1,637 research outputs found

    On Local Mechanical Properties of Thin Pressurized Shells with Combined Geometric and Material Anisotropies

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    Thin elastic shells are ubiquitous in nature. Indentation measurements (i.e., poking) provide a useful way for probing mechanical properties of these shell structures. While spherical and cylindrical shells made of isotropic materials are well studied, many shells in nature have geometric anisotropy (e.g., ellipsoidal pollen grains) and/or material anisotropy (e.g., cells that have special growth directions), and mechanics of these shells are relatively less understood. I will present some new insights on indentation responses and buckling pressure of shells with geometric and material anisotropy using the shallow-shell theory. First, I will describe the indentation stiffness of pressurized ellipsoidal and cylindrical elastic shells that are made of isotropic materials. We are able to derive a closed form for the indentation stiffness of shells with arbitrary asphericity and internal pressure. Our results provide theoretical support for previous scaling and numerical results on the stiffness of ellipsoids and allow us to isolate the distinct contributions of geometry and pressure-induced stresses on shell elasticity. I will then add the effects of material orthotropy, which assigns different elastic properties along orthogonal directions. For a commonly used model of orthotropy, we find a simple rescaling transformation that can effectively map a rectilinearly orthotropic shallow shell to an isotropic one with a different local geometry. With the rescaling transformation, we obtain new analytical insights for indentation responses and buckling of orthotropic shells. Our results provide a new perspective on how isotropic and orthotropic materials are related, isolate the effect of material orthotropy on shell elasticity, and can provide experimentalists with a means to analyze the internal pressure of biological structures that are made of orthotropic materials using atomic force microscopes

    A new smoothed particle hydrodynamics method based on high-order moving-least-square targeted essentially non-oscillatory scheme for compressible flows

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    In this study, we establish a hybrid high-order smoothed particle hydrodynamics (SPH) framework (MLS-TENO-SPH) for compressible flows with discontinuities, which is able to achieve genuine high-order convergence in smooth regions and also capture discontinuities well in non-smooth regions. The framework can be either fully Lagrangian, Eulerian or realizing arbitary-Lagrangian-Eulerian (ALE) feature enforcing the isotropic particle distribution in specific cases. In the proposed framework, the computational domain is divided into smooth regions and non-smooth regions, and these two regions are determined by a strong scale separation strategy in the targeted essentially non-oscillatory (TENO) scheme. In smooth regions, the moving-least-square (MLS) approximation is used for evaluating high-order derivative operator, which is able to realize genuine high-order construction; in non-smooth regions, the new TENO scheme based on Vila's framework with several new improvements will be deployed to capture discontinuities and high-wavenumber flow scales with low numerical dissipation. The present MLS-TENO-SPH method is validated with a set of challenging cases based on the Eulerian, Lagrangian or ALE framework. Numerical results demonstrate that the MLS-TENO-SPH method features lower numerical dissipation and higher efficiency than the conventional method, and can restore genuine high-order accuracy in smooth regions. Overall, the proposed framework serves as a new exploration in high-order SPH methods, which are potential for compressible flow simulations with shockwaves.Comment: 36 pages, 15 figures, accepted by Journal of Computational Physics on June 1st, 202

    Peering into the Dark: Investigating dark matter and neutrinos with cosmology and astrophysics

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    The LCDM model of modern cosmology provides a highly accurate description of our universe. However, it relies on two mysterious components, dark matter and dark energy. The cold dark matter paradigm does not provide a satisfying description of its particle nature, nor any link to the Standard Model of particle physics. I investigate the consequences for cosmological structure formation in models with a coupling between dark matter and Standard Model neutrinos, as well as probes of primordial black holes as dark matter. I examine the impact that such an interaction would have through both linear perturbation theory and nonlinear N-body simulations. I present limits on the possible interaction strength from cosmic microwave background, large scale structure, and galaxy population data, as well as forecasts on the future sensitivity. I provide an analysis of what is necessary to distinguish the cosmological impact of interacting dark matter from similar effects. Intensity mapping of the 21 cm line of neutral hydrogen at high redshift using next generation observatories, such as the SKA, would provide the strongest constraints yet on such interactions, and may be able to distinguish between different scenarios causing suppressed small scale structure. I also present a novel type of probe of structure formation, using the cosmological gravitational wave signal of high redshift compact binary mergers to provide information about structure formation, and thus the behaviour of dark matter. Such observations would also provide competitive constraints. Finally, I investigate primordial black holes as an alternative dark matter candidate, presenting an analysis and framework for the evolution of extended mass populations over cosmological time and computing the present day gamma ray signal, as well as the allowed local evaporation rate. This is used to set constraints on the allowed population of low mass primordial black holes, and the likelihood of witnessing an evaporation

    Sloshing reduced-order model trained with Smoothed Particle Hydrodynamics simulations

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    The main goal of this paper is to provide a Reduced Order Model (ROM) able to predict the liquid induced dissipation of the violent and vertical sloshing problem for a wide range of liquid viscosities, surface tensions and tank filling levels. For that purpose, the Delta Smoothed Particle Hydrodynamics (δ-SPH) formulation is used to build a database of simulation cases where the physical parameters of the liquid are varied. For each simulation case, a bouncing ball-based equivalent mechanical model is identified to emulate sloshing dynamics. Then, an interpolating hypersurface-based ROM is defined to establish a mapping between the considered physical parameters of the liquid and the identified ball models. The resulting hypersurface effectively estimates the bouncing ball design parameters while considering various types of liquids, producing results consistent with SPH test simulations. Additionally, it is observed that the estimated bouncing ball model not only matches the liquid induced dissipation but also follows the liquid center of mass and presents the same sloshing force and phase-shift trends when varying the tank filling level. These findings provide compelling evidence that the identified ROM is a practical tool for accurately predicting critical aspects of the vertical sloshing problem while requiring minimal computational resources

    Ein Verfahren zur Kopplung der Smoothed-Particle-Hydrodynamics- und der Finite-Volumen-Methode

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    Beim Einsatz flüssigen Kraftstoffs in Gasturbinen sind der Verbrennung komplexe zweiphasige Strömungsprozesse vorgelagert. Hier ist insbesondere die Primärzerstäubung des Kraftstoffs zu nennen. Mit der Smoothed-Particle-Hydrodynamics(SPH)-Methode kann die Primärzerstäubung detailliert simuliert werden. Dieser Ansatz ist aufgrund seines hohen Berechnungsaufwands zurzeit jedoch auf kleine räumliche Bereiche begrenzt, wodurch die Kopplung mit den umgebenden Strömungsprozessen, die ohnehin effizienter und genauer mit der Finite-Volumen(FV)-Methode zu berechnen sind, eingeschränkt ist. Es ist daher erstrebenswert, detaillierte SPH-basierte Zerstäubungssimulationen in FV-Simulationen der umgebenden Strömung einzubetten. Dieser Forschungsbericht befasst sich mit der Entwicklung eines solchen hybriden Ansatzes zur direkten Kopplung von SPH- und FV-Rechengebieten. Der Ansatz wird hinsichtlich grundlegender numerischer Aspekte, wie der Massenerhaltung, sorgfältig beleuchtet und optimiert. Die Aufprägung von Rand- und Kopplungsbedingungen wird vereinheitlicht, wobei auch weitere Verbesserungen für Randbedingungen eingeführt werden. Durch geeignete Testfälle wird die Anwendbarkeit der Kopplungsschnittstelle auf brennkammertypische Strömungseigenschaften, wie Rezirkulation und signifikante Instationarität, demonstriert. Hierdurch werden somit wichtige Voraussetzungen zur Weiterentwicklung des Verfahrens für turbulente und mehrphasige Strömungen sowie technische Geometrien geschaffen

    Simulating incompressible thin-film fluid with a Moving Eulerian-Lagrangian Particle method

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    In this thesis, we introduce a Moving Eulerian-Lagrangian Particle (MELP) method, a mesh-free method to simulate incompressible thin-film fluid systems: soap bubbles, bubble clusters, and foams. The realistic simulation of such systems depends upon the successful treatment of three aspects: (1) the soap film\u27s deformation due to the tendency to minimize the surface energy, giving rise to the bouncy characteristics of soap bubbles, (2) the tangential fluid flow on the thin film, causing the thickness to vary spatially, which in conjunction with thin-film interference creates evolving and highly sophisticated iridescent color patterns, (3) the topological changes due to collision, separation, and fragmentation, which may create partition surfaces and non-manifold junctions that spontaneously settle into honeycomb structures due to force balance. The interleaving complexities from all three fronts render the task of accurately and affordably simulating thin-film fluid an open problem for the Computational Physics and Computer Graphics community. The proposed MELP method tackles these multifaceted challenges by employing a novel, bi-layer particle structure: a sparse set of Eulerian particles for dynamic interface tracking and PDE solving, and a fine set of Lagrangian particles for material and momentum transport. Such a design provides crucially advantageous numerical traits compared to existing frameworks. Compared to mesh-based methods, MELP\u27s particle-based nature makes it topologically agnostic, which allows it to conveniently simulate topological changes such as bubble-cluster formation and thin-film rupture. Furthermore, these Lagrangian structures carry out fluid advection naturally, conserve mass by design, and track sub-grid flow details. Compared to existing particle methods, our bi-layer design improves drastically on the computational performance in terms of both stability and efficiency. The advantage of this design will manifest in a wide range of experiments, including dynamic foam formation, Rayleigh-Taylor instability, Newton Black Films, and bubble bursting, showing an increased level of flow detail, increased number of regions in bubble clusters, and increased flexibility to recreate multi-junction formation on-the-fly. Furthermore, we validate its physical correctness against a variety of analytical baselines, by successfully recovering the equilibrium dihedral and tetrahedral angles, the exponential thickness profile of drainage under gravity, the curvature of partition surfaces, and the minimum surface area of double-bubbles

    Experimental and computational models for simulating the oral breakdown of food due to the interaction with molar teeth during the first bite

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    The first bite involves the structural breakdown of foods due to the interaction with teeth and is a crucial process in oral processing. Although in vitro experiments are useful in predicting the oral response of food, they do not facilitate a mechanistic understanding of the relationship between the intrinsic food mechanical properties and the food behaviour in the oral cavity. Computer simulations, on the other hand, allow for such links to be established, offering a promising design alternative that will reduce the need for time consuming and costly in vivo and in vitro trials. Developing virtual models of ductile fracture in soft materials, such as food, with random and non-predefined crack morphology imposes many challenges. One of the most important is to derive results that do not depend on numerical parameters, such as Finite Element (FE) mesh density, but only physical constants obtained through independent standard mechanical tests, such as fracture strain and/or critical energy release rate. We demonstrate here that this challenge can be overcome if a non-local damage approach is used within the FE framework. We develop a first bite FE modelling methodology that provides mesh independent results which are also in agreement with physical first bite experiments performed on chocolate. The model accounts for key features found in chocolate and a wide range of compliant media, such as rate dependent plasticity and pressure dependent fracture initiation strain. As a result, our computational methodology can prove valuable in studying food structure-function relationships that are essential in product development

    Data-driven deep-learning methods for the accelerated simulation of Eulerian fluid dynamics

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    Deep-learning (DL) methods for the fast inference of the temporal evolution of fluid-dynamics systems, based on the previous recognition of features underlying large sets of fluid-dynamics data, have been studied. Specifically, models based on convolution neural networks (CNNs) and graph neural networks (GNNs) were proposed and discussed. A U-Net, a popular fully-convolutional architecture, was trained to infer wave dynamics on liquid surfaces surrounded by walls, given as input the system state at previous time-points. A term for penalising the error of the spatial derivatives was added to the loss function, which resulted in a suppression of spurious oscillations and a more accurate location and length of the predicted wavefronts. This model proved to accurately generalise to complex wall geometries not seen during training. As opposed to the image data-structures processed by CNNs, graphs offer higher freedom on how data is organised and processed. This motivated the use of graphs to represent the state of fluid-dynamic systems discretised by unstructured sets of nodes, and GNNs to process such graphs. Graphs have enabled more accurate representations of curvilinear geometries and higher resolution placement exclusively in areas where physics is more challenging to resolve. Two novel GNN architectures were designed for fluid-dynamics inference: the MuS-GNN, a multi-scale GNN, and the REMuS-GNN, a rotation-equivariant multi-scale GNN. Both architectures work by repeatedly passing messages from each node to its nearest nodes in the graph. Additionally, lower-resolutions graphs, with a reduced number of nodes, are defined from the original graph, and messages are also passed from finer to coarser graphs and vice-versa. The low-resolution graphs allowed for efficiently capturing physics encompassing a range of lengthscales. Advection and fluid flow, modelled by the incompressible Navier-Stokes equations, were the two types of problems used to assess the proposed GNNs. Whereas a single-scale GNN was sufficient to achieve high generalisation accuracy in advection simulations, flow simulation highly benefited from an increasing number of low-resolution graphs. The generalisation and long-term accuracy of these simulations were further improved by the REMuS-GNN architecture, which processes the system state independently of the orientation of the coordinate system thanks to a rotation-invariant representation and carefully designed components. To the best of the author’s knowledge, the REMuS-GNN architecture was the first rotation-equivariant and multi-scale GNN. The simulations were accelerated between one (in a CPU) and three (in a GPU) orders of magnitude with respect to a CPU-based numerical solver. Additionally, the parallelisation of multi-scale GNNs resulted in a close-to-linear speedup with the number of CPU cores or GPUs.Open Acces

    The Investigation Of A Likely Scenario For Natural Tornado Genesis And Evolution From An Initial Instability Profile

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    A likely mechanism for the little-understood tornado genesis is proposed and its numerical implementation is presented. The Burgers-Rott vortex with its axis in the vertical direction is introduced as an instability mechanism, and the flow field then evolves under the influence of the atmospheric pressure, temperature and density variations with altitude. Buoyancy effects are implemented using the Boussinesq model. Results are presented and discussed for a set of conditions including mesh type and size, different turbulence models, and a few different boundary conditions. Post-processed results of the transient simulations including animations contain a wealth of information to help analyze tornado behavior. Velocity contours, pressure contours, vorticity contours, streamlines, and iso-surfaces show the evolution of a complex flow field possessing many characteristics of a tornado. At longer times from the start, the flow field becomes more asymmetric with the vortex core becoming more twisted, and the eye of the vortex drifting away from the axis of the computational domain. The single initial vortex then transitions into multiple vortices of varying size and orientation. These high Reynolds number (ReΓ ∼109) simulation results show flow fields that resemble highly unsteady, turbulent flows with large regions of flow separation, and large eddy size range
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