High-fidelity models in computational mechanics, applied in structural engineering and material research, are developed to be accurate, detailed and robust. These models enable new ways of research, such as developing highly-tailored microstructures in materials. To bypass excessive computational times needed to execute these models, Reduced Order Models (ROMs) can be implemented, which reduce the dimensionality of a problem by projecting it onto a reduced-order latent space. While projection-based ROM usually makes use of Proper Orthogonal Decomposition (POD) to obtain a linear basis needed for Galerkin projections, this thesis describes the development of a Variational Autoencoder-based (VAE) approach, which allows for learning a nonlinear latent space. POD-based and a VAE-based techniques are developed and applied for a case study of a simply supported beam, loaded into plasticity by a single movable point load. The ROM results are compared to the Full Order Model (FOM) results. Results are analysed and compared between the POD- and VAE-based techniques, and for different (hyper)parameters within the VAE-ROM results. The results show the VAE-based ROM outperforms POD-counterparts, especially in extrapolation and with the condition that a large enough dataset was used for training the VAE. Of the analysed parameters used for training the VAEs, the influence of dataset size and latent space dimensionality is observed to be significant, while the degree of regularization in the VAE and the activation function are of limited influence. Furthermore, this study shows that the validation loss of a VAE during training is not a good indicator for the performance of the VAE-based ROM, and suggests to consider the VAE-ROM error already during training of the VAE.

The use of Glass Fiber Reinforced Composites is increasing across the world in its use in booming industries such as wind energy, construction and electronics due to the advantages it offers. A replacement for glass fiber composites is being researched widely in Europe because of sustainability reasons. Bio-based composites such as Flax Fiber Reinforced Composites offer higher degradability and better mechanical properties for the same specific weight ratio as glass fiber composites. Although flax composites are an attractive alternative to traditional, petroleum-based composites, they have higher susceptibility to moisture degradation due to the presence of hygroscopic natural fibers. The moisture degradation of flax composites negatively affects its durability and strength performance.

In this thesis work, existing work employing the use of state of the art numerical techniques used to model hygrothermal aging of glass fiber composites is used to model moisture aging mechanisms seen in flax composites. A literature review is performed to identify the crucial degradation mechanisms affecting flax composites due to moisture aging. Interface debonding between phases is found to be a possible crucial damage mechanism due to moisture uptake. Presently, there is a lack of experimental studies on the effect of moisture degradation effect on the interface the significance of the same in the loading configuration of transverse flax-epoxy composites in literature. There is also presently a lack of numerical modelling efforts that describe the complex multi-physics and multi-scale nature of natural fibers and bio-based composites consistently and wholistically in literature. The goal of this thesis is to carry out exploratory work in the numerical modelling of swelling and tensile behaviour of transverse flax composites, based on existing modelling techniques for GFRP and supported by parameters from literature and experiments.

The swelling and transverse tensile behaviour of the flax fiber reinforced composites is modelled at the micro-scale. The state-of-the-art numerical framework used to model moisture degradation and quasi-static and fatigue behaviour in glass fiber composites is adapted for simplified micro-scale modelling using a Representational Volume Element (RVE). The sensitivity of the modelling parameters obtained from literature is studied to understand the effects of geometry variation and material degradation on the swelling strain in a linear-elastic micro-scale RVE analysis.

An experimental campaign is carried out to obtain relevant parameters for the numerical model that is missing from literature. The aim of the experimental campaign is also to characterize the moisture aging behaviour of transverse flax composites and its constituent phases. The material stiffness degradation of transverse flax composites and epoxy is studied with tensile tests before and after moisture uptake in the climate chamber. The swelling co-efficients of both transverse flax composites and epoxy are calculated. Microscopy imaging is used to qualitatively assess damage mechanisms due to moisture uptake and the fracture surface from tensile tests.

An elasto-plastic material for epoxy is calibrated with the tensile test experiments performed on the epoxy. A final iteration of the swelling numerical model based on the experimental benchmark is presented. The transverse tensile tests for composites from experiments are numerically simulated. The capabilities and the shortcoming of the final model are discussed for improvements in future work.

A novel surrogate model to approximate microscopic behaviour and accelerate concurrent multiscale finite element simulations is proposed. The study serves as a proof of concept, focusing exclusively on 2D, geometric non-linear lattice materials. Despite numerous successful implementations of surrogate modelling techniques in literature, challenges remain, mainly with the black-box nature of most of these models, suffering from lack of interpretability. To tackle these issues, this study reintroduces physics into the model through the use of beam theory in so-called Beam Neural Networks. These networks are tested against a benchmark feed-forward neural network in both interpolation and extrapolation. Although the findings do not satisfy the requirements for practical application, they do indicate that the introduction of beam theory to the model has improved the model's extrapolation ability, suggesting that the proposal has improved robustness and interpretability of the model. Given further optimization, there is promise of Beam Neural Networks to become an useful tool to accelerate concurrent multiscale modelling in the future.

The growing use of composite materials in engineering applications accelerated the demand for computational methods, such as multiscale modeling, to accurately predict their behavior. Combining different materials with target mechanical properties helps achieve optimal structural performance. Nevertheless, the complex nature of composite materials poses several challenges. Current multiscale methods, such as the $\text{FE}^2$ method, are hindered by a computational bottleneck, limiting their widespread industrial adoption. Most of the existing surrogate modeling techniques that address this bottleneck are limited to predicting homogeneous materials or require an extensive dataset. The application of surrogate models in the fracture mechanics field is largely unexplored, where the existing models are highly convoluted.

The goal of this thesis is to apply surrogate modeling to predict cohesive damage in the fracture mechanics field. It focuses on one of the existing techniques using Physically Recurrent Neural Networks (PRNN). The core idea behind PRNNs is to implement the exact material models from the micromodel into the material layer of the network. The PRNN, which incorporates an elastoplastic model in what is referred to as bulk material points has resulted in exceptional performance when predicting elastoplastic behavior in composite materials. The primary objective of this thesis is to extend the existing PRNN to predict the effect of debonding at the fiber-matrix interface while capturing path-dependent behavior and minimizing the size of the training dataset with excellent extrapolation ability.

The fundamental capabilities of the existing PRNN with bulk material points only are evaluated in the microscale cohesive damage framework, particularly when interface elements are implemented at the fiber-matrix interface of the micromodel. This initial step reveals the limitations of the existing architecture and it becomes apparent that all types of nonlinearities present in the micromodel must also be implemented in the network.

This thesis extends the PRNN by incorporating a Cohesive Zone Model (CZM) within the existing material layer. This new architecture introduces cohesive integration points with the CZM along with the bulk integration points. Through model selection, various configurations of bulk and cohesive points are explored, along with different training dataset types and sizes, to maximize predictive accuracy and extrapolation capabilities. It is observed that training with non-monotonic data is required for the network to learn both types of nonlinearities. The limitations of the network's prediction are noted, which are due to the fact that its architecture does not represent the stress homogenization step of the multiscale method. This realization highlights the importance of the layout of the PRNN.

Further study investigates new PRNN architectures to improve the physical representation of the micromodel. The networks are trained on a single curve to select the optimal architecture. The most promising option is discussed in detail, in which the history parameter of the cohesive points is input to the bulk points. The network is proven to provide accurate prediction on a small training dataset when tested on the training dataset. Constraints of the PRNN are discussed and further improvements are recommended to extend the modified PRNN to a larger dataset.

This research contributes to the field of surrogate modeling for composite materials by investigating the predictive capabilities of the PRNNs and exploring new architectures. The results provide a promising outlook for accurately predicting the complex behavior of composite materials, specifically in the context of cohesive microscale damage considering debonding at the fiber-matrix interface. The proposed PRNN has the potential to increase computational efficiency of multiscale modeling in engineering applications.

The increasing demand for sustainable energy, results in more wind turbines being built offshore. The blades of wind turbines consist of composites which makes them difficult to design. Because composites consist of a micro- and macro-structure of which their interplay determines the global behavior under loads. Therefore, traditional methods of analysis are often infeasible: full-scale experiments take too long and are too costly, small-scale experiments can not capture the interaction between the micro- and macro-structure, and analytical theories are often only tractable for simple cases.

$FE^2$ is one such method that can analyze the behavior of multi-scale materials, such as composites. It consists of a macro finite element model where the constitutive behavior of each integration point is obtained by homogenizing representative volume elements (RVE) that represent the microstructure. Although this method is capable of accurately predicting composites, the computational cost is high, as for each integration point another finite element model must be computed.

This process can be sped up by replacing the RVE with a surrogate that is more efficient to compute. Recently, Gaussian Process Regression (GPR), a probabilistic machine learning model, is used as a surrogate for the RVEs. It uses prior knowledge and observations of the RVE to make its predictions. It is based on Gaussian Processes, meaning that the predictions exhibit a multivariate Gaussian distribution which provides an uncertainty measure besides its prediction. This is useful in determining where new observations must be collected from the RVE.

To fully capture the RVE a lot of observations are needed from it. This is still a computational bottleneck for the surrogate as they are expensive to compute. The GPR model can be enhanced with observations from a low-fidelity model, for example, linear elastic, which is called GPR with multi-fidelity. The low-fidelity observations, inexpensive and inaccurate, enhance the prediction of the high-fidelity model, which uses high-fidelity observations that are expensive but accurate. This is shown to decrease the number of observations needed for the high-fidelity model. Thus, fewer observations need to be collected from the RVE. However, the correlation between the low- and high-fidelity is often assumed to be constant in these models. This presents a problem as the correlation in the case of surrogate modeling is often non-linear. The literature investigates several extensions of the GPR with multi-fidelity that assume a non-linear correlation, but these models become more complex and lose their simplicity as their predictions are not Gaussian anymore.

Instead, this thesis keeps the constant correlation assumption but improves the correlation inference by splitting the model. Splitting means that multiple independent GPR with multi-fidelity models are used in different regions. As splitting results in discontinuous predictions, the thesis also investigates two stitching methods to remove these discontinuities. The first, the constrained boundary (CB) method, constrains the predictive mean and predictive variance of to neighboring models to be equal at their respective boundaries. These constraints to the optimization procedure of the hyperparameters of the local GPR with multi-fidelity models. The second stitching method, the random variable mixture (RVM) uses a weighing procedure based on a mixture of experts approach. However, this method mixes the random variables instead of the probability density distributions. This creates a much simpler and analytically tractable method. For both of these stitching methods, only the high-fidelity uses the stitching procedure while the low-fidelity is split...

Various engineering applications rely on efficient, high performance materials to overcome design challenges. This high performance can be achieved by engineering micro-heterogenous materials also known as composites. Since the behavior of composites relies heavily on micro-scale interactions between different components, modeling macrostructures with fully-represented microscopic geometry is needed. Thus, the standard finite element modeling approach becomes impractical. Computational homogenization, also known as concurrent finite element analysis (FE$^2$), is a method that is employed to model materials with distinct multi-scaled structure. FE$^2$ employs the concept of embedding a representative volume element (RVE), at each integration point of the macro-scale problem and obtaining the macroscopic constitutive behavior through homogenization, thus bypassing the need to develop a macro-scale constitutive model. Although it succeeds in upscaling the microscopic material behavior accurately, this method comes with the major drawback of being computationally expensive due to its nested structure. Developing methods to bypass the aforementioned computational bottleneck of FE$^2$ is an ongoing research endeavor. Employing machine learning algorithms to create surrogate constitutive models for microscopic behavior is one possible approach. However, creating surrogate models is not an easy task. A thoroughly collected training set is needed for the surrogate model to be representative. Thus, investigation of surrogate model creation strategies with machine learning while trying to reduce the computational burden of this \textit{offline} training process is a compelling area of study. Gaussian Process Regression (GPR) is a probabilistic machine learning model. It can be utilized to create surrogate constitutive models effectively in the aforementioned context. Moreover, the computational burden of the training procedure can be decreased by extending the conventional GPR technique into a co-kriging regression with multi-fidelity information (multiGPR). This surrogate modeling strategy reduces the need to collect high-fidelity information by collecting information from a low-fidelity model thoroughly. Thus, enabling accurate training datasets to be created from a less representative, but computationally less taxing models. In this work, the multiGPR approach is used to construct accurate and efficient surrogates for the behavior of fiber-reinforced composite materials. Training data is obtained from selected RVE configurations that consist of linear-elastic fibers randomly embedded in a matrix that has pressure-dependent plasticity and used to train single and multi-fidelity GPR constitutive models. Both approaches are trained with various combinations of loading scenarios and their prediction capabilities are investigated to represent the training cases in addition to their prediction capabilities under unseen load cases.

Modern material systems with properly designed microstructures offer new avenues for engineering materials with advantageous mechanical properties and functionalities in various applications. With the increasing desire to design structures that have complex shapes or that are simply cheaper and more efficient, the demand for complex numerical simulations intensifies. Capturing the behaviour of composites relies on the interaction between the macroscopic and microscopic components, which can make direct numerical simulation too computationally expensive. Concurrent finite element analysis (FE²) links the different length scales in a multiscale approach. In each integration point of the macroscale a representative volume element (RVE) is embedded to address the microscopic heterogeneity. However, the need to evaluate the micromodel many times will come with the drawback of high computational costs. Various surrogate models have been proposed to accelerate computational models. One possible approach is employing machine learning techniques to substitute the evaluation of the RVE. Currently, artificial neural networks are being used in a wide variety of fields, due to their exceptional ability to recognize patterns. Although these techniques are able to construct models for complex input–output relations, their applications to mechanics of materials are still limited. These techniques are usually problem-dependent and may suffer from the danger of extrapolation beyond the original sampling space, e.g. different loading paths. This is not naturally resolved, mainly due to the loss of physics in the current machine learning models. The newly proposed Deep Material Network (DMN) by Liu et al. is a data-driven multiscale material modelling method that aims to resolve this issue by composing a network constructed from an assembly of mechanistic building blocks, where each building block resembles an analytical homogenization. Because the fitting parameters of this network are interpretable with physical meaning and because sampling the DMN still involves evaluation of classical constitutive relations, the loss of essential physics in minimized. The material network can effectively be trained using stochastic gradient descent with backpropagation, based on linear elastic data of an RVE. The extrapolation capabilities to unknown loading paths are investigated with a matrix-inclusion composite, with the focus on the accuracy of the model for loading-unloading scenarios, and an extension to the training process is proposed where the fidelity of a trained DMN is assessed by generating and grading a yield stress envelope. The results show that a well trained DMN is capable of predicting the response for unseen loading paths involving unloading exceptionally well. The complete learning and extrapolation procedures of the DMN establish a reliable data-driven framework for concurrent multiscale material modelling and design.

Numerical simulations have become an essential part of design in every field of engineering, and the boundaries of technology are pushed further out every year. In structural engineering, the desire to design structures that have complex shapes or that are simply cheaper and more efficient, has necessitated the use of complex numerical simulations. This necessity is further substantiated when taking into consideration structures such as wind turbines that are subjected to extreme environmental conditions. In many cases, however, such simulations are prohibitively expensive due to complex material behaviour or the many-query nature of design optimization. The lack of knowledge and understanding of the behaviour and failure mechanisms is compensated by adopting less complex designs and/or high safety factors, which leads to less efficient and more expensive designs. In recent years, methods to circumvent such high computational costs have been developed. Acceleration techniques such as model-order reduction (MOR) are now widely researched, and significant developments are being made to overcome the issues of prohibitively expensive high-fidelity models. This thesis uses Proper Orthogonal Decomposition (POD) to drastically reduce the degrees of freedom of a simply supported beam that is loaded in the downwards direction along the span. The result of the MOR process is a reduced-order model (ROM) that accurately approximates the behaviour of the full-order model (FOM). The ROM is constructed by determining a set of basis vectors that contain compressed information of representative full-order solutions collected in an \textit{offline} training phase. The goal in this thesis is so collect the information and construct the reduced basis as efficiently as possible while guaranteeing a given accuracy of the ROM. Two methods are presented to iteratively construct the reduced basis. The first one is the \textit{Surrogate Parameter Space} (SPS) method, where greedy sampling is performed on incrementally finer grids of points along the beam. Each individual grid is referred to as an SPS, and they are exhausted by selecting the load location that in each iteration will add the most new information to the ROM. The other method is the \textit{Gaussian Process Regression} (GPR). Greedy sampling using a Bayesian machine learning algorithm involving GPR is used to predict load locations along the beam that add the most new information to the ROM. A method to efficiently combine and compress information obtained in each iteration was also developed. The results showed that the SPS method is efficient to construct an accurate ROM for the beam model in this thesis, but the GPR managed to recognize that some areas in the span did not have to be sampled as much as others. This makes GPR the more promising method for other high-fidelity models when high accuracy is desired. The results also showed that both methods depend greatly on input parameters that define how much information is kept in each iteration, and for GPR an additional parameter that determines how much accurate the regression itself should be. In order to execute an efficient offline phase, these parameters must be chosen carefully, and it is recommended for future work to develop methods to adaptively choose them. It was also shown that the number of ROMs that have to be run as part of the greedy sampling is the bottleneck of efficiency for both methods. For high-fidelity models with higher-dimensional parameter spaces, this bottleneck necessitates the use of hyper-reduction techniques such as the Empirical Cubature Method (ECM) to reduce the computation time of the ROM itself. It is recommended that the methods investigated and the corresponding results in this thesis are used as a stepping stone to implement automatic and efficient sampling methods to other high-fidelity models.

Epoxy resins are increasingly used in critical structural components with widespread applications in the transportation, construction and energy industries. The wind energy sector is one of the fastest growing commercial markets for epoxy resins, meaning that the structural behaviour of epoxy resins is becoming a key area of research, especially regarding its application to wind turbines. Wind turbines, particularly those in off-shore installations, are subject to a wide range of environmental conditions, most notably large variations in humidity and temperature. Both moisture and increased temperatures have been observed to have a significant impact on the stiffness and strength of epoxy resins. These environment effects, coupled with complex time dependent mechanical behaviour, means that the accurate prediction of the structural performance of epoxy resins has not yet been fully described.

This thesis presents a multiphysics framework for the simulation of hygrothermal ageing in epoxy resins. The constitutive model formulated in this thesis consists of a non-linear viscoelastic and viscoplastic mechanical model, physically coupled with a Fourier heat conduction model and a Fickian diffusion model. Degradation based on a glass transition surface is implemented to describe the multi-state behaviour of epoxy resins. To justify the model assumptions, DMA and creep tests are performed on epoxy resin specimens and their temperature dependent mechanical behaviour is established. A number of numerical benchmark tests and case studies are performed using a finite element implementation of the numerical framework. It is shown that the multiphysics framework can capture the characteristic mechanical and hygrothermal ageing behaviour exhibited by epoxy resins. Recommendations are provided for further development of the numerical model and calibration of the material properties. In a secondary study, a mesh sensitivity analysis is performed on an existing viscoelasitc-viscoplastic-damage model and recommendations for an improved formulation are provided.