Stochastic analysis of different rough surfaces

This paper shows in detail the application of a new stochastic approach for the characterization of surface height profiles, which is based on the theory of Markov processes. With this analysis we achieve a characterization of the scale dependent complexity of surface roughness by means of a Fokker-Planck or Langevin equation, providing the complete stochastic information of multiscale joint probabilities. The method is applied to several surfaces with different properties, for the purpose of showing the utility of this method in more details. In particular we show the evidence of Markov properties, and we estimate the parameters of the Fokker-Planck equation by pure, parameter-free data analysis. The resulting Fokker-Planck equations are verified by numerical reconstruction of conditional probability density functions. The results are compared with those from the analysis of multi-affine and extended multi-affine scaling properties which is often used for surface topographies. The different surface structures analysed here show in details advantages and disadvantages of these methods.Comment: Minor text changes to be identical with the published versio

Fractal analysis in particle dissolution: a review

Fractal is a geometric language to describe the objects, the systems, and the phenomenon spatially and temporally. This paper reviews the literature on fractal models developed to describe the dissolution of particles. Dissolution, the process by which a solid forms a homogeneous mixture with a solution, is the behavior of a population of particles rather than a single one in most of the cases. The fractal models developed for the particle population are reviewed on the basis of two key particle surface properties, namely, the surface fractal nature and the chemical reactivity of particle surfaces. In terms of the surface fractal nature, fractals have been used to describe the change in the superficial roughness of particles, surface area-particle size relation, and particle size distribution (PSD). In terms of the reactive fractal dimensions, the models that describe the dissolution process have been developed to obtain the empirical noninteger exponent, the reactive fractal dimension that can dictate the chemical reactivity of a solid surface. The comparison between the surface fractal dimension and the reactive fractal dimension provides the dissolution mechanisms in many aspects of surface morphology. Further research is necessary to modify the current models to coincide with the real industrial processes and production and to develop the specific models for a better understanding of many processes involving the dissolution of particles encountered in many areas, including pharmaceutical and chemical applications and hydrometallurgy

Information Extraction and Modeling from Remote Sensing Images: Application to the Enhancement of Digital Elevation Models

To deal with high complexity data such as remote sensing images presenting metric resolution over large areas, an innovative, fast and robust image processing system is presented. The modeling of increasing level of information is used to extract, represent and link image features to semantic content. The potential of the proposed techniques is demonstrated with an application to enhance and regularize digital elevation models based on information collected from RS images

A computational study of the influence of surface roughness on material strength

In machine component stress analysis, it usually assumed that the geometry specified in CAD provides a fair representation of the geometry of the real component. While in particular circumstances, tolerance information, such as minimum thickness of a highly stressed region, might be taken into consideration, there is no standard practice for the representation of surface quality. It is known that surface roughness significantly influences fatigue life, but for this to be useful in the context of life prediction, there is a need to examine the nature of surface roughness and determine how best to characterise it. Non-smooth geometry can be represented in mathematics by fractals or other methods, but for a representation to have a practical value for a manufactured component, it is necessary to accept that there is a lower limit to surface profile measurement resolution. Resolution and mesh refinement also play a part in any computational analysis undertaken to assess surface profile effects: in the analyses presented, a nominal axi-symmetric geometry has been taken, with a finite non-smooth region on the boundary. Various surface roughness representations are modelled, and the significance of the characterized surface roughness type is investigated. It is shown that the applied load gives rise to a nominally uni-axial stress state of 90% of the yield, although surface roughness features have the effect of modifying the load path, and give rise to localized regions of plasticity near to the surface. The material of the test model is assumed to be elasto-plastic, and the development and evolution of plastic zones formed within the geometry are shown for multiple load cycles

Mehrskalige Modellierung von Gummi-Hysteresereibung auf rauen Oberflächen

The performance of car tires on road tracks is strongly affected by hysteretic friction. In order to optimize driving characteristics, like minimizing fuel consumption, improving skid resistance, increasing tire durability, and increasing vehicle controllability during steering and braking, the rolling friction coefficient should be predicted properly. The accurate and efficient modeling and prediction of the hysteretic friction is still a challenge. In the past decade, two different modeling frameworks have attracted significant attention. They are the viscoelastic half-space (VHS)-based contact mechanics model, based on linear kinematics and implemented with the boundary element method (BEM), and the viscoelastic contact model in the finite deformation framework implemented with the finite element method (FEM). The first one has the ability to model all involved length scales at once with a reduced computational cost under the assumption of a flat geometry of the rough surface and small deformations. The second one does not have these limitations and is able to predict the friction coefficient accurately in the finite deformation framework, but at much higher computational cost. It is not able to investigate all involved length scales at once since it needs an extremely fine mesh refinement, which leads to an impractically slow simulation. This work has two major aims. The first goal is to study the accuracy of geometrical and rheological linearity assumptions in evaluation of rolling friction coefficient. This is done by comparing the simulation results of tire tread block in contact with a sinusoidal road track surface using the linear VHS-based model and the finite deformation model in terms of rolling friction coefficient, contact area, and pressure distributions. It has been found that accurate rolling friction predictions can be obtained through the linear VHS-based model within Reynolds assumption for moderate values of root mean square slopes, whereas finite deformation computations should be adopted for large root mean square slopes. The contact area is much more sensitive to the geometrical and rheological nonlinearities than the rolling friction coefficient. The second goal of the thesis is to establish a new hybrid (nonlinear FEM/linear BEM) multiscale method which combines the advantages of both methods. The presented hybrid multiscale approach has proven to be a suitable tool to study rolling-friction coefficient within a plausible degree of accuracy for relative large contact area and low sliding velocities. It allows a more faster calculation of friction coefficient than the finite deformation model.Das Verhalten von Pkw-Reifen auf Straßenoberflächen wird stark von hysteretischer Reibung beeinflusst. Um die Fahreigenschaften zu optimieren, beispielsweise zur Reduktion des Kraftstoffverbrauchs, der Verbesserung der Griffigkeit, der Erhöhung der Reifenhaltbarkeit und der Verbesserung der Kontrolle während des Lenkens und Bremsens, sollte die hysteretische Reibung richtig vorhergesagt werden. Die genaue und effiziente Vorhersage von hysteretischer Reibung, sowohl von theoretischer wie numerischer Seite, ist eine Herausforderung. Im letzten Jahrzehnt haben zwei verschiedene Modellierungsverfahren an Aufmerksamkeit gewonnen. Sie sind: das viskoelastische Halbraummodell, das auf einer linearen Kinematik basiert und mit der Randelemente-Methode implementiert wurde, sowie das viskoelastische Kontaktmodell im Rahmen finiter Deformationen, das mit der Finite-Elemente-Methode implementiert wurde. Mit der ersten Methode können alle beteiligten Längenskalen gleichzeitig und mit reduziertem Berechnungsaufwand simuliert werden, wobei eine flache Geometrie der rauen Oberfläche und lineare Verformungen angenommen werden. Die zweite Methode hat diese Einschränkungen nicht und kann den Reibkoeffizienten genau vorhersagen, jedoch bei weitaus höherer Berechnungszeit. Hierbei können jedoch nicht alle beteiligten Längenskalen gleichzeitig untersucht werden, da ein sehr feines Netz benötigt würde, was zu inakzeptabel langen Simulationen führt. Diese Arbeit hat zwei Hauptziele. Das erste Ziel besteht darin, die Auswirkungen geometrischer und rheologischer Linearitätsannahmen bei der Berechnung des Reibkoeffizienten zu untersuchen. Dies erfolgt durch Vergleich der Simulationsergebnisse eines Reifenprofilblocks in Kontakt mit einer sinusförmigen Oberfläche, unter Verwendung des linearen viskoelastischen Halbraummodells, das mit der Randelemente-Methode implementiert wurde, und des viskoelastischen Kontaktmodells im Rahmen finiter Deformationenund der Finite-Elemente-Methode. Betrachtet wurden Reibkoeffizient, Kontaktfläche und Druckverteilung. Es wurde festgestellt, dass mit dem viskoelastischen Halbraum Modell innerhalb der Linearitätsannahmen genaue Vorhersagen der Reibung für kleine Werte der lokaler Oberflächen-Steigung erhalten werden können, wohingegen für große Steigungen finite Deformationen berücksichtigt werden sollten. Das zweite Ziel dieser Arbeit ist die Etablierung einer neuen, hybriden (nichtlinearerFiniten-Elemente / linearer Randelemente) -Multiskalenmethode, die die Vorteile beider Verfahren kombiniert. Die vorgestellte Hybrid-Multiskalen-Methode hat sich als geeignetes Werkzeug erwiesen, um den Reibkoeffizienten mit einem angemessenen Genauigkeitsgrad für niedrige Gleitgeschwindigkeiten zu untersuchen; Sie ermöglicht eine schnellere Berechnung des Reibkoeffizienten als das nichtlineare FE-Modell

Rising from the ground: Distributed drag parameterization of urban environments for numerical weather prediction

Urban environments in numerical weather prediction models are currently parameterised as part of the atmosphere-surface exchange at ground level. The vertical structure of buildings is represented by the average height, which does not account for heterogeneous building forms at the subgrid level. This thesis investigates aerodynamic effects of subgrid heterogeneity and develops a distributed drag parameterization that represents buildings at their real height. Urban flow at neighbourhood scale is studied using large-eddy simulations of idealised, heterogeneous urban morphologies with identical building plan area index and frontal area index. Large differences in estimated roughness parameters and total canopy drag, which are strongly correlated to the maximum height and height variability of the buildings, mean-wind profiles and vertical momentum transport suggest that subgrid heterogeneity is inadequately represented by current models. A height-dependent frontal area function is introduced to capture a vertical urban morphology profile with full height extent and variability. The morphology profiles correlate to the distinct distributed-drag profiles of the simulations, and a drag parameterization was derived by a third-order polynomial function of the morphology profiles. Morphology profiles were calculated for Greater London and parameterised by an exponential distribution with the ratio of maximum to mean building height as parameter. A case study with the high-resolution London Model and the new drag parameterization appears to capture more realistic features of the urban boundary layer compared to the standard parameterization. The simulation showed increased horizontal spatial variability in total surface stress, identifying a broad range of morphology features (densely built-up areas, high-rise building clusters, parks and the river). Vertical effects include heterogeneous wind profiles, extended building wakes, and internal boundary layers. This thesis demonstrates the potential of height-distributed urban parameterizations to improve urban weather forecasting, with further research into distribution of heat- and moisture-exchange necessary.Open Acces

Interfacial Dissipative Phenomena in Tribomechanical Systems

The book is a collection of articles on the themes of contact mechanics and non-linear dynamics. In particular, the contribution focus on the mechanisms that lead to interfacial energy dissipation, which is a crucial quantity to determine in order to correctly predict the non-linear dynamic response of mechanical systems. The book is a collection of nine journal papers, among those one editorial, one review paper, and seven articles. The papers consider different dissipative mechanisms, such as Coulomb friction, interfacial adhesion, and viscoelasticity, and study how the system response and stability is influenced by the interfacial interactions. The review paper describes old and recent test rigs for friction and wear measurements, focusing on their performance and range of operability

Characterization and Generation of 3D Realistic Geological Particles with Metaball Descriptor based on X-Ray Computed Tomography

The morphology of geological particles is crucial in determining its granular characteristics and assembly responses. In this paper, Metaball-function based solutions are proposed for morphological characterization and generation of three-dimensional realistic particles according to the X-ray Computed Tomography (XRCT) images. For characterization, we develop a geometric-based Metaball-Imaging algorithm. This algorithm can capture the main contour of parental particles with a series of non-overlapping spheres and refine surface-texture details through gradient search. Four types of particles, hundreds of samples, are applied for evaluations. The result shows good matches on key morphological indicators(i.e., volume, surface area, sphericity, circularity, corey-shape factor, nominal diameter and surface-equivalent-sphere diameter), confirming its characterization precision. For generation, we propose the Metaball Variational Autoencoder. Assisted by deep neural networks, this method can generate 3D particles in Metaball form, while retaining coessential morphological features with parental particles. Additionally, this method allows for control over the generated shapes through an arithmetic pattern, enabling the generation of particles with specific shapes. Two sets of XRCT images different in sample number and geometric features are chosen as parental data. On each training set, one thousand particles are generated for validations. The generation fidelity is demonstrated through comparisons of morphologies and shape-feature distributions between generated and parental particles. Examples are also provided to demonstrate controllability on the generated shapes. With Metaball-based simulations frameworks previously proposed by the authors, these methods have the potential to provide valuable insights into the properties and behavior of actual geological particles