Mines and improvised explosive devices are the cause of many mortalities of vehicle occupants. Both experimental and numerical research in this field aims to improve the safety of military vehicles. TNO has advanced Finite Element (FE) models to simulate such events. The numerical research is done to better understand mine blasts. Another aim is to reduce experimental costs for Defence Material Organization (DMO). For full vehicle simulations the empirical Westine model is the basis of the in-house TNO mine blast model. The model consists of a triangular pressure pulse consistent with the Westine impulse which is calibrated using the a test rig developed by TNO and DMO. Experiments are compared with numerical results using the TNO mine blast model and the jump height, representative for total impulse transferred, shows scattered results for different vehicle tests. A possible cause can be accuracy of the current mine blast model. This research will study a new technique to validate mine blast models. When this new technique results in improvements in validation of mine blast models it can be used to study and improve the current TNO model. The aim of the new validation method is to calculate the interaction pressure of an plate excited by a mine blast loading. The obtained pressure can be compared with existing mine blast models for validation of the mine blast model. The methodology is based on solving the inverse problem which requires transient Digital Image Correlation (DIC) measurements of the deforming plate for the duration of the mine blast loading. Such measurements are done with the state of the art test setup from TNO and DMO. Several methods to solve the inverse problem will be studied. The proposed best way to solve the problem at hand is by solving the corresponding optimization problem using an iterative gradient of descent algorithm. The main difficulty in this approach will be the calculation of the gradient of the objective function. To do this the corresponding transient adjoint problem has to be solved. First an algorithm to solve the inverse problem is implemented for a linear Kirchhoff Love plate model to study the behaviour of the inverse problem for a relatively simple test case. For this algorithm the transient adjoint problem is derived. The forward and adjoint problem are numerically solved. The implementation is verified using the method of manufactured solutions and a convergence study. The algorithm is verified using three different bench mark test pressures. It was found that without any exception the displacement of the algorithm converged with great accuracy to the applied displacement. The corresponding pressure converged good for smooth pressure distributions. Non smooth pressure distributions representative for mine blast interaction pressure did not converge. This shows the non-uniqueness of the solution of the inverse problem. It was realized after these tests that the forward problem acts as a low pass filter for time and spatial oscillations of the pressure distribution. This implies that the inverse problem in non-unique and that noise in the displacement data will be amplified in the obtained pressure from the inverse solution. The total force and radial position as function of time, obtained after integration over the spatial domain, for a localized load are accurately captured back. These parameters could be useful to validate a mine blast model such that research was continued for a continuum model. A non-linear elastic material model is proposed to model the deforming plate assuming monotonically increas- ing strain. This model is used and calibrated against the Johnson-Cook plasticity model. One plate simulation excited by the TNO mine blast model verifies that the non-linear elastic and Johnson-Cook material model result in almost the same displacement. The adjoint problem for a general continuum with elastic material model is derived. The same optimization algorithm is implemented for the continuum model using the calibrated non-linear elastic material model. The forward and adjoint problem are solved using the author’s transient FEM implementation which is verified using commercial software. From the benchmark tests it was verified that the displacement converged quite well however less compared to the linear problem studied earlier. The corresponding pressures behaved similar. It was concluded that the total force and centroid position of a localized load are not always in agreement for the benchmark and solved pressure. This research shows that the limitations of the inverse problem shed light on the limitations in the validation methods employed by many researchers in the field.

In this thesis, a new data-driven finite element is developed, which is referred to as a neuromorphic element (designated as NmT2). Its goal is to reduce the computational expense of FEA models with- out compromising solution accuracy by embedding a neural network, trained on an element level. The neural network is developed such that the traditional trial-and-error approach to determin- ing its hyperparameters may be bypassed. This is achieved through a multi-objective optimization algorithm that builds networks with random configurations and uses Latin Hypercube sampling to test them on a fraction of the overall data repository. Once the algorithm reaches a state of diminish- ing returns over the development of multiple networks, the program is halted and the best perform- ing neural network is saved. The resultant network is then trained over the entire data repository consisting of over half a million datasets. The entire process of a self-designing neural network is called a neuromorphic engine. The neuromorphic engine is designed to determine the local nodal force vector of a truss mem- ber based on the structure’s geometry and axial nodal displacements. Axial tension and compres- sion are the two modes of loading that are considered and are pushed to the nonlinear regimes by including post-buckling and material plasticity. In addition, the user is provided with the option of including structural defects in the truss members. Once trained, the neuromorphic engine can be inserted within a user-element subroutine and deployed in ABAQUS. The neuromorphic element is essentially a truss element which includes the deformation ca- pabilities of beam elements. Unlike traditional FEA methods requiring multiple beam elements, a single NmT2 element can be used when meshing a truss member to model complex behaviour such as post-buckling deformation. To test the capabilities of the neuromorphic element, three case studies are designed as a proof of concept, comparing the performance of NmT2 elements against traditional FEA elements (T2D2 or B22). Overall, the NmT2 elements managed to accel- erate the computing time of an FEA model by up to 1,000%, while maintaining solution accuracy within 5%. These results affirm the potential of neural networks within active FEA simulations in the field of data-driven computational mechanics as a means to define complex nonlinear element formulations.

Designing and modeling compatibilized polymer blends require accurate interface model. In addition, it is possible that crazing occurs during failure of the interfaces leading to large deformation prior to complete failure and therefore must be accounted for by the interface model. A preliminary literature review showed that existing formulations for the large deformation account for the nonlinearity by adjusting the assumptions. For example, Van den Bosch et al. (2007) proposed redefining the local basis at each integration point. In contrast, Reinoso and Paggi (2014) argued that this did not account for geometric nonlinearity and proposed including the first derivative of rotation vector in the finite element equation. However, the mixed-mode responses of the models were not characterized and validated thoroughly. Therefore, we studied the response from standardized mixed-mode tests to compare the large displacement formulation with the commonly used small-displacement formulation of the cohesive zone model. The standardized tests used by Moreira et al. (2020) for characterizing the mixed-mode behavior of ductile interfaces inspired the tests used in this study. When implemented with the BK criteria, the mode partitioning method used by Moreira et al. (2020) results in a wider spread of the mean predicted mode ratio and the mean predicted fracture toughness. However, the corresponding mode ratio predictions are similar when the predicted fracture toughness is close to expected. Therefore, while the power-law is better for implementing the mode partitioning method, we can use the predictions from the mode partitioning method implemented with the power-law to find the BK parameter. Further, simulating the mixed-mode fracture tests with properties presented by Moreira et al. (2020) showed that bulk materials with high modulus or stiffness, such as carbon fiber reinforced plastics, do not undergo nonlinear deformation to require the large deformation formulation. However, for bulk materials with lower modulus or stiffness, the responses of the two formulations in question are different. Additionally, for a given load case, a cohesive zone with anisotropic fracture properties experiences a different mode ratio when implemented with the large displacement formulation than the small displacement formulation. Moreover, more significant influence of the stronger mode on the load case results in greater difference between the mode ratio experienced at the interface. Nevertheless, the large displacement formulation is also applicable for stronger mode-II interfaces. However, a further investigation involving physical experiments is required to compare the response of the two formulations to the behavior of real material systems.

The aerospace engineering industry is continuously striving for faster methods to solve and optimize engineering and research problems with a higher degree of accuracy. It is therefore relevant to investigate possibilities that are expected to accelerate computational speed, such as quantum computing. For this reason, the objective of this thesis is to investigate the feasibility of optimizing 2D determinate truss structures with a quantum algorithm run on a Gate-Based Quantum Computer (GBQC). The Quantum Approximate Optimization Algorithm (QAOA) is currently expected to be the most suitable quantum algorithm candidate for optimization problems, because of its simplicity and robustness. The most important take-away from this thesis is that it is possible to map a truss structure to QAOA format to optimize it on a GBQC. The program proves to be working on quantum virtual machines. However, it is currently not possible to obtain correct results when running on real quantum hardware due to noise.

Composite delamination represents one of the most critical failure mechanisms occurring in composite structures. In case complex structures are being designed, numerical methods need to be employed. One of the methods to numerically simulate delamination in a Finite Element environment is through the employment of the Cohesive Elements, which embed the theory constituting the Cohesive Zone Model. Nonetheless, the computational time required to assess delamination simulations by implementing the Cohesive Elements is restrictive, because the presence of a strong stress gradient at the crack tip imposes the adoption of a small-size mesh at the same location. In this context, a sensible improvement is deemed to be necessary, such as to promote these methodologies from an instrument used in academia to an effective solution. A novel type of Cohesive Element is here proposed, aiming to loosen the compelling requirement on the mesh size and, by extension, to reduce the computational time required to achieve numerical simulation of composite delamination. The High Oder CE has been validated through comparison with benchmark solutions of delamination processes occurring in Mode I, Mode II and Mixed Mode opening.

One of the novel methodologies in computational physics research is to use mimetic discretisation techniques. Among these, the mimetic spectral element method holds special promise as it not only has the benefits of mimetic methods but also the additional benefit of higher-order discretisations using higher polynomial degrees. These methods are aided by the development of algebraic dual polynomials, resulting in a sparser system for better computational efficiency. This combination was used to develop a formulation that would result in topological relations for equilibrium of forces as well as the symmetry of the stress tensor for linear elasticity as well as the first steps for Stokes flows in an orthogonal domain. As a result, this study was extended to look at how a modified formulation would behave for an unsteady linear elastic solid, with the intention to extend this method to Fluid-Structure Interaction cases. However, the choice of both primal and nodal basis functions makes it impossible to undertake this challenge, demanding a rethink in strategy towards looking at linear elastic solids when the physical domain is not orthogonal. With the use of bundle-valued forms to represent physical quantities, a new hybrid formulation is developed where the equivalent of the physical problem is computed on a reference domain, which is orthogonal and thus can utilise the spectral bases defined before. The physical problem is defined on a skewed domain, where partial transformation of components results in a formulation that can conserve linear momentum point-wise, but not conservation of angular momentum, although angular momentum does converge on refinement of polynomial degree and mesh parameters. A change in bases with partial transformation aiming to make angular momentum conservation topological is not fruitful, although the value of the error decreases in the process. The final attempt is through full transformation, which results in a formulation with an inherent error in the formulation, owing to erroneous assumptions.

The high specific strength and stiffness of composite materials have resulted in a widespread introduction of composite structures in the commercial aviation industry. Although composite materials offer the possibility to design lightweight structures, they also suffer from complex failure modes of which damage progression is badly understood. This thesis research is about Structural Health Monitoring (SHM) for composite aircraft structures. By permanently attaching a sensor network to a structure, maintenance activities can be improved by reducing costs and by optimizing maintenance scheduling. SHM could furthermore be used to increase the understanding of composite behavior. This research focuses on investigating an image reconstruction algorithm which can be used to visualize impact damage on a composite plate using piezoelectric (PZT) sensors. The relationship between the reconstructed images and damage growth is analyzed using different excitation frequencies and different formulations of a damage index while also assessing the influence of sensor failure on the algorithm. Moreover, an experimental campaign is performed during which composite plates are subjected to Quasi-Static Indentation (QSI) testing in order to create impact damage and monitored to obtain data.

The wide adoption of composite structures in the aerospace industry asks for reliable numerical methods to account for the effects of damage, among which delamination. Cohesive elements (CEs) are a versatile and physically representative way of reproducing delamination, but, using their standard form, at least 3 elements are required in the narrow cohesive zone, hindering the applicability in practical scenarios. This limitation is due to the inability of current models to capture the deformation of the delaminating substrates. The present work focuses on the implementation and testing of triangular thin plate substrate elements and compatible cohesive elements, which satisfy C1-continuity at their boundary. The improved regularity meets the continuity requirement coming from the Kirchhoff Plate Theory and the triangular shape allows for conformity to complex geometries. After verification of plate and cohesive element singularly, the overall model is validated for mode I delamination. Very accurate predictions of the limit load and crack propagation phase are found, using CEs as large as 11 times the cohesive zone.

Compressive failure mechanisms of fiber reinforced polymers represent a significant challenge when accurately modeling common industrial problems. This thesis aims to deliver a physically representative computational framework capable of simulating Open Hole Compression. A novel approach, the Floating Node Method is adopted for modeling discontinuities. Furthermore, a constitutive law for fiber kinking, incorporating the microscale bending stress of a fiber under the assumptions of the Euler-Bernoulli beam theory, is proposed. This meso-scale Continuum Damage Model poses three requirements for kinking onset: 1) local failure of the matrix in the kink band; 2) fibers fracture due to bending; 3) the longitudinal compressive stress is sufficiently large to satisfy the previous requirement when the kink plane shear stresses is smaller than the traverse shear strength of the ply. The model is validated against experiments of different sized [45/90/-45/0]s laminates. The predicted panel strengths match experiments by less than 8%.

This thesis presents a model that is able to predict fatigue crack growth and damage directionality in non-conventional Fibre Metal Laminates (FMLs) in CentreCracked Tension (CCT) specimens. Non-conventional FMLs encompass all FMLs other than standardised ones such as GLARE. FMLs can be made non-conventional by using multiple fibre types, any fibre orientation, multiple alloy types or thicknesses, or a combination thereof. These characteristics provide much more tailorability than standardised FMLs and thereby extend the applicability of FMLs to, for example, door corner reinforcements and wing structures. Contrary to standardised FMLs, the damage in non-conventional FMLs is non-uniform, necessitating the ability to compute the crack growth rate in the metal layers and the delamination at the metal-fibre interfaces separately.

Near free edges of fibre reinforced composite laminates modelled with homogeneous layers, the presence of high gradient interlaminar stresses has been found theoretically. Over a span of nearly 50 years, various methods, including numerical and analytical have been employed for analysis of the high gradient stresses which sometimes exist to an extent of a singularity. The analysis of such free edge stresses is found to be computationally expensive. However, since the interlaminar stresses have been found to play a role in initiating delamination in composite laminates, it becomes imperative to get an estimate of the interlaminar stresses near the free edge to be able to predict delamination initiation through suitable criteria. The abrupt material discontinuity between dissimilar layers in a homogeneously modelled laminate is believed to be a reason for the appearance of high gradients or singularities theoretically. The mitigation of material discontinuities at such interfaces could be done by modelling the laminate heterogeneously so that the interface is modelled by matrix material and hence, a discontinuity of material could be avoided. This idea of modelling the layers of laminate with explicit definition of fibre and matrix materials has inspired the thesis project with a view to investigate the difference in free edge stresses between the two models and to further draw a correlation between the stresses from the two models to predict delamination initiation. In previously published literature, the use of average interlaminar stresses up to a certain characteristic distance from the free edge through criterion for delamination initiation prediction is reported. Further it is also found that a single averaging distance can be proposed for a combination of laminates made of the same material. This encourages the idea of determination of averaging distance for a material and find its application on a laminate susceptible to delamination initiation. In the course of the current work, a correlation is proposed between the stresses of homogeneous and heterogeneous model [0/90]s cross-ply laminate of equivalent stiffness made of T300/934 material to determine the averaging distance and apply the determined averaging distance on [±25/90]s laminate to predict delamination initiation due to high gradient free edge stresses. An averaging distance of 0.125 mm is determined for [±25/90]s laminate made of T300/934 material to find average stresses for incorporation into criterion for delamination initiation. It is found that the determined averaging distance predicts delamination initiation successfully for experimentally reported delamination initiation strain range for the [±25/90]s laminate. Further, the convergence of average of high gradient interlaminar stress is found to be computationally more efficient than the convergence of high gradient interlaminar stress themselves. This indicates that use of average of high gradient interlaminar stresses is an efficient means for predicting free edge stress induced delamination initiation.

Type IV composite pressure vessels (CPVs) are used commercially for the gaseous storage of hydrogen in fuel cell electric vehicles (FCEVs). However, their economic implementation requires material optimization and a reliable prediction of the vessel strength. In this regard, their burst when loaded under internal pressure is impacted by the combined effect of the stacking sequence design and the variability of mechanical properties resulting from the manufacturing process. This work shows a framework for analysis that accounts for some of these manufacturing-induced characteristics in the mechanical response, namely the relation between the vessel stacking sequence, its final geometry, and the material properties. Furthermore, vessel burst pressures are alternatively estimated from the failure criteria evaluation in constitutively elastic analyses and the modeling of damage progression. Predictions are reasonably accurate when the collapse occurs in the cylinder (+2.2 %), although a more considerable discrepancy exists with experimental results when vessels fail in the dome transition region (+12.3 %).

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.

Quantum computing is a new form of computational technology, which can potentially be used to solve certain problems faster than is possible using classical computers. For this reason, there is an industry drive to develop early quantum computing applications. In this thesis, an overview of quantum computing technologies is provided, along with a practical discussion of the Traveling Salesman Problem, making use of the D-Wave quantum annealer. Subsequently, the main objective of the thesis can be investigated, which is to explore how quantum computing can be used to aid in solving structural optimization problems. Two methods are developed with which simple 2-dimensional truss systems can be optimized using the D-Wave quantum annealer. The methods aim to find the most lightweight choices for the truss cross-sectional areas while complying with material limit stress constraints. The first method directly casts such an optimization problem into a QUBO format. However, due to difficulties with formulating the stress constraint, this method was found to produce a trivial optimization problem. The second method attempts to symbolically solve a truss finite-element problem, using the resulting symbolic expressions to set up an optimization objective function. Although these objective functions are confirmed to work via classical brute-force analysis, the quantum annealer is shown to have difficulty finding the global optimum solution for truss systems with three or more elements. These results indicate that it is not currently beneficial to use quantum annealing for these structural optimization problems. Nevertheless, some improvements to the method for setting up the objective functions are suggested. The next generation of quantum annealers is expected to perform better for these practical applications, potentially becoming a useful tool in the engineering toolbox.

Fibre-reinforced composites have become increasingly attractive for many engineering applicationsin the last decades. A very interesting aspect of these materials is that their mechanical properties canbe tailored for optimum strength and stiffness by controlling the orientation of the fibers embeddedin the matrix material. Composites are characterized by high strength properties, strong corrosionresistance, improved damage tolerance and can lead to considerable weight and cost reduction whencompared to their metallic counterparts. However, accurate modelling of damage in composites is stillan active research topic, as their progressive failure involves the interaction of various intra- and inter-laminar damage mechanisms, which often lead to complex fracture paths. To this regard, the FloatingNode Method (FNM) proved to be particularly suited for the modelling of complex cracking scenarioswithin a finite element. However, its use has so far been limited to geometric linear analyses, wheredeformations and rotations are small enough and the conventional linear FEM formulation is used. Thisthesis work investigates the modelling of geometric non-linear fracture problems in composites usingthe Floating Node Method. A co-rotational approach is proposed as a convenient, conceptually simpleway to include geometric non-linear effects in problems characterized by large rotations but smalldeformations. This approach allows re-use of the conventional linear FEM formulation by separatingrigid body and purely deformational motions at the element level. The co-rotational procedure, firstimplemented and validated on a linear solid brick element, is subsequently applied to the FloatingNode (FN) element. Finally, a demonstration of the element’s potential in capturing geometric non-linear effects is offered, addressing the modelling of crush and impact loading on composite laminates.

This work develops a stand-alone Finite Element-based Unit Cell for the modelling of Fibre Reinforced Composites, capable of capturing 3D stress states and geometrical imperfections at the micro-scale. The project considers different beam and 3D elements for this purpose and draws comparisons between them based on computational efficiency, accuracy, and ease of implementation. A new setup is proposed to greatly reduce computational effort and facilitate user interaction and parametrisation by drawing from some of the most promising concepts identified from the present literature. The thesis presents such an FE model which can model a Multi-Fibre-matrix Unit Cell including codes for the generation and perturbation of the geometry, multi-scale meshing, solving, and post-processing. Some typical results for Micro-scale Unit Cells are presented to validate and demonstrate the capabilities of the model, and avenues for improvement and development of this concept are also detailed.