Truss-based architected cellular materials offer a promising solution for shielding spacecraft from hypervelocity impacts (HVI) by micrometeoroids and orbital debris (MMOD). Numerical modelling plays a crucial role in developing these shields, as physical testing is resource intensive. Accurate contact modelling is essential for impact simulations, yet current finite element techniques like Lagrange multiplier and penalty methods can be computationally demanding or require extensive tuning. This study presents a novel momentum-based contact formulation for geometrically exact slender beams, avoiding the need for Lagrange multipliers and penalty parameters. A series of applications show that this new formulation effectively models low-velocity impacts and captures the contact stiffening effect, where strut self-contact in a collapsed lattice is reflected in the load response. The use of idealized pin joints for lattice modelling is nevertheless identified as a significant limitation. By advancing beam-to-beam contact modelling, this research supports the development of HVI shields and provides a foundation for future improvements.

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.

Finite Element Methods (FEMs) are widely employed for damage simulation in composites, with the Cohesive Zone Model (CZM) being particularly favored for its robustness and scalability. Despite the CZM's mesh-dependent nature, the Discontinuous Galerkin Cohesive Zone Model (DG/CZM) formulation allows for relatively arbitrary crack propagation thanks to highly refined meshes and its strong suitability for parallel implementation, which is crucial for fracture simulation in composites.

However, a challenge with the CZM in modeling damage in composites lies in determining which damage mechanism occurs at a given numerical interface. To date, fracture simulation in composite laminates has mainly relied on methods designed for isotropic materials, which come with notable modeling constraints such as limiting the arbitrariness of damage evolution and requiring experimental data on fracture propagation.

In this thesis, a novel approach is proposed to ensure arbitrary damage development solely based on the structural stress state using the DG/CZM approach.

The rising number of objects in low Earth orbit heightens the likelihood of orbital debris impact on spacecrafts at an increasingly fast pace. Thus, the need for lightweight shielding from hypervelocity impacts has grown considerably. Direct observation of hypervelocity impacts are almost impossible and experimental campaigns are expensive, and so numerical simulation has become a fundamental tool for hypervelocity impact modelling. These simulations involve multiple coupled physics mechanism, including fragmentation and stress waves propagation. While various simulation techniques exist for this problem, none effectively capture the interaction between fragmentation and stress wave propagation within the velocity range relevant to orbital impacts while being suitable for modelling of full-scale satellite fragmentation events. The objective of this thesis is to address this limitation by proposing an approach for a fragmentation framework based the Discontinuous Galerkin/Cohesive Zone Method finite element formulation and the Decomposition Contact Response contact algorithm.

Thin-walled composite structures are critical in aerospace engineering, making it essential to understand their failure mechanisms. However, manufacturing test samples and conducting high-fidelity experimental tests are both complex and expensive, making advanced modeling techniques essential. The Cohesive Zone Model (CZM) is a widely used method for modeling delaminations in composites, but it typically depends on artificial elastic compliance, which can compromise accuracy. This thesis introduces a high-fidelity finite element model that integrates the Discontinuous Galerkin method with geometrically exact shell elements to explicitly model each lamina during large deformations and buckling in multi-layered materials. By coupling the layers, this approach eliminates the need for artificial compliance. Numerical simulations show the model’s accuracy in predicting structural behavior under various loading conditions, although challenges remain in maintaining proper layer separation during deformation. This study lays the groundwork for modeling delaminations along arbitrary interfaces.

Finite Element Analysis (FEA) is one of the most established techniques to approximate the solution of complex nonlinear solid mechanics problems. Modeling realistic applications utilizing FEA is computationally intensive and it is often necessary to split the computing load among different processes running concurrently on a cluster of Central Processing Units (CPUs) to reduce the simulation runtime. Such parallel computing is traditionally performed by clusters of Central Processing Units (CPUs). However, the overhead associated with inter-CPU communication eventually deteriorates performance as the number of processes increases. At that point, Graphical Processing Units (GPUs) can be utilized to decrease the computation time even further. In fact, despite GPUs generally exhibit slower processing speed than CPUs, they can run thousands of threads concurrently, resulting overall in better performance. The objective of this thesis is to explore various GPU implementations aiming to determine how GPUs can act as co-accelerators alongside CPUs within a finite element calculation. To this end, the algorithmic steps of a solid mechanics finite element solver were analyzed to identify those that best lend themselves to GPU parallel computing. Consequently, two alternative GPU parallelization strategies were proposed, each of which was benchmarked on three different representative material models with the aim of comprehensively evaluating the ramifications of integrating a GPU-accelerated implementation. Results show a speed-up ranging between 31.5x and 37.7x for the evaluated material models. In addition, this thesis presents effective strategies to systematically optimize the CPU-GPU interaction in the context of FEA for solid mechanics, thus enabling highly resolved thirty million element calculations with tailored performance to heterogeneous multi-CPU and multi-GPU hardware.

The design of wind turbines is an iterative process in which load calculations and system performance analyses are done under various environmental conditions. Due to the complexity of wind turbine systems, fully coupled aero-hydro-servo-elastic codes are indispensable to represent the nonlinear behaviour of the system. However, nonlinear codes are known to be costly and time-consuming. In consequence, fast methods of assessing the loads on the system are required to speed up the wind turbine design process, especially in its early stages. This research comprehends a linearised version of the BHawC model and provides fast methods of evaluating wind turbine loads under turbulent inflow conditions. For wind turbines in isotropic conditions and low turbulence intensity, the model is studied as a linear time-invariant (LTI) system through the Coleman transformation, which describes the rotor degrees of freedom in the inertial frame. The dynamic response of the system is obtained through a frequency-domain procedure based on computing the system's transfer function and using the fast Fourier transform (FFT) algorithm. In addition, model-order reduction (MOR) techniques are used to lower the run times of the simulations.

The verification of the fast model is accomplished by comparing the response of the linear model with that of the Siemens in-house aeroelastic simulation tool, BHawC. The comparison is made both in the time domain and the frequency domain through the power spectra of the time series. Results of the tower-top displacements and the tower-bottom loads are presented at three operating points. From the time-domain responses, the maximum root-mean-square error of the tower-base loads related to the fore-aft and the vertical motion of the turbine is around 10%. Besides, the tower-base lateral force and moment present large discrepancies of around 20% with respect to BHawC. The fatigue side-side moment is greatly overpredicted, whereas the differences for the other load channels are less than 20%.

For isotropic conditions and high turbulence intensity, the dependency on the variations in the controller is considered by modelling the system as a linear parameter-varying (LPV) system. In this case, a discrete-time approach is used together with model-order reduction techniques to reduce the computational requirements in terms of memory and run time. The methodology requires knowledge of the state at the steady-state equilibrium. Nevertheless, the linearised BHawC model describes the rotational degrees of freedom differently to the linearised model. Therefore, the implemented methodology is instead used in an analytical wind turbine model. There, the LPV system is able to capture the variability in the system while greatly reducing the computational expense of the simulations.