Modeling of Fiber bond fracture using X-FEM and Element Removal

Abstract

The aim of this thesis is to investigate the mechanical response of paperboard in the out-of-plane direction by incorporating its microstructural characteristics, with a particular focus on fiber-fiber interactions and fracture mechanisms. These features are implemented into models of varying complexity to evaluate their influence on material behavior.
Two fracture modeling techniques, the Extended Finite Element Method (XFEM) and Element Removal, are implemented and assessed through finite element simulations. The models are developed using both idealized fiber geometries and realistic structures derived from X-ray tomography. Simulations are performed in two and three dimensions to evaluate each method’s capability to capture fiber separation and delamination.
The results indicate that XFEM enables smooth crack propagation in structured geometries but encounters limitations in complex fiber networks. In contrast, Element Removal demonstrates greater robustness and adaptability to unstructured geometries, although it is sensitive to mesh resolution. The study also emphasizes the importance of accurately identifying fiber bonds, as they significantly affect the out-of-plane strength. A segmentation approach using Ilastik is explored for this purpose, though its limitations suggest the need for more advanced machine learning techniques.
This work contributes to the development of more accurate and efficient fiber-based models for paperboard, providing insights that support the design of lighter and more sustainable packaging solutions.

Popular Abstract

What really happens when paper is folded, torn, or deformed? In the pursuit of more sustainable packaging, this thesis explores how paper fibers interact and separate to better simulate the mechanical behavior of paperboard.
Paperboard is one of the most widely used packaging materials, valued for its recyclability and low environmental impact. However, to further reduce its environmental footprint, it is essential to optimize its structural design. This means making it stronger while using less material. Achieving this requires accurate simulations of how paperboard behaves under mechanical stress, particularly in its weakest direction: through the thickness (ZD).
Traditional models treat paperboard as a homogeneous, anisotropic material. These models work well for in-plane behavior (MD and CD directions), but they fail to capture the complex microstructural processes that occur when fibers separate in the out-of-plane direction. This thesis presents a more detailed approach, modeling individual fibers based on X-ray tomography scans of real paperboard.
Two fracture modeling techniques were implemented and compared: the Extended Finite Element Method (XFEM) and Element Removal. Both methods were tested in 2D and 3D, on both simple and complex fiber structures. The results show that Element Removal is more robust and better suited for realistic, irregular geometries. XFEM, on the other hand, is limited to simpler, controlled cases due to restrictions in how cracks can initiate and propagate.
A key challenge was identifying the locations of fiber bonds, which are critical zones where fibers are joined and where fractures typically begin. To address this, an AI-based image analysis tool (Ilastik) was used to classify regions in the tomography data. While promising, the method was not sufficiently accurate, leading to some fibers remaining incorrectly connected in the simulations.
The study concludes that it is possible to model the out-of-plane mechanical behavior of paperboard while preserving its in-plane strength. However, further improvements are needed in identifying fiber bonds, potentially through more advanced machine learning techniques. Such models could pave the way for lighter, stronger, and more sustainable packaging materials.

• author: Thylén, Nils
• supervisor: Eric Borgqvist; Matti Ristinmaa
• organization: Solid Mechanics; Department of Construction Sciences
• course: FHLM01 20251
• year: 2025
• type: H3 - Professional qualifications (4 Years - )
• subject: Technology and Engineering
• keywords: Paperboard Mechanics, Fiber Bond Fracture, Extended Finite Element Method (XFEM), Element Removal, Microstructural Modeling, Paperboard Fiber Modeling, X-ray Tomography, Finite Element Simulation, Out-of-Plane Strength, Sustainable Packaging Design
• publication/series: TFHF-5000
• report number: TFHF-5268
• language: English
• id: 9200147
• date added to LUP: 2025-07-03 11:39:53
• date last changed: 2025-07-03 11:39:53