Heterogeneous materials are vital for both the modern engineer and inquisitive scientist alike. They make up a vital material class that can either form inevitably as a result of material processing (such as crystallization in metals) or can be intentionally designed for to gain desirable properties (such as anisotropy in composites). As such, due to their prevalence and applicability to various engineering problems, predicting their behavior has become a topic of great interest in the solid mechanics community over the last few decades.

One particularly pressing challenge is performing fast mechanical simulations along multiple length scales in heterogeneous materials. To this end, the reduced order method known as Self-Consistent Clustering Analysis (SCA) has been proposed as an effective means of striking a balance between accuracy and efficiency. Underpinning this is SCA's ability to decompose a domain into clusters in a preliminary offline stage (learning), efficiently reducing the problem's degrees of freedom. It has been shown to be remarkably accurate in predicting plasticity without significantly degrading accuracy compared to other methods, such as the finite element method. However, the offline stage requires a quantity known as the Cluster Interaction Tensor (CIT) to be computed, whose computational complexity scales quadratically with the number of clusters, thus causing a bottleneck in the method. Additionally, the CIT is recomputed during the online stage (prediction) in the recently proposed extension called adaptive Self-consistent Clustering Analysis (ASCA), which further stresses the need to speed up their computation.

To address this limitation, a data-driven surrogate model is proposed to compute the CIT efficiently. The behavior of the local CIT components is first analyzed, from which it is concluded that a surrogate model shall be developed to predict upper off-diagonal terms. This decision is made due to the bi-modal nature of certain components in the tensor and the quadratic scaling behavior of off-diagonal terms versus the linear scaling of diagonal ones. Following that, a sensitivity study shows how various magnitudes of noise affect the homogenized response's accuracy and convergence performance. Furthermore, it is shown that the solution accuracy and convergence behavior are degraded when the number of clusters is increased. With a proper understanding of the CIT's behavior and its function within SCA, the surrogate can be created.

The surrogate's feasibility is first shown using the ResNet-18 architecture, a CNN model derived from computer vision. It is demonstrated that ResNet-18 can make accurate predictions for a range of different microstructural parameters. This includes the number of clusters and samples in the dataset's distribution and out of distribution. Composite RVEs are used as out-of-distribution samples to test the robustness of the surrogate to realistic inputs. An attempt is made to improve the model's performance by training it on an unbalanced dataset, and although it improves the overall CIT prediction in specific regimes, the resulting stress-strain generalizability is degraded. Subsequently, a lighter version of ResNet-18, known as ResNet-lite, is tested and shown to give faster predictions than the baseline method. This, however, comes at a cost to the accuracy of the solution.

Additionally, deemed as a critical aspect of the study, the efficient generation of a large representative training dataset is discussed. A novel method for generating clustered microstructures efficiently using gradient noise is introduced. By leveraging datasets derived using this method, the surrogate can learn the fundamental interactions needed to make accurate predictions on realistic, out-of-distribution samples. The need for a large dataset is further emphasized using a dataset size sensitivity study.

This thesis project focuses on the evaluation of the Extended Finite Element Model (XFEM) for modelling skin-stringer separation in thermoplastic composite stiffened panels. The study uses test results from a reference study in the literature on a PEKK-FC carbon composite panel with three stringers joined to the skin using a short-fibre reinforced butt joint. The modelling strategy was developed using Double Cantilever Beam (DCB) specimens. The XFEM-based panel models were then developed using two different damage initiation criteria: Quadratic Stress Criterion (QUADS) and Maximum Principal Stress Criterion (MAXPS). These models were compared with the Virtual Crack Closure Technique (VCCT) model from the reference study. The project also addresses the challenges posed by the crack tip impingement problem in the XFEM-based model with MAXPS and tests different strategies to overcome it. A proof of concept is provided for using the UDMGINI subroutine to address these challenges, setting the stage for future studies and algorithm development.

Fibre-reinforced composites are increasingly used in aircraft structures as an alternative to traditional metallic components due to their lighter weight and tailorable mechanical properties. However, certifying these materials for critical aircraft components still relies heavily on extensive mechanical testing, which is both resource-intensive and expensive. This reliance highlights the need for virtual testing frameworks that can accurately predict trans-laminar failure behaviour in composite laminates and assess large damage capabilities to create damage-tolerant designs critical for the certification process. Addressing this need, this thesis introduces a novel global-local modelling approach for analyzing trans-laminar damage growth in notched composite laminates. This approach aims to facilitate large-scale structural analysis with reduced computational demands, making it suitable for comprehensive damage assessment in composite aircraft structures.

This research investigates progressive failure analysis in notched composite laminates, with a particular focus on simulating stable damage growth and arrest within the transition region of tapered laminates. A multi-fidelity modelling approach was adopted using flat laminates as a baseline for evaluating damage growth behaviour in the transition regions. Consistent ply stack orientations in both tapered and flat laminates allow for direct comparisons of their distinct failure behaviours. The methodology includes a low-fidelity model that utilizes cohesive elements to simulate self-similar crack growth initiating from notch tips. For more detailed predictions, a high-fidelity model incorporating a discrete ply-by-ply approach with cohesive interactions was used to capture both intra-laminar and inter-laminar damage mechanisms. In this high-fidelity approach, two intralaminar damage models are compared: a user-defined continuum damage model (VUMAT) and a built-in Hashin damage model available in ABAQUS. The VUMAT model applies specific softening laws and element sizes for each failure mode to ensure accurate energy dissipation, while the Hashin model serves as a simpler built-in alternative.

The results show that, despite simplifications, low-fidelity models provide reasonable estimates of failure loads and stiffness in the elastic region, aligning closely with high-fidelity models and existing experimental data. The high-fidelity model effectively captures complex damage modes, with the VUMAT model outperforming the Hashin model in accuracy. The global-local approach proves reliable, offering results comparable to a globally refined meshing approach. It shows potential for use in analyzing larger, computationally demanding structures. Overall, the findings also highlight the importance of fibre-aligned meshing and precise cohesive zone modelling in predicting damage initiation and progression in notched composite laminates, providing insights for designing damage-tolerant composite structures.

The Koiter methodology is a reduced-order model that can predict the initial post-buckling characteristics of structures. Incorporating the Koiter approach within finite element simulations resulted in challenges. These included mesh sensitive initial post-buckling coefficients, computationally expensive high-order derivatives, and phenomena such as locking, which led to unrealistic behaviour of structures. The displacement-based Koiter methodology is introduced to overcome these issues due to the clear connection between the theory and the implementation. The objective of this thesis is to enhance this approach by introducing imperfections, which enables the analysis of initial post-buckling characteristics of imperfect structures. The preliminary results show that the inclusion of imperfections was successful for a plate with linear pre-buckling, but more verification is required. If the inclusion is verified to be successful the current displacement-based approach can be extended to cylinders and used in sensitivity studies to establish guidelines for an imperfection-insensitive cylinder.

Gaussian process regression (GPR), a potent non-parametric data modeling tool, has gained attention but is hindered by its high com- putational load. State-of-the-art low-rank approximations like struc- tured kernel interpolation (SKI)-based methods offer efficiency, yet lack a strategy for determining the number of grid points, a pivotal factor impacting accuracy and efficiency. In this thesis, we tackle this challenge.
We explore existing low-rank approximations that facilitates the computation, dissecting their strengths and limitations, particularly SKI-based methods. Subsequently, we introduce a novel approxima- tion framework, MKISSGP, which dynamically adjusts grid points us- ing a new hyperparameter of the model: density, according to changes in the kernel hyperparameters in each training iteration.
MKISSGP exhibited consistent error levels in the reconstruction of the kernel matrix, irrespective of changes in hyperparameters. This robust performance forms the bedrock for achieving accurate approx- imations of kernel matrix-related terms. When employing our rec- ommended density value (i.e., 2.7), MKISSGP achieved a comparable level of precision to that of precise GPR, while requiring only 52% of the time compared to the current state-of-the-art method.

In-space manufacturing (ISM) is an upcoming technology in the space industry. Unprecedented applications can be achieved by producing objects in space, as opposed to bringing objects to space that were produced on Earth. For solar arrays, this means that extremely large array sizes can be achieved, because with ISM the array size is not limited by the maximum payload volume of the launch vehicle. Additionally, the array can be lighter, because the structure does not need to withstand the harsh launch conditions. Additive manufacturing, wire based directed energy deposition in particular, was identified as the best in space manufacturing method for solar array structures. This thesis aims to find the best system to achieve this and investigate the limitations and challenges to applying metal additive manufacturing in space. A top-level system design is proposed and thermal, power and mechanical limitations are explored. This technology is still at a low TRL level and a lot of development is needed. Therefore, the most important points for future research are provided.

Composite materials have multiple failure modes. Most of these failure modes are dedicated to the different layers, e.g., delamination. Unfortunately, these damages can occur internally, causing it to be invisible to the naked eye. A better understanding of how this happens and what causes it, is required to ensure safety. Therefore, for this research, delamination is the most interesting failure mode. Previous researches have primarily been focusing on quasi-statically loaded UD specimen. However, since a layup in a structural part of an aircraft consists of multiple layers with different fibre orientations, it is not guaranteed that a delamination will occur between two 0º plies. Furthermore, an aircraft is designed to be in service for decades and consequently is loaded thousands of times. A structure which is subjected to a cyclic loading will behave differently than one to a quasi-static loading. Hence, in aviation industries, tests with cyclically loaded specimens are more relevant. This research project focused on fatigue delamination crack growth of multi-directional interfaces. In order to generate mode I delamination, DCB specimens were manufactured and tested. Fatigue experiments were conducted to see the influence of the interface angle as well as that of the orientation of the interface angle. To cover most relevant delamination planes, tests with the following interface were conducted: 0º//0º, 45º//45º, 90º//90º, 0º//45º, 0º//90º, 45º//−45º and 30º//−60º. Furthermore, the crack fronts were monitored by means of C-scans and the fracture surfaces were examined. It was found that for all different interface orientations, fibres bridged. This was demonstrated with an increased delamination resistance for a longer crack. The nature of these bridging fibres, however, differed. Fibre bridging regarding to nesting showed a less significant increase in fracture resistance than bridging fibres due to oscillatory crack propagation behaviour. Furthermore, the different interfaces showed various crack fronts. The crack front tends to propagate towards the direction of the fibres of either of the fibre orientations around the interface.