Advanced computational methods for predicting the mechanical responses of engineering materials
File(s)
Author(s)
Liu, Tongrui
Type
Thesis
Abstract
Materials exhibit hierarchical structures, encompassing a diverse range of behaviors including elasticity, plasticity, and fracture, which present significant challenges in predicting their mechanical responses due to their complexity and multiscale nature. These challenges stem from the need to establish suitable variational frameworks, constitutive models, and computational techniques capable of conducting numerical simulations with both efficiency and accuracy. This thesis focuses on addressing the latter challenge by using advanced computational methods for predicting the mechanical behavior of engineering materials. The original contributions are twofold: (i) the development and refinement of multiscale model order reduction (MOR) techniques, and (ii) the advancement of numerical discretization methods and element technology.
This thesis introduces a multiscale MOR technique utilizing a three-stage data-driven self-consistent clustering analysis (SCA) for homogenization and full-field analysis of 3D anisotropic woven composite. A novel strain refinement step is proposed to reconstruct point-wise field variables from cluster-wise ones, requiring minimal modifications from the original two-stage SCA framework and FFT-based homogenization. Additionally, a discrete Green’s operator based on finite differences is introduced to alleviate numerical artifacts, arising in the reconstructed point-wise field variables. This approach significantly enhances the accuracy of local fields predictions compared to methods using a continuous Green's operator.
This thesis further extends the application of the virtual element method (VEM) to solve partial differential equations in computational fracture mechanics. Fracture phenomena, including brittle and dynamic fractures as well as hydrogen-assisted cracking, are analyzed using variational phase field modeling. The versatility of VEM allows efficient and accurate PDE solutions on arbitrary meshes, such as 2D polygonal and 3D polyhedral. Through simulations, validations and comparisons, the VEM outperforms the finite element method in both computational efficiency and memory usage, demonstrating its promise in tackling real-scale fracture mechanics problems.
This thesis introduces a multiscale MOR technique utilizing a three-stage data-driven self-consistent clustering analysis (SCA) for homogenization and full-field analysis of 3D anisotropic woven composite. A novel strain refinement step is proposed to reconstruct point-wise field variables from cluster-wise ones, requiring minimal modifications from the original two-stage SCA framework and FFT-based homogenization. Additionally, a discrete Green’s operator based on finite differences is introduced to alleviate numerical artifacts, arising in the reconstructed point-wise field variables. This approach significantly enhances the accuracy of local fields predictions compared to methods using a continuous Green's operator.
This thesis further extends the application of the virtual element method (VEM) to solve partial differential equations in computational fracture mechanics. Fracture phenomena, including brittle and dynamic fractures as well as hydrogen-assisted cracking, are analyzed using variational phase field modeling. The versatility of VEM allows efficient and accurate PDE solutions on arbitrary meshes, such as 2D polygonal and 3D polyhedral. Through simulations, validations and comparisons, the VEM outperforms the finite element method in both computational efficiency and memory usage, demonstrating its promise in tackling real-scale fracture mechanics problems.
Version
Open Access
Date Issued
2024-03
Date Awarded
2024-11
Copyright Statement
Creative Commons Attribution NonCommercial Licence
License URL
Advisor
Aliabadi, Mohammad
Publisher Department
Department of Aeronautics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)