A numerical method commonly referred to as smooth particle hydrodynamics (SPH) is implemented in two dimensions for solid mechanics in general and fracture mechanics in particular. The implementation is tested against a few analytical cases: a vibrating plate, a bending plate, a modus I crack and a modus II crack. A conclusion of these tests is that a better way of treating a shortcoming of SPH called tensile instability is needed. A study is made on the best choice of a vital parameter called the smoothing radius, and it is found that a good choice of the smoothing radius is roughly 1.5 times the initial particle spacing.

Context. In computer graphics, realistic looking fluid is often desired. Simulating realistic fluids is a time consuming and computationally expensive task, therefore, much research has been devoted to reducing the simulation time while maintaining the realism. Two of the more recent optimization algorithms within particle based simulations are two-scale simulation and regional time stepping (RTS). Both of them are based on the predictive-corrective incompressible smoothed particle hydrodynamics (PCISPH) algorithm. Objectives. These algorithms improve on two separate aspects of PCISPH, two-scale simulation reduces the number of particles and RTS focuses computational power on regions of the fluid where it is most needed. In this paper we have developed and investigated the performance of an algorithm combining them, utilizing both optimizations. Methods. We implemented both of the base algorithms, as well as PCISPH, before combining them. Therefore we had equal conditions for all algorithms when we performed our experiments, which consisted of measuring the time it took to run each algorithm in three different scene configurations. Results. Results showed that our combined algorithm on average was faster than the other three algorithms. However, our implementation of two-scale simulation gave results inconsistent with the original paper, showing a slower time than even PCISPH. This invalidates the results for our combined algorithm since it utilizes the same implementation. Conclusions. We see that our combined algorithm has potential to speed up fluid simulations, but since the two-scale implementation was incorrect, our results are inconclusive.

<div>Thermal barrier coatings (TBCs) made of low thermal conductivity ceramic topcoats have been extensively used in hot sections of gas turbine engines, in aircraft propulsion and power generation applications. TBC damage may occur during gas turbine operations, due to either time- and cycle-dependent degradation phenomena, external foreign object damage, and/or erosion. The damaged TBCs, therefore, need to be removed and repaired during engine maintenance cycles. Although several coating removal practices have been established which are based on the trial-and-error approach, a fundamental understanding of coating fracture mechanisms during the removal process is still limited, which hinders further development of the process.</div><div>The objective of the thesis is to develop a particle-based coating removal modeling framework, using both the smoothed particle hydrodynamics (SPH) and discrete element modeling (DEM) methods. The thesis systematically investigates the processing-property relationships in the TBC removal processes using a modeling approach, thus providing a scientific tool for process design and optimization.</div><div>To achieve the above-mentioned objective, the following research tasks are identified. First a comprehensive literature review of major coating removal techniques is presented in Chapter 2. Chapter 3 discusses an improved SPH model to simulate the high-velocity particle impact behaviors on TBCs. In Chapter 4, the abrasive water jet (AWJ) removal process is modeled using the SPH method. In Chapter 5, an SPH model of the cutting process with regular electron beam physical vapor deposition (EB-PVD) columnar grains is presented. In Chapter 6, a 3D DEM cutting model with regular EB-PVD column grains is discussed. In Chapter 7, a 2D DEM cutting model based on the realistic coating microstructure is developed. Finally, in Chapter 8, based on the particle-based coating removal modeling framework results and analytical solutions, a new fracture mechanism map is proposed, which correlates the processing parameters and coating fracture modes.</div><div>The particle-based modeling results show that: (1) for the SPH impact model, the impact hole penetration depth is mainly controlled by the vertical velocity component. (2) The SPH AWJ simulation results demonstrate that the ceramic removal rate increases with incident angle, which is consistent with the fracture mechanics-based analytic solution. (3) The SPH model with regular EB-PVD columnar grains shows that it is capable to examine the stress evolutions in the coating with columnar grain structures, which is not available if a uniform bulk coating model was used. Additional analysis reveals that the fracture of the columnar grains during the cutting process is achieved through deflection and fracture of the grains, followed by pushing against neighboring grains. (4) The 3D DEM model with regular coating columnar grains shows that, during the coating removal process, a ductile-to-brittle transition is identified which depends on the cutting depth. The transition occurs at the critical cutting depth, which is based on the Griffith fracture criterion. At small cutting depths, the ductile failure mode dominates the cutting process, leading to fine cut particles. As the cutting depth exceeds the critical cutting depth, a brittle failure mode is observed with the formation of chunk-like chips. (5) The 2D DEM model with the realistic coating microstructure shows that there are densification and fracture during the foreign object compaction process, which qualitatively agrees with the experimental observations. (6) The newly proposed coating fracture mechanism map provides guidance to predict three fracture modes, i.e., ductile brittle, and mixed ductile-brittle, as a function of processing parameters, including the cutting depth and cutting speed. The map can be used to determine the processing conditions based on required TBC removal operations: rough cut (brittle mode), semi-finish (mixed ductile-brittle mode), and finish (ductile mode).</div><div><br></div>

High strain rate plastic deformation of metals results in the formation of localized zones of severe shear strain known as adiabatic shear bands (ASBs), which are a precursor to shear failure. The formation of ASBs in a high-strength low alloy steel, namely AISI 4340, was examined based on prior heat treatments (using different austenization and tempering temperatures), testing temperatures, and impact strain rates in order to map out grain size and grain deformation behaviour during the formation of ASBs. In the current experimental investigation, ASB formation was shown to be a microstructural phenomenon which depends on microstructural properties such as grain size, shape, orientation, and distribution of phases and hard particles—all controlled by the heat treatment process. Each grain is unique and its material properties are heterogeneous (based on its size, shape, and the complexity of the microstructure within the grain). Using measurements of grain size at various heat treatments as well as dynamic stress-strain data, a finite element model was developed using Matlab and explicit dynamic software LSDYNA to simulate the microstructural deformation of grains during the formation of ASBs. The model simulates the geometrical grain microstructure of steel in 2D using the Voronoi Tessellation algorithm and takes into account grain size, shape, orientation, and microstructural material property inhomogeneity between the grains and grain boundaries. The model takes advantage of the Smooth Particle Hydrodynamics (SPH) meshless method to simulate highly localized deformation as well as the Johnson-Cook Plasticity material model for defining the behavior of the steel at various heat treatments under high strain rate deformation.The Grain Model provides a superior representation of the kinematics of ASB formation on the microstructural level, based on grain size, shape and orientation. It is able to simulate the microstructural mechanism of ASB formation and grain refinement in AISI 4340 steel, more accurately and realistically than traditional macroscopic models, for a wide range of heat treatment and testing conditions.

<p>This thesis project addresses the need for an interactive, real-time water animation tech-<br> nique that can showcase visually convincing effects such as splashes and breaking waves while<br> being computationally inexpensive. Our method couples SPH and wave equations in a one-<br> way manner to simulate the behavior of water in real-time, leveraging OpenGL’s Compute<br> Shaders for interactive performance and a novel Uniform Grid implementation. Through a<br> review of related literature on real-time simulation methods of fluids, and water animation,<br> this thesis presents a feasible algorithm, animations to showcase interesting water effects,<br> and a comparison of computational costs between SPH, wave equations, and the coupled<br> approach. The program renders a water body with a planar surface and discrete particles.<br> This project aims to provide a solution that can meet the needs of various water animation<br> use-cases, such as games, and movies, by offering a computationally efficient technique that<br> can animate water to behave plausibly and showcase essential effects in real-time.</p>

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Los sistemas flexibles de alta resistencia anclados al terreno son una de las distintas técnicas existentes para la estabilización de taludes, ya sean de roca o de suelos. Están constituidos por una membrana (red de cables o malla de alambre) sujeta al terreno mediante placas de anclaje, cables de refuerzo y bulones. En la mayor parte de los modelos de cálculo existentes se supone un comportamiento activo del sistema, es decir, que evita que se produzcan deslizamientos a través de una supuesta pretensión del sistema y convexidad del terreno. El sistema ejercería una presión normal al terreno que incrementa la tensión tangencial en la superficie potencial de deslizamiento evitando que se alcance la rotura del terreno. En esta tesis se han medido las fuerzas en distintos componentes del sistema desde el momento de la instalación, y se ha comprobado que la pretensión es muy reducida. Por otro lado, la supuesta convexidad del terreno raramente tiene lugar. Todo esto conduce a demostrar la hipótesis de comportamiento pasivo del sistema, es decir, que éste contiene a la masa inestable una vez que se ha producido la rotura. Es por ello que se ha considerado el desarrollar un nueva metodología de cálculo basada en un comportamiento pasivo. La nueva metodología consiste en realizar una simulación numérica dinámica en 2D de la interacción sistema flexible - masa inestable – talud estable. Partiendo de las dimensiones de un círculo de rotura en suelos o una cuña en roca, se deja caer la masa inestable con la fuerza de la gravedad. En su caída, la masa inestable deformará a la membrana, cables de refuerzo y bulones desarrollándose en ellos tensiones que deberán considerarse para su correcto dimensionamiento. En el caso particular de los taludes de suelos, se ha recurrido a la modelización de la masa inestable mediante la discretización por puntos SPH (Smooth Particle Hydrodynamics). / Highly resistant flexible systems anchored to the ground are among the techniques for slope stabilisation, either soil or rock. The system is formed by a membrane (cable net or wire mesh) tightened to the ground through spike plates, reinforcement cables and bolts. In the majority of the existing design models, an active behaviour of the system is considered; which means, that it is able to avoid ground sliding through a pretension of the system and the convexity of the slope surface. The system would exert a normal pressure over the ground that increases the shear stress in the potential slip surface avoiding that failure takes place. In this thesis, forces on different system components have been measured, finding that the pretension force is very low. On the other hand, the supposed ground convexity rarely exists. All this demonstrates that actual system behaviour is passive; which means that it is able to contain the unstable mass once the failure has already occurred. Therefore, a new design methodology based on a passive behaviour has been developed. The new methodology consists in performing a dynamic numerical simulation in 2D of the interaction flexible system – unstable mass – stable slope. Starting from specific known dimensions of slip circle in soils or a wedge in rocks, unstable mass falls only under the action of gravity. During its falling, the unstable mass deforms the membrane, reinforcement cables and bolts. Maximum stresses developed in these components should be considered for their design. In the particular case of soil slopes, unstable mass has been discretised with the mesh free method SPH (Smooth Particle Hydrodynamics).