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

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 Bézier 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.

Immersed boundary-conformal isogeometric LaTIn method for multiple non-linear interfaces

“…Indeed, multivariate B-splines and NURBS come with a rigid tensor-product structure, therefore precluding the simple modeling of local behaviors. More advanced splines, such as locally refined splines [22], hierarchical splines [33,23], T-splines and hierarchical T-splines [65,24], have emerged to offer local mesh refinement, but the integration of arbitrary local models (e.g., inclusions) within spline patches (e.g., matrix) still remains an issue [63,10,69,68,45]. From a general point of view, mainly two approaches can be followed.…”