From micro-CT TO A NURBS-based interface-enriched generalized finite element method

In the solid mechanic community, the finite element method is widely used to simulate the mechanical or thermal response of materials and structures. In most cases, conforming meshes are used to discretize the simulated geometry. However, this traditional method is not efficient in the analysis of complex microstructures, since the shape of most microstructures is quite irregular. Creating a conforming mesh with good element quality requires a tremendous amount of time and effort. Furthermore, conventional meshing techniques typically yield a large number of elements, thereby increasing the computational cost of the analysis. In this work, a structured non-conforming mesh generation process is proposed and demonstrated for the analysis of heterogeneous materials with complex microstructures using a NURBS-based Interface-enriched Generalized Finite Element Method (NIGFEM) developed in Prof. Geubelle’s group over the past few years. The NIGFEM relies on structured meshes that do not conform to the material interfaces, and uses NURBS (Non-Uniform Rational B-Spline)-based enrichments of the finite element approximation in the elements intersected by the material interfaces. These enrichments capture the key features of the solution along the material interfaces (e.g., C0 or C-1 continuity) and provide a very accurate description of the interface geometrical features. The proposed meshing method uses an octree structure to subdivide the computational domain iteratively. At each iteration, the topology relation between nodes, edges, and surfaces within the subdivided elements are calculated and classified into different types. A set of hierarchical mesh refinement rules are defined to continuously divide the element if they meet specific criteria. To accurately capture the material interfaces that falls inside the structured mesh grid, NURBS are used as basis functions to capture the boundary geometry shape. This hierarchical NURBS-based structured mesh can largely reduce the number of elements without sacrificing the accuracy of discretization. The method is particularly attractive for the computational analysis of real microstructures captured through X-ray tomography, as the micro-CT images are converted into a set of NURBS representations of the material interfaces using a set of steps also described in this thesis.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Aerospace Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2019

Author dc:creator

• Dang, Qi

Contributors dc:contributor

• Geubelle, Philippe H.

• NURBS
• NIGFEM
• Computational Geometry

Statement dc:rights

• Copyright 2019 Qi Dang

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/104980

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/104980