Flared folding wing tips (FFWTs) improve aerodynamic efficiency but present aeroelastic challenges. This study develops an FFWT aeroelastic model using: (i) multibody constraint formulation for kinematics, (ii) non-linear static analysis for equilibrium under aerodynamic loading, and (iii) linearised dynamic analysis for time-dependent behaviour.

The multibody formulation defines the wing tip’s motion through hinge constraints, while the non-linear static analysis examines the effects of flare angles on equilibrium fold angles and reaction forces. The wing root bending moment (WRBM) decreases by 17% compared to a locked configuration but increases by 23.4% as the flare angle grows from 0o to 20o. For flare angles below 10o, the solver characteristics and initial equilibrium positions at lower velocities can lead to numerical issues such as zero-division errors and poorly conditioned matrices.

The linearised dynamic model, based on the static solution, is evaluated with different configurations: a locked hinge, a free hinge, and a locked-free hinge. Smaller flare angles allow higher fold angles but introduce minor anomalies in the inner wing tip’s response, while larger flare angles improve numerical stability yet cause more persistent oscillations. The locked-free case assesses hinge release during a gust encounter, where releasing the hinge at peak gust intensity leads to larger persistent oscillations. Artificial numerical diffusion and structural damping effectively reduce numerical noise in reaction moments, revealing underlying trends and improving stability.

This thesis introduces a new computational methodology to solve partial differential equations within cracked domains, focusing on coupling in-crack physics with the adjacent environment. The crack is represented discretely, allowing to describe explicitly the crack opening, which is a key parameter in the description of the in-crack physics. The governing equations are projected onto the tangential direction of the crack to obtain a hybrid formulation of the weak form. Because the fracture is reduced to a lower dimensional domain, this methodology leads to a discontinuity in the primal solution field. Therefore, a discontinuous Galerkin approach is employed in discretizing the equations, yielding results that align well with the analytical model across various configurations and increasing the model’s possibilities. The results obtained for the electric governing equations show potential for developing a model incorporating mechanical and chemical aspects, enabling a fully coupled model for dendrite propagation in solid-state batteries.

Components of novel propulsion systems in electric aviation contain materials defined as critical by the European Union: electric motors contain Rare Earth Elements neodymium and dysprosium, and state-of-the-art batteries materials like lithium and cobalt. Such critical raw materials have high supply risks but are crucial for the economy. The demand of all these materials is forecasted to increase drastically in the coming years, which means that the rate of supply might no longer suffice to fill the demand. Circular economy principles have been suggested as a solution. Materials recovered from end-of-life components can secure supplies and reduce the environmental impact of products.

In this research, the implementation of circular economy approaches to address critical raw material demand in electric aviation is studied. According to the developed models, the material demand is negligible in comparison to other industries until 2050. However, as the electric aircraft technologies are still in development, there is a lot of uncertainty around the demand.

Beyond 2050, components will start reaching their end-of-life stage. In this case, a circular strategy considered feasible for electric motors is remanufacturing. After the Rare Earth Element magnets in the motors become obsolete, they can be recycled to recover the critical raw materials. Both hydrogen decrepitation and a combination of hydro- and pyrometallurgical processes can be used to regain materials for magnets in aviation or other applications.

Although circular economy strategies will not be able to significantly reduce the primary material demand in electric aviation by 2050, these can still lower the environmental impacts from production. Additionally, well-established circular practices could address the material demand more substantially in the future, after 2050, if electric technologies are more widely adopted then.

The aim of this Design Synthesis Exercise was to design a floating large-scale wind farm of 1 GW in deep water using an Airborne Wind Energy System (AWES) that is cost-competitive, largely recyclable and uses less material than conventional wind turbines. By exploring the project foundation, carrying out an iterative single-system design process, and delving into the farm layout and management, this project assesses the feasibility of this novel concept. This report proposes an initial design with the resources currently available to the team while highlighting the next steps that need to be taken in order to pursue further design iterations, prototyping, and testing of this concept. This initial design, the tool developed to carry out the sizing, and a detailed reflection on the limitations of this design process and concept could be stated as the main contribution of this project to the field of airborne wind energy.

The safety of a commercial aircraft is a factor to consider from the early stages of its design to guarantee that this one's structure can protect the occupants inside in a low-speed crash. In an aircraft's primary structure such as a fuselage, where the occupants and cargo should be protected, the design regulations imposed by the EASA have been applied for decades to conventional metallic designs. These designs had aluminum as the main constituent for being a lightweight material. Nevertheless, this project improves a component's design from a fully thermoplastic fuselage. While two commercial aircraft (A350, and B787) have already implemented some composite parts in their design to aim for sustainable and lightweight components, thermosets were the composites used in primary structures mainly. Composite materials do not present the plasticity metals do, which means that the regulations from EASA can no longer apply in the A350 and B787 hybrid designs. With the introduction of composite materials in these aircraft, organizations like the FAA and EASA had to write some new guidelines for these aircraft structures. These enable the protection of the passengers and cargo from the loads exerted on the aircraft during a survivable crash. Therefore, the new regulations are the ones taken into account for this thesis project, since these can be applied to similar composite structural designs, such as the fully thermoplastic fuselage section, whose numerical model is inherited from the Clean Sky STUNNING project.

What is wanted for the fuselage section's crashworthiness is for its structure to absorb as much energy as possible from the crash. All while minimizing the peaks of force that this one experiences. That way, the loads that arrive at the cabin of the aircraft are reduced and the structure becomes safer for a low-speed crash of under 30 ft/s (about 10 m/s), meaning that the passengers inside have a higher chance of survival and it is less probable they suffer from severe injuries. That is the aim of this project, focusing only on the structure's behavior caused by the changes in the fuselage struts.

The numerical analyses performed in LS-DYNA increase single components’ structural complexity until optimizing the layup of a tube to improve its crashworthiness behavior. It is after this optimization that the component is introduced as a strut in the STUNNING fuselage section. To further improve its global crushing in low-speed crushing conditions, the struts (or energy absorbers) keep the square geometry cross-section from the tube exercise, as well as the optimized layup. However, these are changed in size to improve the fuselage’s crushing behavior with little to no increase in mass. This study considers a fuselage section that neglects the passengers’ mass, their cargo, and the upper part of the fuselage airframe in the section's model. Considering only the cargo mass for six passengers on the model causes a change in the fuselage’s final design crashworthiness, which proves that a more representative crushing conditions setup should be considered in future studies to better predict the structure’s crushing behavior numerically.

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.

Launch vehicle structures are commonly composed of cylindrical and conical shells, which are inherently sensitive to buckling. The axial compression experienced during launch can consequently be a sizing load case, so it is important to understand the axial buckling behavior of these shells. Experimental testing is an essential part of studying this phenomenon because manufacturing imperfections can cause large discrepancies between theory and reality. In addition, conical shells have been researched less frequently than cylindrical shells, such that their behavior is less well understood. Experimental testing of launch vehicle structures is difficult and expensive due to their large size, hence it is preferred to test reduced-scale shells, representative of the full-scale ones. In this thesis, a scaling methodology is developed which allows designing representative reduced-scale conical shells for full-scale composite conical shells buckling in axial compression. The conical shells are assumed to have a symmetric, balanced layup with negligible flexural anisotropy. The scaling methodology is developed using the nondimensional governing equations, obtained through Nemeth's procedure, which allows to directly use the coefficients of the equations as scaling parameters. It also provides a framework to not only compare the buckling load of the shells of different sizes, but also the displacement upon buckling, the deformation shape, and the radial displacement. The methodology is set up such that the reduced-scale design parameters are determined sequentially. The buckling behavior of the two shells is compared using a semi-analytical approach, linear eigenvalue, and implicit dynamic finite element analyses. The eigenmode imperfection sensitivity is also evaluated. The methodology is successfully applied to isotropic, cross-ply, quasi-isotropic, and sandwich conical shells. The prediction accuracy is mainly affected by not being able to simultaneously satisfy all scaling parameters, by non-negligible flexural anisotropy and transverse shear, and by differences in imperfection sensitivity between the full-scale and reduced-scale shells. In any case, accurate results are obtained for the considered shells. The radial displacement is most difficult to predict, which is attributed to the membrane prebuckling assumption and neglecting the presence of imperfections. Finally, it is observed that larger eigenmode imperfections affect the accuracy, but they do not cause the methodology to fail. For future work, it is recommended to validate the methodology through experimental testing.

The demand for composites is rising in industries for instance, in aircraft and automobile engines. In these applications, composites encounter high thermal gradients service condition, and composites exhibit material discontinuous gradient field. It is essential to study how high thermal gradients and material discontinuities influence on the composites’ behavior. Composites are usually modelled with the standard finite element method (FEM), but mesh refinement is required near material interfaces and regions with high thermal gradients to obtain accurate solutions. Enriched finite element procedures are able to solve this issue. The Generalized Finite Element Method (GFEM) can approximate high thermal gradients by adding enriched degrees of freedom (DOFs) to original mesh nodes. In addition, the Interface-enriched Generalized Finite Element Method (IGFEM) can cope with material discontinuities by creating nodes at the intersection between discontinuities and edges of elements in the mesh. Yet, GFEM and IGFEM have their own limitations when implemented: while GFEM needs extra enrichments to resolve the material interfaces in composites, and IGFEM requires mesh refinement if thermal gradients are too high in cut elements. Then we can combine the best of both methods.

In this thesis, a new Generalized Finite Element Method with spread and discrete enrichments (GFEM^sd) is developed to simulate heat transfer problems with high thermal gradients in composites. By combining GFEM and IGFEM formulations, GFEM^sd is capable of dealing with high thermal gradients and material discontinuities simultaneously in an effective manner. We show that GFEM^sd obtains accurate results when compared with analytical solutions in numerical examples. A convergence study illustrates that fewer DOFs are required in GFEM^sd for achieving the same level of accuracy comparable to that of IGFEM. We then apply GFEM^sd to simulate a twill pattern composite and derive effective heat conductivity values. Lastly, based on the composite’s minimum effective heat conductivity, fiber shape optimization is conducted to obtain the best design for a fixed fiber volume fraction.

Origami structures have become of increasing importance in the field of engineering, due to their lightweight, compact and stiff properties. To design these structures, progress is being made into incorporating origami modeling in the Finite Element Method. To implement an arbitrarily located fold on an existing mesh, either re-meshing or enriched finite elements are required. In fold pattern optimisation of origami structures, re-meshing each intermediate design would not be time efficient, whereas enriched elements may be very time efficient. In this thesis foldable Kirchhoff-Love plate elements are derived using a mixed/hybrid element formulation in combination with an enriched Finite Element formulation. The use of a mixed/hybrid element formulation enables great simplification of the enrichment functions, since the discontinuous rotation field is evaluated at the boundaries of the enriched plate elements, instead of the element domain. Six foldable plate elements are derived and tested for accuracy and stability. The stability is improved by either local condensation of the enriched elements or by applying a precondition matrix.

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.

A novel continuum damage mechanics model for 2D woven fabrics has been developed and implemented in a VUMAT subroutine for Abaqus/Explicit. The model takes into account the shear non-linearity, the toughening mechanisms associated to tensile failure, and the influence of shear stresses in the initiation and propagation of tensile damage.

The non-linear shear behavior is reproduced by means of a Ramberg-Osgood equation. Permanent deformation, and the degradation of the secant shear modulus associated to the accumulation of matrix damage have been coupled to the formulation of this unidimensional plasticity law. The physical reference required to define completely the shear constitutive response proposed can be obtained from the experimental tensile test of ±45 off-axis coupons. Failure initiation in tension is identified using Hashin's quadratic failure criterion, which accounts for the interaction of shear stresses in the promotion of tensile failure. A bilinear softening relation was selected to represent the combination of fibre breakage and toughening mechanisms characteristic of the intralaminar tensile fracture of these materials. Effort was placed on the development of a procedure for calibrating the softening relation associated to this failure mode. Specifically, this work addresses the applicability of linking the definition of a bilinear tensile damage law in homogenized continuum damage mechanics models for woven composites to the shape of a crack growth resistance curve measured with compact tension tests.

The constitutive model was validated including it in a set of finite element models of unnotched and open hole coupons with different multistacking sequences, under quasi-static tensile loading conditions, and comparing the results obtained by the simulation of the coupons against an experimental benchmark. A good correlation was achieved between the ultimate strength predicted with finite element analysis and the experimental data.

Striving to improve structural efficiency the aerospace industry shows increasing interest in variable-stiffness composite laminates. Advanced fiber placement is a hybrid manufacturing technique that offers the flexibility of both filament winding and automated tape laying. With the development of this novel system curved tows can be placed and a spatially variable-stiffness laminate can be designed with continuous changing stiffness from point to point.

The increased design freedom to tailor a structure by in-plane stiffness variation leads to a challenging design optimization problem. A multi-step framework is developed by the aerospace structures and materials department to optimize variable-stiffness laminates. Variable-stiffness laminate design allows for sophisticated designs. Based on this premise it is investigated how such design could improve the structural performance of an engine thrust frame, a structural application that transfers the thrust loads from the rocket engine to the rest of the launch system. The engine thrust frame is subject to cryogenic thermal loads, something not incorporated in the available optimization framework. The goal of this work is to add thermal loads to the laminate analysis routine and to adjust the optimization routine to incorporate thermal influences.

With the thermomechanical optimization framework in place the engine thrust frame is modeled. Conceptual design optimization of the engine thrust frame under thermomechanical loads is performed to increase buckling resistance. A mismatch in the coefficient of thermal expansion is used by the optimal variable-stiffness design. The stiffened areas contract less than the inter-stiffener bay regions. Consequently a stabilizing tensile stress is induced in the prone to buckling bay regions, whereas compressive stresses are distributed to the stiffened areas. Based on the stabilizing thermal stresses and load distribution significant gains in performance are found.

The autonomous filling of creep-induced grain-boundary cavities by tungsten-rich precipitates has been studied for Fe-W alloys at various temperatures, loading conditions and creep rupture times. To this aim, scanning electron microscopy, energy-dispersive spectroscopy and X-ray nano-tomography were used. Additionally, the effect of local plastic deformation, followed by ageing processes, on the surface precipitation in these alloys has been studied by means of scanning electron microscopy, together with energy-dispersive spectroscopy. Finally, a diffusion-based finite element analysis has been performed to study cavity filling for different combination of diffusion mechanisms. From scanning electron micrographs it can be confirmed, that Fe-W alloys show damage-selective precipitation of the Laves phase (Fe2W). Furthermore, the filling ratios of individual cavities are determined and it is found, that the autonomous healing strongly depends on the duration of the loading at of elevated temperature. From the quantitative analysis of the size and shape of the precipitates and cavities it is found, that the orientation of grain boundaries to the stress direction has an influence on the morphology of the induced-cavities, as well as, the filling ratio. The grain-boundary cavities orientated favourably for the cavity growth show low filling ratios, due to the fact, that their propagation proceeds with a higher rate than the solute transport. The critical volume of a cavity, that can be fully filled with solute atoms, is found to be of the order of 10 μm3, while the average filling ratio for Fe-W alloys is found to be around 50% for the sample loaded to 100% of its lifetime. Moreover, the scanning electron micrographs of the indentation-deformed samples subjected to ageing revealed surface precipitates (Fe2W), which existence has to be further researched. The hardness measurements of Fe-W samples showed that after 200 hours of ageing at 580oC, the strength of the alloy is only reduced if the material has been pre-strained, but it remains constant for the solution heat treated specimens. This result shows, that the process of dislocation recovery dominates over work-hardening only in the case of a high dislocation density. Finally, the finite element analysis revealed, that during the diffusive cavity filling of an equilibrium-shaped void, three different diffusion profile regimes are plausible. Namely, a diffusive filling dominated by volume diffusion, which occurs for a relatively small spacing between neighbouring cavities and is independent of the ratio of bulk and grain-boundary diffusion. Secondly, a diffusive filling governed by volume diffusion with contributing grain-boundary diffusion, which occurs for relatively low ratios of bulk and grain-boundary diffusion. And ultimately, a diffusive filling governed by grain-boundary diffusion, which occurs for relatively high ratios of bulk and grain-boundary diffusion.

Generalized finite element methods have proved a great potential in the mesh-independent modeling of both weak and strong discontinuities, such as the ones encountered when treating materials with inclusions or cracks. By removing the constraint of a conforming mesh, more freedom is offered to modeling exact geometries by means of splines. However, very few studies have been published which combine Non-Uniform Rational B-Splines (NURBS) to interface-enriched methods, addressing uniquely weak discontinuities. Therefore, the aim of this thesis is to propose a NURBS-based enhancement to the Discontinuity-Enriched Finite Element Method (DE-FEM) in two dimensions and to discuss the potential of its application. The main advantage of this method is the possibility to study problems that present discontinuities with arbitrary smooth shapes, while maintaining exact geometries throughout the analysis: in this way, the equivalence between design and computational geometry is preserved. To this purpose, a suitable NURBS-based analysis technique is selected and implemented within the framework offered by the group's finite element library, Hybrida.
The capabilities of the NURBS-enhanced DE-FEM to solve several weakly discontinuous problems are assessed for composites of different complexities. Furthermore, a novel study is presented which extends this technique to the treatment of strong discontinuities, in the context of fracture mechanics. The accuracy, convergence properties and numerical efficiency of the proposed method are investigated, in particular in comparison with the standard DE-FEM. Based on these observations, further insights are provided into the convenience and the limitations of adopting NURBS enhancements within the DE-FEM formulation. Lastly, some recommendations about possible directions of improvement are provided.

Fatigue is the weakening of a material or structure due to cyclic loading and unloading. As such fatigue is very important in engineering fields like aerospace, where structures are exposed to cyclic loads. Therefore theories on the initiation and propagation of fatigue have been extensively researched In the past century. The main Fatigue Crack Growth (FCG) prediction models are based on a Stress Intensity Factor (SIF), ΔK. Representing FCG data as a function of this SIF causes a stress ratio (R-)effect, which is accounted for by means of plasticity induced crack closure. Crack closure causes the crack to close before a zero tensile load is applied, as such influencing the effective SIF. If FCG data is presented as a function of the effective SIF ΔKeff instead of ΔK, the data correlates very well and the R-effect disappears.
However, the theories based on a SIF and crack closure have recently been subject of discussion. The prediction models using ΔK for similitude are empirically derived and thus do not have any physical explanation. Furthermore ΔK has been derived for quasi-static loading conditions and as such it cannot be blindly adopted for fatigue loading conditions. Besides there is a lot of confusion about the phenomenon (plasticity induced) crack closure, load-displacement observations attributed to crack closure could for instance also be attributed to residual compressive stresses. Especially early test results in vacuum environment do not agree with theories based on SIF and crack closure.
An alternative proposed in literature is to approach fatigue from a Strain Energy Release (SER) perspective. This theory approaches fatigue conform the laws of thermodynamics, and claims that not the amount of energy released under quasi-static load conditions should be considered, but the energy released during a complete fatigue load cycle. It also claims that the R-effect is only an artefact of choosing ΔK for similitude. Treating fatigue as a SER dominated phenomenon instead of a SIF dominated phenomenon, might result in a proper description, prediction and understanding of fatigue.
As such the first goal of this research was to investigate if ΔK is a correct similitude parameter for FCG. This was investigated by comparing experimental results in air and vacuum. According to conventional fatigue theories based on SIF, there should be no difference between air and vacuum. Experiments were designed and similar test conditions were applied with the only difference the environment tested in. Experimental results in air showed -as expected- a clear R-effect that could be accounted for by the plasticity induced crack closure corrections proposed in literature. However, the results in vacuum did not show this R-effect, while the results of crack opening experiments and plasticity did not differ compared to results of experiments in air. It was therefore concluded that ΔK is improper to use as similitude parameter for FCG prediction...

Nonlinear analysis of dynamic problems has become important for modern industrial design applications. The increasing pressure on airlines to decrease fuel costs demands the design of more efficient aircraft. This requires aircraft manufacturing companies to design lighter structural components. The result is the need for more realistic and accurate modelling of critical structural components. Over the years, more powerful finite element discretization methods and improved numerical methods and programming techniques for dynamic analyses of structures have been introduced. Despite these advances and the increase in available computer power, the analysis of nonlinear dynamic problems is yet a computationally demanding task, implying it is very expensive. To reduce the computational time of nonlinear finite element analyses, reduction methods have been developed. These methods have as aim to reduce the number of degrees of freedom, while retaining sufficient accuracy of the solution.

Recently, a new reduction method, applicable to nonlinear static stability problems, has been developed at Delft University of Technology. The aim of this thesis is to extend the reduction method for statics to nonlinear dynamics. This is achieved by using the Hamiltonian formulation to describe the motion of a system. A reduced order model (ROM) is constructed for free vibrations, forced vibrations and damped vibrations, using Hamilton’s equations of motion. These are integrated to obtain the response of the ROM, in terms of displacements and momenta. The displacements of the full finite element model are computed by back-substituting the reduced response into the displacement expansion. The ROM is implemented in a finite element framework.

The ROM is applied to beams, to plates as well as to shells. Overall, good agreement is found between the ROM and Abaqus. The big advantage of the ROM is found when the computational times for beams and plates are compared to that of Abaqus. A drastic reduction in time is observed for the ROM, while still maintaining accurate results. The ROM thus saves valuable computational time.