A NURBS-enhanced Discontinuity-Enriched Finite Element Method

Abstract

Generalized finite element methods have proved a great potential in the mesh-independent modeling of both weak and strong discontinuities, such as the ones encountered when treating materials with inclusions or cracks. By removing the constraint of a conforming mesh, more freedom is offered to modeling exact geometries by means of splines. However, very few studies have been published which combine Non-Uniform Rational B-Splines (NURBS) to interface-enriched methods, addressing uniquely weak discontinuities. Therefore, the aim of this thesis is to propose a NURBS-based enhancement to the Discontinuity-Enriched Finite Element Method (DE-FEM) in two dimensions and to discuss the potential of its application. The main advantage of this method is the possibility to study problems that present discontinuities with arbitrary smooth shapes, while maintaining exact geometries throughout the analysis: in this way, the equivalence between design and computational geometry is preserved. To this purpose, a suitable NURBS-based analysis technique is selected and implemented within the framework offered by the group's finite element library, Hybrida.
The capabilities of the NURBS-enhanced DE-FEM to solve several weakly discontinuous problems are assessed for composites of different complexities. Furthermore, a novel study is presented which extends this technique to the treatment of strong discontinuities, in the context of fracture mechanics. The accuracy, convergence properties and numerical efficiency of the proposed method are investigated, in particular in comparison with the standard DE-FEM. Based on these observations, further insights are provided into the convenience and the limitations of adopting NURBS enhancements within the DE-FEM formulation. Lastly, some recommendations about possible directions of improvement are provided.