isogeometric code with any robust FE code suitable for the modelling of complex local behaviors. The method also easily extends in case the users only have at their disposal FE codes. This is the situation that is considered for the numerical illustrations. More precisely, we only make use of the FE industrial software Code Aster to perform efficiently and accurately the hybrid global-IGA/local-FEM simulation of structures subjected locally to cracks, contact, friction and delamination.