Discrete Surface Research Articles

An isogeometric b-rep mortar-based mapping method for non-matching grids in fluid-structure interaction

In this study the isogeometric B-Rep mortar-based mapping method for geometry models stemming directly from Computer-Aided Design (CAD) is systematically augmented and applied to partitioned Fluid-Structure Interaction (FSI) simulations. Thus, the newly proposed methodology is applied to geometries described by their Boundary Representation (B-Rep) in terms of trimmed multipatch Non-Uniform Rational B-Spline (NURBS) discretizations as standard in modern CAD. The proposed isogeometric B-Rep mortar-based mapping method is herein extended for the transformation of fields between a B-Rep model and a low order discrete surface representation of the geometry which typically results when the Finite Volume Method (FVM) or the Finite Element Method (FEM) are employed. This enables the transformation of such fields as tractions and displacements along the FSI interface when Isogeometric B-Rep Analysis (IBRA) is used for the structural discretization and the FVM is used for the fluid discretization. The latter allows for diverse discretization schemes between the structural and the fluid Boundary Value Problem (BVP), taking into consideration the special properties of each BVP separately while the constraints along the FSI interface are satisfied in an iterative manner within partitioned FSI. The proposed methodology can be exploited in FSI problems with an IBRA structural discretization or to FSI problems with a standard FEM structural discretization in the frame of the Exact Coupling Layer (ECL) where the interface fields are smoothed using the underlying B-Rep parametrization, thus taking advantage of the smoothness that the NURBS basis functions offer. All new developments are systematically investigated and demonstrated by FSI problems with lightweight structures whereby the underlying geometric parametrizations are directly taken from real-world CAD models, thus extending IBRA into coupled problems of the FSI type.

Discrete Oxidation of a Hard Carbide Tool

Comparative investigations of the effect of discrete surface hardening by standard ion-plasma technology and discrete oxidation technology on the structure and hardness of high-speed steels are carried out. It is shown that, after hardening in the ion-plasma installation on the surface and in the thickness of the layer, droplet-shaped defects, craters and bundles are formed. Metallographic studies showed that the hardened discrete oxidation layer after repeated hardening has a dense, uniform structure. It has been established that the discrete oxidation technology allows to increase the wear resistance of a complex-profile cutting tool 2 times more, compared to a tool hardened by standard ion-plasma technology after regrinding.

The Role of Grain Size and Effective Normal Stress on Localization and the Frictional Stability of Simulated Quartz Gouge

AbstractFor earthquakes to occur on tectonic faults deformation localizes onto discrete slip surfaces within the gouge material of the fault core. Here, we investigate how localization is promoted in quartz gouge, a material known to exhibit unstable stick‐slip behavior, by assessing the role of grain size and effective normal stress () on microstructural evolution and frictional behavior. We observe stable sliding, slow‐slip instability, and stick‐slip with increasing displacement. We find that initially fine‐grained gouge and high promotes unstable stick‐slip behavior, whereas slow‐slip is more prevalent at low . Microstructural analyses of the sheared gouges show that stick‐slip behavior occurs after localization of deformation on to discrete Y‐shears, which undergo a significant cataclastic grain size reduction relative to the bulk of the gouge, a process enhanced by high . Our results show that localization and instability are promoted by high effective normal stress and small grain size.

The Ribaucour families of discrete R-congruences

While a generic smooth Ribaucour sphere congruence admits exactly two envelopes, a discrete R-congruence gives rise to a 2-parameter family of discrete enveloping surfaces. The main purpose of this paper is to gain geometric insights into this ambiguity. In particular, discrete R-congruences that are enveloped by discrete channel surfaces and discrete Legendre maps with one family of spherical curvature lines are discussed.

Determination of vehicle requirements of AGV system based on discrete event simulation and response surface methodology

The determination of AGV vehicle requirements in a manufacturing system has a great impact on the system performance. This paper first defines the AGV vehicle requirement determination as a general optimization problem, and secondly develops a new AGV vehicle requirement determination method capable of effective solving the problem. This method features with the combination of discrete event simulation (DES), sensitivity analysis, fractional factorial design (FFD) and response surface methodology (RSM). Tests and comparisons with other simulation based methods have shown that the proposed method combining the simulation method with analytical method, can make full use of their respective advantages and overcome the defects of existing methods. It is more practical.

Debye-Hückel Free Energy of an Electric Double Layer with Discrete Charges Located at a Dielectric Interface.

Poisson–Boltzmann theory provides an established framework to calculate properties and free energies of an electric double layer, especially for simple geometries and interfaces that carry continuous charge densities. At sufficiently small length scales, however, the discreteness of the surface charges cannot be neglected. We consider a planar dielectric interface that separates a salt-containing aqueous phase from a medium of low dielectric constant and carries discrete surface charges of fixed density. Within the linear Debye-Hückel limit of Poisson–Boltzmann theory, we calculate the surface potential inside a Wigner–Seitz cell that is produced by all surface charges outside the cell using a Fourier-Bessel series and a Hankel transformation. From the surface potential, we obtain the Debye-Hückel free energy of the electric double layer, which we compare with the corresponding expression in the continuum limit. Differences arise for sufficiently small charge densities, where we show that the dominating interaction is dipolar, arising from the dipoles formed by the surface charges and associated counterions. This interaction propagates through the medium of a low dielectric constant and alters the continuum power of two dependence of the free energy on the surface charge density to a power of 2.5 law.

Mesh size objective fatigue damage propagation in laminated composites using the multiscale discrete damage theory

A mesh size objective multiscale modeling is developed for fatigue failure prediction of long fiber-reinforced composites based on the multiscale discrete damage theory (MDDT). MDDT tracks the failure processes along discrete failure surfaces at the microscale and concurrently bridges it to continuum-based description of damage at the macroscale. The proposed approach achieves mesh-size objectivity by introducing a length scale operator which effectively adjusts the microstructure size as a function of macroscale element size; and when a non-additive fatigue damage evolution law is used to describe progressive cracking at the microscale. Temporal multiscaling is used to track long-term fatigue damage evolution with high computational efficiency. The performance of the proposed model is demonstrated by the analysis of unnotched and open-hole laminate configurations. The results indicate mesh-size objectivity even in the presence of multiple failure mechanisms including splitting, delamination and transverse matrix cracks. The interaction between splitting and transverse cracks is investigated by a parametric study, which reveals the effects of mode I and mode II dominated degradation on the failure behavior under fatigue loading.

Full-Field Strain Reconstruction Using Uniaxial Strain Measurements: Application to Damage Detection

This work investigates the inverse problem of reconstructing the continuous displacement field of a structure using a spatially distributed set of discrete uniaxial strain data. The proposed technique is based on the inverse Finite Element Method (iFEM), which has been demonstrated to be suitable for full-field displacement, and subsequently strain, reconstruction in beam and plate structures using discrete or continuous surface strain measurements. The iFEM uses a variationally based approach to displacement reconstruction, where an error functional is discretized using a set of finite elements. The effects of position and orientation of uniaxial strain measurements on the iFEM results are investigated, and the use of certain strain smoothing strategies for improving reconstruction accuracy is discussed. Reconstruction performance using uniaxial strain data is examined numerically using the problem of a thin plate with an internal crack. The results obtained highlight that strain field reconstruction using the proposed strategy can provide useful information regarding the presence, position, and orientation of damage on the plate.

On Discrete Conjugate Semi-Geodesic Nets

Abstract We introduce two canonical discretizations of nets on generic surfaces, which consist of an one-parameter family of geodesics and its associated family of conjugate lines. The two types of “discrete conjugate semi-geodesic nets” constitute discrete focal nets of circular nets, which mimics the classical connection between surfaces parametrized in terms of curvature coordinates and their focal surfaces on which one corresponding family of coordinate lines are geodesics. The discrete surfaces constructed in this manner are termed circular-geodesic and conical-geodesic nets, respectively, and may be characterized by compact angle conditions. Geometrically, circular-geodesic nets are constructed via normal lines of circular nets, while conical-geodesic nets inherit their name from their intimately related conical nets, which also discretize curvature line parametrized surfaces. We establish a variety of properties of these discrete nets, including their algebraic and geometric 3D consistency, with the latter playing an important role in (integrable) discrete differential geometry.

Discrete Gaussian Curvature Flow for Piecewise Constant Gaussian Curvature Surface

A method is presented for generating a discrete piecewise constant Gaussian curvature (CGC) surface. An energy functional is first formulated so that its stationary point is the linear Weingarten (LW) surface, which has a property such that the weighted sum of mean and Gaussian curvatures is constant. The CGC surface is obtained using the gradient derived from the first variation of a special type of the energy functional of the LW surface and updating the surface shape based on the Gaussian curvature flow. A filtering method is incorporated to prevent oscillation and divergence due to unstable property of the discretized Gaussian curvature flow. Two techniques are proposed to generate a discrete piecewise CGC surface with preassigned internal boundaries. The step length of Gaussian curvature flow is adjusted by introducing a line search algorithm to minimize the energy functional. The effectiveness of the proposed method is demonstrated through numerical examples of generating various shapes of CGC surfaces.

Geometry of random potentials: Induction of two-dimensional gravity in quantum Hall plateau transitions

In the context of the Integer Quantum Hall plateau transitions, we formulate a specific map from random landscape potentials onto 2D discrete random surfaces. Critical points of the potential, namely maxima, minima and saddle points uniquely define a discrete surface $S$ and its dual $S^*$ made of quadrangular and $n-$gonal faces, respectively, thereby linking the geometry of the potential with the geometry of discrete surfaces. The map is parameter-dependent on the Fermi level. Edge states of Fermi lakes moving along equipotential contours between neighbour saddle points form a network of scatterings, which define the geometric basis, in the fermionic model, for the plateau transitions. The replacement probability characterizing the network model with geometric disorder recently proposed by Gruzberg, Kl\"umper, Nuding and Sedrakyan, is physically interpreted within the current framework as a parameter connected with the Fermi level.

Three dimensional seismic deformation-shear strain-swelling performance of America-California Oroville Earth-Fill Dam

Structural design of the vertical displacements and shear strains in the earth fill (EF) dams has great importance in the structural engineering problems. Moreover, far fault earthquakes have significant seismic effects on seismic damage performance of EF dams like the near fault earthquakes. For this reason, three dimensional (3D) earthquake damage performance of Oroville dam is assessed considering different far-fault ground motions in this study. Oroville Dam was built in United States of America-California and its height is 234.7 m (770 ft.). 3D model of Oroville dam is modelled using FLAC3D software based on finite difference approach. In order to represent interaction condition between discrete surfaces, special interface elements are used between dam body and foundation. Non-reflecting seismic boundary conditions (free field and quiet) are defined to the main surfaces of the dam for the nonlinear seismic analyses. 6 different far-fault ground motions are taken into account for the full reservoir condition of Oroville dam. According to nonlinear seismic analysis results, the effects of far-fault ground motions on the nonlinear seismic settlement and shear strain behaviour of Oroville EF dam are determined and evaluated in detail. It is clearly seen that far-fault earthquakes have very significant seismic effects on the settlement-shear strain behaviour of EF dams and these earthquakes create vital important seismic damages on the swelling behaviour of dam body surface. Moreover, it is proposed that far-fault ground motions should not be ignored while modelling EF dams.

Oil/water separation membranes with a fluorine island structure for stable high flux

Membranes with fluorine island structures consist of discrete low surface energy (LSE) domains at sub-microscale and consecutive hydrophilic domains. The former can effectively control oil fouling while the latter can provide high basic flux.

A method for non-contact determination of the amplitude of deformation of accumulated operational damage to a metal structure

It has been shown that to study the kinetics of operational damage to materials and structural elements, it is necessary to develop modern means and methods for diagnosing damage occurring in laboratory samples and structural elements. In this paper, in order to determine the deformation state of the surface layer of a structural material, using austenitic steel samples as an example, we used the method of optical measurement of microplastic deformation, which is based on the correlation between the energy of a coherent light source reflected by the surface of a metal polycrystal and the amplitude of microplastic deformation of the deformed surface. According to this method, the local area of the material sample surface under investigation is irradiated at certain stages of loading with coherent light beams with a wavelength that corresponds to the scale of localization of microplastic deformations of the sample surface. An optical system is used to generate an image of the speckle-modulated beam, which has the parameters of the deformed surface relief. As a measure of the depth of the deformation relief, the integral value of the image brightness intensity parameter is used as the ratio of the number of light pixels to the total number of pixels in the specklegram image. As a result of the analysis of the statistical parameters of the specklegram, which correlate with the characteristics of the state of microplastic deformation of the surface of austenitic steel samples, the characteristic parameters of the scattered damage to the structure of discrete deformations of the surface of a metal polycrystal were determined. On the basis of the experimental data obtained, the regularities of the influence of static and cyclic deformation on the shape of the distribution of discrete surface properties were revealed. In particular, as a result of analyzing the statistical characteristics of the correlation diagrams, a linear dependence of the parameters of the distribution of discrete properties of the deformed surface relief on the loading factor was obtained.

Differential geometry of discrete surfaces

Differential geometry of discrete surfaces

Increased Wear Resistance of High-Speed Tools Due to Diffusion Discrete Oxidation

Comparative studies of the effect of discrete surface hardening by standard ion-plasma technology and discrete oxidation technology on wear resistance have been carried out. Metallographic studies have shown that discrete oxidation has a polycrystalline structure. It was found that the technology of discrete oxidation makes it possible to increase the hardness by 31% in relation to the uncoated material, and the wear resistance of the cutting tool with oxidation is 1.5-3 times higher than that of the tool hardened by the standard ion-plasma technology.

The case of the braided river that meandered: Bar assemblages as a mechanism for meandering along the pervasively braided Missouri River, USA

Abstract This paper offers a mechanism for meandering in an otherwise braided river and then discusses its general implications for river processes and fluvial deposits. Braided rivers manage to meander without the paired point bars and single-thread channels that are instrumental in developing bends in other meandering rivers. The driving processes for meandering in these braided systems remain enigmatic. The unchannelized and prechannelized Missouri River is an example of a braided meandering river, and it provides an opportunity to gain insight into these processes. This study utilized historical maps, sequential air photos, and surficial geologic maps both to define the processes by which this braided river meanders, and to characterize the deposits produced by these processes. These data show that the Missouri River meanders by building point assemblages instead of point bars. Repeated accretion of midchannel and lateral bars to a common point on the bank forces development of a meander bend around a point assemblage comprising multiple amalgamated compound bars. This differs from single-thread systems, which expand and translate bends around a single compound point bar. Alternating development of point assemblages forces meandering over successions of meander bends. Braided meander loops grow by expansion and translation like single-thread rivers, but they also may contract to produce counterpoint assemblages. Contraction appears to be the more common means of loop abandonment compared to loop cutoff for the braided Missouri River. This differs from single-thread meandering rivers, where contraction is limited, and loop cutoff is consistently the dominant abandonment process. Deposits of the braided meandering Missouri River differ from deposits of single-thread rivers in the rarity of both meander scrolls and single-thread channel fills. Instead, point and counterpoint assemblages comprise fusiform bar elements bound by small filled remnants of anabranch channels. These assemblages are commonly bound by meander cutbank scars. Cutbank scars associated with contraction, however, tend to be composite rather than discrete erosional surfaces, and they do not tend to bind river-scale abandoned channel fills. The braided meandering Missouri River also differs from wandering rivers because wandering rivers meander by building compound bars instead of assemblages, are more gravelly, have less pervasive and much less mobile midchannel bars, and appear to reflect a transitional intermediate pattern instead of a stable hybrid pattern. Braiding and meandering both expend stream power, and both are mechanisms for achieving channel equilibrium. The Missouri River exhibits both of these processes in tandem; thus, meandering and braiding are not mutually exclusive processes. Braided meandering rivers like the Missouri River are less common than either straight-braided or single-thread-meandering rivers, but they are not unique. The long-held distinction of braided versus meandering patterns for rivers thus may be practical but is not definitive.

Voss Surfaces: A Design Space for Geodesic Gridshells

The design of envelopes with complex geometries often leads to construction challenges. To overcome these difficulties, resorting to discrete differential geometry proved successful by establishing close links between mesh properties and the existence of good fabrication, assembling and mechanical properties. In this paper, the design of a special family of structures, called geodesic shells, is addressed using Voss nets, a family of discrete surfaces. The use of discrete Voss surfaces ensures that the structure can be built from simply connected, initially straight laths, and covered with flat panels. These advantageous constructive properties arise from the existence of a conjugate network of geodesic curves on the underlying smooth surface. Here, a review of Voss nets is presented and particular attention is given to the projection of normal vectors on the unit sphere. This projection, called Gauss map, creates a dual net which unveils the remarkable characteristics of Voss nets. Then, based on the previous study, two generation methods are introduced. One enables the exploration and the deformation of Voss nets while the second provides a more direct computational technique. The application of theses methodologies is discussed alongside formal examples.

Bijective projection in a shell

We introduce an algorithm to convert a self-intersection free, orientable, and manifold triangle mesh T into a generalized prismatic shell equipped with a bijective projection operator to map T to a class of discrete surfaces contained within the shell whose normals satisfy a simple local condition. Properties can be robustly and efficiently transferred between these surfaces using the prismatic layer as a common parametrization domain. The combination of the prismatic shell construction and corresponding projection operator is a robust building block readily usable in many downstream applications, including the solution of PDEs, displacement maps synthesis, Boolean operations, tetrahedral meshing, geometric textures, and nested cages.

Merzifon–Esençay splay fault within the North Anatolian Fault system: segmentation and timing of the last two surface faulting events on Esençay segment

North Anatolian Fault (NAF) as a seismically active intracontinental plate boundary is characterized by splay faults in a half fishbone geometry, reaching into the Anatolian plate. Recent crustal deformations within Central Anatolia Tectonic Province are accommodated by dextral and sinistral strike-slip splay fault systems. Sinistral splays extend conjugate to the NAF and subparallel to the East Anatolian Fault (EAF), while the dextral splays are subparallel to the NAF. Sungurlu–Ezinepazar (SEF) and Merzifon–Esencay (MEF) faults are two major dextral splays bifurcating from Niksar pull-apart basin, which distinguish eastern and central NAF. Geodetic and geological data suggest a total of 3 mm/year slip rate along these splays in a setting of slip partitioning with the main strand of the NAF. These two splays undertake 12–13% of the lateral motion within a broad deformation zone of the NAF where the MEF accommodates 1/3 of this amount. 227 km-long MEF is divided into six fault segments, which are separated from each other’s by releasing and restraining jogs. Cumulative offsets up to 3.0 km on Kizilirmak River valley and tributaries of Yesilirmak River since latest Pliocene-Early Pleistocene (~ 3 Ma) suggest an approximately 1 mm/year long-term geological slip rate on the MEF. Paleoseismological findings from Esencay segment reveal two discrete surface faulting events within the last 7 ka with a return period of maximum 2200 and minimum 1320 years. The lapse time since the last event is about 3700 years. This implies ~ 3.7 m of strain accumulation on the Esencay segment for present. The segments have the potential to produce induvial earthquakes with magnitudes varying between Mw 6.8 and Mw 7.2. Existing information imply that major fault splays have the potential to produce multi-segment large earthquakes within the NAF zone in addition to well-known Yedisu and Central Marmara seismic gaps.