Fiber-reinforced polymer (FRP) composites are used in various engineering applications due to their many advantageous properties, but predicting failure remains challenging due to complex failure behavior. The Computational Mechanics group at TU Delft uses an inter-element cohesive zone method, referred to as the Ortiz model, to analyze microscale crack propagation. Although effective for modeling complex failure processes, the method suffers from severe mesh dependency, restricting large-scale simulations. This research implements and investigates the shifted fracture method (SFM) as an alternative to reduce mesh dependency while maintaining computational complexity. The SFM modifies key aspects of the Ortiz model, including an area correction term, crack propagation algorithm, and shifted weak form equations and cohesive zone conditions using Taylor expansions. Three versions of the SFM were tested: (1) full SFM implementation, (2) reduced SFM with only the area correction and crack propagation algorithm, and (3) an extended Ortiz model with only the area correction term. Numerical simulations show that the reduced SFM is robust, mesh-independent, and efficient in basic fracture tests. The area correction term proved critical in reducing mesh dependency. The extended Ortiz model, on the other hand, showed less accurate results in predicting cracks, despite the additions of the area correction term. Furthermore, the maximum principal tensile stress criterion for determining the crack direction was unsuitable for mixed-mode scenarios, resulting in inaccurate paths. Although the reduced SFM shows promising results, it requires further development to handle complex fracture scenarios like FRP composites. Features such as crack initiation, merging, and termination were implemented and showed potential but require further validation. This research concludes that while the reduced SFM is effective for basic testing, further refinements are needed for broader application to FRP composites.

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.

Military vehicles are often subjected to dynamic loads from mines. To protect these vehicles, steel plating underneath the vehicle is applied. However, these steel plates can be quite heavy, resulting in a slower vehicle. Composite laminates, however, are much lighter and also prove to be capable of protecting these vehicles from mines.
During an explosion, the energy released from the blast will be absorbed by the composite material. This often results in the delamination of plies within the laminate. Due to the delamination, bending loads will be taken over by membrane loads. This is proven advantageous for composite materials as they are stronger in membrane loading.
Unfortunately, modelling sizeable composite structures with a Direct Numerical Simulation (DNS) requires the use of a lot of elements. This, in turn, results in long computational times, particularly for non-linear analyses. Multiscale modelling is a possible solution to this problem.
This study explores the method of Computational Homogenisation for delamination in composite laminates as an alternative to 3D DNS modelling. Two-dimensional Shell-Interface-Shell elements (SIFS elements) are introduced on the macroscale. These double-layered shell elements consist of two stacked Mindlin-Reissner shell elements with an interface element connecting the two shells. Each integration point of a SIFS element is linked to a mesoscopic 3D coupled Representative Volume Element (cRVE), which is also split into two shells with an interface in between. By applying linear and periodic boundary conditions that incorporate the macroscopic strains on the cRVE, mesoscopic stresses are determined, leading to macroscopic stresses and the macroscopic stiffness matrix.
The proposed multiscale framework is validated by a set of load cases with different ply configurations. The results are then compared to those of a 3D DNS. The multiscale framework performs reasonably well; however, it is not without its limitations. Firstly, the cRVE exhibits width dependence, requiring the implementation of a sufficiently narrow cRVE for accurate results. Additionally, SIFS elements may lack kinematic consistency with 3D solid elements, constraining certain deformations and resulting in overly stiff responses for SIFS analyses. The proposed multiscale framework might not perform as accurately as the 3D DNS in specific load cases, one of which is explored in this work.
Returning to the original goal of this work for the multiscale model, certain extensions still need to be implemented to design composite laminates for blast protection. Implementation of the arc-length method will provide insight into snapback behaviour that could occur during loading. Next, the macroscale and mesoscale models need to be adapted for multiple delaminations over the height of a laminate. Furthermore, the implementation of dynamic loading is a necessary step, as blast loads induce strong dynamic behaviour. Finally, the integration of Artificial Intelligence / Machine Learning into the framework could improve the model by further reducing computational time.

Structuresmade of fiber-reinforced polymer (FRP) composites are usually considered lightweight. On account of this feature, polymeric composites find their application in many engineering disciplines, where the expected service lifetimemay extend to decades. The advent of thermoplastics has brought about cost-effective processing and the possibility to recycle structural components, among other features. However, the viscous nature of the polymer matrix poses a challenge to the straightforward application of FRP composites in load-bearing situations: the material response is a function of time and temperature. In addition, structural components may be subjected to long-term cyclic loading, that may lead to failure irrespective of the viscous nature of the material constituents. Hence, for an optimal application of (thermoplastic) FRP composites in load-bearing situations, it is necessary to understand, and eventually to predict their long-termperformance....

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.

Concrete is widely used in civil engineering and despite its long history, accurate prediction of the hardening process, particularly in partially restrained conditions, remains a challenge. During the hardening of partially restrained concrete, residual stresses occur due to restrained deformations caused by factors such as heating/cooling and shrinkage of the concrete. Accurately predicting the development of these residual stresses during restrained hardening is critical for proper design calculations, as cracking must be controlled by reinforcement. However, predicting the development of these design stresses is complex and depends on a number of processes and parameters, including temperature development, development of mechanical properties and the degree of restraint. These stresses also decrease with time due to creep and relaxation, which further complicates predictions, especially when dealing with restrained concrete combined with shrinkage.

In addition, hardening concrete will eventually be subjected to external loads, resulting in additional stresses that may require additional reinforcement. However, when it is difficult to accurately predict the development of design stresses, approximations must be made. These approximations may either take full account of the stresses from both hardening and external loading, or reduce the residual stresses by some factor. Such factors may be based on design codes or rough estimates. Consequently, these approximations can lead to either over- or underestimation of the reinforcement required in the design, mainly due to a lack of understanding of the actual design stresses. Therefore, the research question investigated in this thesis is as follows:

What is the effect of applying time-dependent finite element analysis, including the combination of hardening processes and external loads, on improving the prediction of the development of design stresses for partially restrained concrete?

The research starts with a comprehensive literature review covering the stress development during hardening of restrained concrete, the current calculation methods and models and a validation experiment. The validation experiment, a Temperature-Stress Testing Machine (TSTM) found in literature, is modelled and the analysis results are compared with the experimental results to validate the accuracy of modelling the hardening of partially restrained concrete. A method is developed to accurately predict the hardening of restrained concrete using a combination of transient heat transfer analysis and structural non-linear analysis. This non-linear analysis uses a combination of time and load steps to apply the required degree of restraint. The finite element analysis, using measured thermal and material properties from the literature, shows good agreement with the TSTM experimental results.

In order to verify the accuracy of commonly used material models, the Eurocode and fib Model Code material models within DIANA FEA are compared with the results of the TSTM experiment. However, it was found that these material models have inaccuracies due to the use of large step sizes for the Kelvin chains that define the creep and Young’s modulus developments. Therefore, a viscoelastic material model based on the fib Model Code was developed and found to be more accurate. This material model was validated against the TSTM experiment and hand calculations. Although differences were found in the development of design stresses between the experimental results and the prescribed standards, these were mainly due to the difference in autogenous shrinkage and coefficient of thermal expansion.

Using the knowledge gained from the modelling of the TSTM experiment and the validated viscoelastic material model, a case study of the railway underpass in Leiden is performed. The chosen modelling approach is a time-dependent non-linear finite element analysis that includes all construction phases, hardening processes, and external loads within a 3D model of solid 3D elements. The model excludes concrete cracking, reinforcement and prestressing of the deck to limit complexity. This calculation method is expected to provide a more detailed insight into the development of design stresses and ensures high calculation accuracy and completeness compared to other methods. The use of a full 3D model was necessary to accurately model the temperature development in the hardening concrete, which has a significant effect on the design stresses…

Probabilistic numerics methods are a novel approach to quantifying the approximation errors in numerical computations as probabilistic uncertainties. A recent method that was developed is the Bayesian Finite Element Method, which aims to determine the discretization errors along a coarse mesh probabilistically. This work analyzes the use of priors in this method. It is shown that the priors in the right-hand side or forcing term of the partial differential equation are superior to applying them directly in the solution. It is demonstrated that the maximum log-likelihood is not an appropriate estimator of hyperparameters, and as solutions, hyperparameters are optimized using objective functions to capture the discretization error with the posterior deviation. The advantages of non-stationary priors are studied in order to have standard deviations that show the error along the mesh. Additionally, this work examines how the optimal hyperparameters change for mesh refinements and different arrangements of elements in the same problem. Finally, the research delves into determining the approximate number of samples necessary for ensembling covariance matrices and obtaining similar results.

This thesis introduces the Discontinuity-Enriched Finite Element Method (DE-FEM) for the modeling of dynamic multiple crack growth problems including branching and merging, as an alternative to eXtended/Generalized Finite Element Method (X/GFEM). DE-FEM differs from X/GFEM by placing the enriched degrees of freedom (DOFs) directly along the discontinuities, and the enrichment functions vanish at standard mesh nodes. This approach allows DE-FEM to preserve the physical meaning of standard mesh nodes and avoid the issues associated with blending elements. Moreover, by adding enrichment directly along the discontinuities, DE-FEM is more straightforward in computer implementation. These properties of DE-FEM facilitate its modeling of complex crack configurations such as the dynamic crack propagation problems with multiple cracks. Here we propose a scheme for dynamic multiple crack propagation using DE-FEM, which covers crack initiation, propagation, and interaction. Numerical examples are provided to validate the effectiveness of DE-FEM in capturing crack patterns that are similar to those observed in other studies. Meanwhile, the reasons for the numerical instabilities observed during crack propagation and methods to mitigate them are also discussed.

Offshore wind energy production is increasing rapidly and optimising the design of support structures has the potential to significantly reduce steel and costs. Jacket structures are commonly selected for deeper waters, and the design of these structures is primarily influenced by the fatigue performance of the tubular joints. The fatigue resistance of these joints can typically be evaluated using different stress assessment methods, each associated with a corresponding S-N curve. While the Hot Spot Stress (HSS) approach is commonly used for design purposes, the Effective Notch Stress (ENS) approach offers higher accuracy by taking into account the stress concentration originating from the weld profile. Consequently, the ENS approach has the potential to provide less conservative fatigue life estimations, leading to the reduction of steel and costs. However, the application to and research of the ENS approach for tubular joints is limited. Therefore, the objective of this thesis is to investigate the application of the ENS approach on a tubular joint. The research was divided into three parts, including an investigation on the required FE mesh, a study on sub-modeling of the ENS approach and a comparative analysis on the fatigue life predictions between the HSS and ENS approaches.

The FE mesh required for the ENS approach was evaluated on a cruciform joint according to the DNV-RP-C203 validation methodology and the Stress Concentration Factors (SCFs) values obtained for different mesh configurations were compared. Two mesh variants were developed, and different element sizes in the notch were evaluated. The results show that with a maximum element size in the notch equal to 0.39 mm, according to DNV, unacceptable SCF errors are obtained of -4% and 4%. Furthermore, with a maximum notch element size of 0.25 mm, according to IIW, SCF errors of -0.3% and -2.2% were obtained, indicating that accurate results can be obtained but are not guaranteed. Additionally, the accuracy of the mesh was found to be primarily influenced by the number of nodes surrounding the notch, rather than the size of the elements in the notch.

The accuracy of sub-modeling for the ENS approach on a tubular T-joint was evaluated by varying global modeling choices and sub-model sizes. The accuracy was measured by comparing sub-modeling stress results against those from a global T-joint FE model with the ENS approach applied. The results show that a global model composed of 3D elements with a weld profile that corresponds to the sub-model is recommended. Simplifying the global model by excluding the weld profile or using 2D elements has been found to provide inconsistent and inaccurate results. Moreover, a sub-model of the weld area with a size as small as 1.67 degrees of the brace radial angle has been found to provide consistent results. Thereby, sub-modeling reduces the required mesh size by a factor of 15, compared to the global modeling approach. Additionally, a rather surprising maximum principal stress error of approximately -6% was observed as a result of sub-modeling for all varied load types and sub-model sizes.

A comparative study between the HSS and the ENS approach was conducted for the computed fatigues of a tubular T-joint. Various FE models were composed for the T-joint subjected to different load cases, and equivalent SCFs were computed by introducing a correction factor based on the S-N curves of both approaches. The results show that the ENS approach provides a lower computed fatigue life over the HSS approach when applied to a tubular joint. This discrepancy is attributed to the FAT225 S-N curve, used for the ENS approach, which is not tailored for tubular joints but for welded straight plates. For the HSS approach, the choice of element type (2D vs 3D) and the inclusion of a weld profile have a significant effect on the stress distribution and the resulting fatigue life prediction. It was found that a model consisting of 3D elements with the inclusion of a weld profile yields the longest computed fatigue life for a tubular joint.

To conclude, the application of the ENS approach was investigated for a tubular joint, by evaluating the mesh sensitivity, examining the accuracy of sub-modeling and comparing the computed fatigue lives with those from the HSS approach. Further research is recommended to improve the computational efficiency of the ENS mesh and to achieve a deeper understanding of the -6% error found by sub-modeling. Additionally, the development of an S-N curve tailored for tubular joints is suggested to improve the accuracy of the ENS approach for this type of joint.

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...

According to experiments the fatigue damage behaviour of fibre reinforced polymers (FRP) experiences a load sequence effect. In this report the ability of the cohesive fatigue damage model of Dávila (2020) to simulate the behaviour after a load amplitude change is investigated. For this a double cantilever beam (DCB) with fictitious material properties is loaded in mode I. Two element layers with each its own cohesive law are used to take into account the different behaviour of the epoxy and the bridging fibres in the wake of the crack. The calculated crack growth rate is compared to the experiments done by Jensen et al. (2021), since the conditions of the simulations are most similar to that of their experiments.
When the base and bridge layer only differ in their quasi-static cohesive law no load sequence effect is seen, since the conditions at the start of the second load block are the same as for the constant amplitude test at the same crack length. By allowing fatigue damage to accumulate only in the base layer and the bridge layer to only experience quasi-static loading, a history effect is seen. However, the high-to-low transition does not give the same transition behaviour as seen in experiments. In addition, the results of the constant amplitude tests are unrealistic.
When the fatigue damage accumulation of the bridge layer is faster than that of the base layer, a transition behaviour comparable, although less profound, to that of experiments is seen. This difference in fatigue damage accumulation is achieved by adjusting the coefficients of the fatigue damage rate function to the values corresponding to another R-ratio. This result may indicate a possible underlying mechanism for the transition behaviour of FRP.

Bayesian system identification has been extensively adopted in Structural Health Monitoring as a way to probabilistically infer unobservable parameters of the physical model of a structure using measurement data. Combining the Bayesian approach with distributed optic fibre sensors can potentially improve the accuracy and reduce the uncertainty in parameter estimation problems, given the large amount of quasi-continuous data produced by this sensing technology; however, its computational cost could be prohibitively high when using conventional methods since Bayesian inference typically involves a large number of samples, each of which entails a physical model evaluation.
The focus of this work is on performing Bayesian system identification for real-world civil engineering structures within an acceptable running time, while using optic fibre measurements with a high spatial resolution. The proposed methodology employs a cheap-to-compute Gaussian process (GP) surrogate that replaces the main bottleneck of the Bayesian workflow for these type of problems: the evaluation of the log-likelihood. The GP surrogate is actively built by sequentially selecting new training points in areas that are expected to highly contribute to the accuracy of the posterior distribution. Once convergence is achieved, the surrogate is used to obtain the parameter estimates via Markov chain Monte Carlo (MCMC) sampling. Additionally, in order to accelerate the Bayesian workflow, cloud-based parallelization is used to perform multiple finite element analyses simultaneously.
A first synthetic case with an inexpensive frame model is used to test the methodology for problems with two and five probabilistic parameters. An encouraging outcome is obtained with the actively learned GP surrogate, with posterior distributions very close to the full MCMC procedure while requiring a number of physical model evaluations orders of magnitude lower. 
After that, a second case study consisting of an existing reinforced concrete bridge with real measurements and a relatively expensive finite element model is investigated. A subset of discrete strain and translation sensors are used to perform an initial parameter estimation that almost exactly resembles the results from previous research on this bridge by Rózsás, et al. (2022), successfully validating the proposed procedure. Then, another parameter estimation is computed using available high resolution optic fibre measurements, after which is shown that the optic fibre provides the best improvements in model predictive capacity among all sensor groups, confirming its potential when combined with Bayesian system identification.
The results of the case studies indicate that the approach presented in this thesis has the capacity to greatly reduce the wall-clock time of Bayesian parameter estimation for real world civil engineering structures with optic fibre measurements, while maintaining a high degree of accuracy. Nevertheless, additional research is required for cases where the statistical parameters governing the measurement and model uncertainty are inferred along with the physical parameters.

To climb up the circular economy hierarchy and meet the goals of the European Green policy in the construction sector, steel profiles may be reused instead of recycled, which is currently the most common practice. An overarching digital database to efficiently match supply and demand of reclaimed structural elements will stimulate their application. To efficiently use the limited availability of reclaimed steel elements in a new structural system, the design process requires a different approach: form following availability. This thesis presents an algorithm to generate truss bridge designs using only reclaimed steel, optimising the material usage in relation to the function and avoiding cut-off waste. The algorithm is inspired by the growth method, a truss topology optimisation method in which truss designs are grown without the need to fit elements into an initial design or grid of possible positions, like the commonly used ground structure method. The growth method is a more intuitive starting point for stock-constrained design, as by attaching available reclaimed elements to each other, a geometry can be generated which effectively follows from availability. The algorithm has been scripted in Python within Grasshopper, resulting in a user-friendly parametric design process. By defining the required width and span of a truss bridge and providing a stock of reclaimed elements, a solution cloud is generated of locally optimal truss bridge designs in terms of capacity utilisation and which comply to Eurocode provisions and constraints regarding the manufacturability of connections. From this solution cloud, an optimal design can be selected with given objectives, e.g. the design with the lowest environmental impact. A comparison shows that the developed growth method, using reclaimed steel elements, can lead to a steel truss with 17% less embodied carbon than a truss design whereby reclaimed elements are fit in afterwards, and 63% less embodied carbon than a traditionally designed new steel truss.

In the past decade, the application of Neural Networks (NNs) has received increasing interest due to the growth in computing power. In the field of computational mechanics, this has led to numerous publications presenting surrogate models to assist or replace conventional simulation methods. A subset of these networks, referred to as Graph Neural Networks (GNNs) impose the graph-like structure of many physical problems as a relational inductive bias. Several time-stepper implementations of these GNNs are reported to be able to simulate the dynamic behaviour of various physical objects. Within this work, it is investigated whether such GNN-based surrogate models can be applied to simulate the dynamic behaviour of lattice structures.
Upon inference of such a GNN surrogate model, the computational time required for studying lattice behaviour could be considerably reduced, thus advancing research into lattice structures as metamaterials. In addition, many large-scale structures also form a composition of beams, which could be modelled with a similar GNN.
To this end the following research question was defined: ”To what extent can GNNs be applied to simulate the dynamic behaviour of lattice structures using time-stepper methods?”. To answer this question, several GNN architectures were constructed and subsequently analyzed.

In this research, it was found that the complexity of lattice structures could not be modelled in such a way as to obtain reliable, generalisable and stable behaviour, using a time-stepper method with an architecture similar to that of Pfaff et al., 2020. It was found that due to the existence of three physically different coupled Degrees of Freedom (DOF) per node the behaviour was too complex to learn for the proposed surrogate.
At the time of writing, there is no publication presenting an effective surrogate model to simulate the dynamic behaviour of a Timoshenko beam using time-stepper methods. It is concluded that the need to capture both bending and shear behaviour using a Timoshenko beam formulation is the bottleneck for successfully modelling lattice structures.

The University of Twente performed experimental uniaxial compression tests of Poly(ether-ether-ketone) (PEEK) and the TU Delft made a comparison with a numerical model; the viscoplastic Eindhoven Glassy Polymer (EGP) model. A higher strain-rate dependency and a higher yield stress at lower temperatures are observed in the experimental results. It is of importance to correctly model the stress-strain behaviour of PEEK for future research in long term behaviour of fibre reinforced PEEK by adapting the EGP model to account for these differences. The viscosity of the EGP model is based on the Ree-Eyring equation in which the three Ree-Eyring parameters (activation volume, activation energy and initial viscosities) are constants within the EGP model. It is observed that all three Ree-Eyring parameters are not constant over the strain when the original Ree-Eyring equation is fitted to the experimental data. Thus, non-constant Ree-Eyring parameters should be included in the EGP model. Evolving all three Ree-Eyring parameters leads to accurate stress-strain results, except for the pre-yield regime. The EGP model does not behave as stiff as the experiment in this region. Thus, a higher stiffness is included by evolving the shear moduli over the pre-yield regime. The evolution of the Ree-Eyring parameters is expressed by a $\tanh()$ function and quadratic function, while the evolution of the shear moduli is only expressed by a $\tanh()$ function. The evolution based on the $\tanh()$ function mostly influences the behaviour at small strains and the evolution based on the quadratic function mostly influences the behaviour at large strains. The evolution of the Ree-Eyring parameters at large strains leads to the insertion of viscous strain hardening in the EGP model. The viscous strain hardening qualitatively describes the Bauschinger effect for a cyclic loading case. The Bauschinger effect can be explained as the change of material behaviour when stresses are present. What occurs when the loading direction reverses within a cyclic loading case. An invariant function that is proportional to the strain determines the strain dependency of the evolution of the Ree-Eyring parameters and shear moduli. This invariant function is prevented from reducing for the evolution based on the $\tanh()$ function when the loading direction is reversed but does reduce for the evolution based on the quadratic function to correctly model cyclic loading. Furthermore, the linearization of the stiffness tensor is updated for the changes to the EGP model and a part of the stiffness tensor which was omitted in the original implementation is added.

Including the evolution of the Ree-Eyring parameters and shear moduli with the mentioned characteristics in the EGP model makes the EGP model correspond very well with the experimental results for all investigated temperatures and strain-rates.

The increase in road traffic intensity and loading capacity of a truck over the last decades causes fatigue problems in existing bridges built in the 1960s and 1970s. For steel bridges, this means that the deck structure does not meet the current demands. A solution would be to replace these existing deck structures with Glas Fibre-Reinforced Polymer (GFRP) sandwich webcore deck panels. However, the ministry of infrastructure in the Netherlands has voiced its concern about the fatigue performance and displacements of these deck panels under the high traffic load and intensity. Furthermore, the knowledge about the fatigue performance of GFRP deck panels, applied in the main road network, is still limited. At the time of writing this report, the technical committee, CEN/TC 250 (responsible for developing structural eurocodes), establishes a technical design specification for Fibre-Reinforced Polymer (FRP) structures. This technical specification requires full-scale fatigue testing due to the complex failure modes that can occur. General fatigue damage summation methods like Palmgren-
Miner [30, 41] are not allowed by this technical specification. This report discusses the development of Virtual Fatigue Stiffness Simulation (ViFaSS), a numerical non-linear fatigue stiffness reduction model that can predict the fatigue performance of in-plane stress dominated Glass Fibre-Reinforced Polymer components, with a wide range of lay-up compositions, based on existing knowledge and experiments, including the damage development under multi-axial stress states and stress redistribution. The damage development includes damage accumulation dependency on damage history and damage development dependency on the load type, e.g. Tension-Tension (T-T) or Compression-Compression (C-C). With the low utilisation of the material strength in civil engineering applications, the research is limited to the stiffness degradation of the material. The numerical model is coupled with the Finite Element (FE) software SOFiSTiK where the component is modelled with shell finite elements. The fatigue material response is characterised on a unidirectional ply level based on principal ply directions and based on experimental results from the Optidat program [36]. The coupon response predicted by ViFaSS for constant amplitude T-T and bending fatigue loading was in reasonable agreement with experimental results. For future work it is recommended to extended the model with the ability to use non-linear material behaviour and to include the strength degradation caused by fatigue.

A common choice for multiscale modeling of the mechanical response of composites is to use periodic boundary conditions (BCs) on square representative volume elements (RVEs). However, these periodic BCs over-constrain the response when strain localization takes place in bands that are not compatible with the imposed periodic constraints. Previously developed improvements are based on aligning the periodic BCs with an evolving localization band. This is either done by applying a rotation to the periodicity frame or by imposing the periodic BCs in a weak sense and then applying a shift to the function that couples points. However, with matrix-inclusion RVEs, this change of the periodicity frame may cause a mis-alignment of inclusions that cross opposing edges, resulting in an artificial reinforcement along the RVE edge, which limits the number of supported localization angles and fails to provide a transversely isotropic response. It is the objective of this thesis to develop a micromodel with transversely isotropic response for strain localization problems. It is shown that circular RVEs with straightforward application of periodic BCs provide a response which is independent of the load orientation but fail to predict full softening behavior. This is due to over-constraining when cracks reach the boundary. Therefore, a modification to the periodic BCs on a circular RVE is proposed, which allows for cracks to cross the edges. This is achieved by adding an unknown jump to the periodic constraint equations, which does not affect the response before localization. Moreover, a parameter that depends on the RVE size is used to make sure that the kinematics are consistent between scales in an average sense. The performance of the formulation is tested with a series of simulations where macroscopic strain rates are imposed under varying angles. Additionally, a circular heterogeneous RVE with periodic material is presented where inclusions are allowed to cross the edge. It is demonstrated that the circular RVE with the modified periodic BCs successfully predicts an isotropic response with full softening. In the simulations that were performed, a priori knowledge of the localization angle was used. However, the framework can be extended such that the BCs adapt to support an orientation of a localization band that is detected during the simulations.

Railway sleepers form an important part of a classic track structure. Sleepers exists in their current form for a long time. The transition from wood to concrete sleeper has been made, but wood is still used and present in many track sections. As creosoted wooden sleepers are not allowed to be installed on the tracks anymore the search for durable and sustainable alternatives has started. One promising type is a hybrid sleeper constructed from recycled plastic (polyethylene) with steel reinforcement. The main part of this thesis is to create a finite element model that is capable of describing hybrid plastic sleepers. The ultimate goal is to be able to use this model to assist in sleeper acceptation. Current rules, regulations and high availability requirements make it difficult to test sleepers in the track under live loading conditions. Not many infrastructure managers are eager to install not already proven technology in their tracks. The general parameters of the model were investigated and combined with some specific finite element modelling methods. Those formed the starting point of the design. Important design methods were the parametrisation of the model as much as possible to allow assessment of slightly different models. Secondly a mapped mesh was preferred above a free mesh to improve on accuracy. Also the amount of detail is kept high to be able to fully investigate the sleepers, e.g. to investigate the reinforcement bond. The ANSYS APDL-language is used to program the FEM parametrically. This resulted in a comprehensive finite element model of one a whole sleeper. Fully modelled with base plate (without detailed fastening), rail pad and rail section. Every part is constructed out of solids and meshed with a mapped mesh including the reinforcement. Two model methods, a general circular and a more element wise optimal octagonal model, were used to generate the reinforcement. All single sleeper models can be connected to form a piece of track with several possibilities in altering the foundation parameters per sleeper or allowing for different types of sleepers inside the track. Concluding all generated finite element analysis (FEA) results could not impress enough to recommend the usage of FEA for sleeper acceptation. Especially with new, very non-linear behaving materials and a very dynamic loads, the effort involved in creating a validated finite element model (FEM) would be too great and the results not usable enough. For some parts a FEM can be beneficial, during design for example. Other simpler models than the one constructed here could be helpful if directly based on test results. But at least at this point in time, with relatively unknown materials, the direct testing of sleepers under loading conditions laboratory and in the track itself with close monitoring are regarded much more informative.

A new approach to applying the finite difference method for solving the shell model problem. By solving the general shell differential equations (Sanders-Koiter equations) with first-order finite-difference approximation only, a finite difference algorithm called shell code has been developed.

To this end, a 1200-line Python program has been built. In the process many versions of shell code were considered, including
1) Two programming languages (Python and R)
2) Three interpolations for approximating gradients (three-point and five-point with two end slopes)
3) Determined and over-determined systems of equations (square and rectangular matrices)
4) Four solvers for the systems of equations

The final version of shell code has the following features; five-point interpolation with zero end slope, rectangular matrix, solver lm.fit.sparse (R). Approximately 80% of the shell code results match the finite element results with a deviation less than 5%. It has been proved that the selected version of shell code can solve shell model problems by solving Sanders-Koiter equations with finite difference method. Many previously assumed important factor for affecting shell code results, like number of nodes and interpolation methods, were actually less significant. However, the most vital difference in results occurred under different computation methods. Maybe under further research of developing mathematic tools, finite difference method could be a more promising and practical method for solving model problems.