Rigid Flat Surface Research Articles

Bifurcation analysis of pressure-induced detachment of a rod adhered to a plate

We study the lift of an elastica adhering to a flat rigid surface induced by a pressure difference. Adhesion is modelled by a cohesive force that decreases linearly with separation. Using a nonlinear local analysis, we determine the bifurcation diagram that governs the peeling process under quasi-static conditions. We show that the delamination emerges through a discontinuous transition: a normal form of the bifurcation diagram allows us to draw in a simple way the main physical mechanism, elucidating the local validity of the theory at the transition. We predict that the pressure, as a function of the detachment length, undergoes an initial drop followed by an approximately constant behaviour, while the detachment length at the transition is always finite and is roughly proportional to the elasto-adhesion length. This analysis can be the starting point to understand more complex-related problems that arise in fracture mechanics or in biology, such as testing of adhesives in a flowfield and the arterial dissection.

Fluid-mediated impact of soft solids

A viscous, lubrication-like response can be triggered in a thin film of fluid squeezed between a rigid flat surface and the tip of an incoming projectile. We develop a scaling for this viscous approach stage of fluid-mediated normal impact, applicable to soft impactors. Under the assumption of mediating fluid being incompressible, the impacting solid displays two limit regimes: one dominated by elasticity, and the other by inertia. The transition between the two is predicted by a dimensionless parameter, which can be interpreted as the ratio between two time scales that are the time that it takes for the surface waves to warn the leading edge of the impactor of the forthcoming impact, and the characteristic duration of the final viscous phase of the approach. Additionally, we elucidate why nearly incompressible solids feature (a) substantial ‘gliding’ prior to contact at the transition between regimes, (b) the largest size of entrapped bubble between the deformed tip of the impactor and the flat surface, and (c) a sudden drop in entrapped bubble radius past the transition between regimes. Finally, we argue that the above time scale ratio (a dimensionless number) can govern the different dynamics reported experimentally for a fluid droplet as a function of its viscosity and surface tension.

Contact mechanical behavior and leakage prediction of metal lenticular gaskets in bolt flange joints of ultrahigh pressure pipelines

Metal lenticular gaskets have been widely applied in the bolt flange joints of high and ultrahigh pressure pipelines due to their semi-self-tightening sealing properties. However, research on the leakage prediction of the metal lenticular gaskets is still lacking, which limits their further optimal design and sealing performance improvement. In this paper, an elastoplastic contact mechanics analysis of a metal lenticular gasket used in the bolted flange joint of ultra-high pressure polyethylene pipelines was firstly carried out. The analytical formulas of contact stress and contact width were derived and compared with corresponding numerical results. Then, based on the surface topography measurement, a leakage model was established, in which the pipe surface was simplified to a smooth rigid flat surface, and the gasket surface was simplified to an equivalent rough surface composed of identical wedges. Finally, an analytical leakage prediction formula for the metal lenticular gasket was proposed. In addition, the effects of influence factors on leakage rate were discussed. It is shown that the analytical formulas can accurately calculate the contact stress and contact width in elastoplastic contact. The leakage rate increases with the decrease of the bolt load and the increase of internal pressure. For the ultrahigh pressure pipeline with internal pressure of 200 MPa, the minimum bolt load should be ensured to be higher than 120 kN in order to meet the T5 tightness level. In addition, the initial contact diameter is basically proportional to the leakage rate, while the change of gasket inclination angle has little effect on the leakage rate. Therefore, the contact diameter can be designed to be as small as possible within a reasonable range. This work can provide a theoretical basis for the sealing optimal design of metal lenticular gaskets.

Traveling wave solutions to the inclined or periodic free boundary incompressible Navier-Stokes equations

This paper concerns the construction of traveling wave solutions to the free boundary incompressible Navier-Stokes system. We study a single layer of viscous fluid in a strip-like domain that is bounded below by a flat rigid surface and above by a moving surface. The fluid is acted upon by a bulk force and a surface stress that are stationary in a coordinate system moving parallel to the fluid bottom. We also assume that the fluid is subject to a uniform gravitational force that can be resolved into a sum of a vertical component and a component lying in the direction of the traveling wave velocity. This configuration arises, for instance, in the modeling of fluid flow down an inclined plane. We also study the effect of periodicity by allowing the fluid cross section to be periodic in various directions. The horizontal component of the gravitational field gives rise to stationary solutions that are pure shear flows, and we construct our solutions as perturbations of these by means of an implicit function argument. An essential component of our analysis is the development of some new functional analytic properties of a scale of anisotropic Sobolev spaces, including that these spaces are an algebra in the supercritical regime, which may be of independent interest.

Higher-order turbulence around simple and complex piers using particle image velocimetry

The objective of this study was to explore the higher-order turbulence statistics of flow and turbulent length scales around a complex pier (CP) and compare the results with those for a simple pier (SP). The velocity data were recorded in a laboratory flume using particle image velocimetry (PIV). The PIV data were analysed to estimate the velocity fluctuations of third order, turbulence production and dissipation rates, turbulent length scales and the contributions of burst–sweep events to the total Reynolds shear stress around the piers mounted on a rigid flat surface. The skewness and advection coefficients indicated a more asymmetric distribution of velocity fluctuations for the SP than for the CP. Ejection and sweep events illustrated the dominance of similar strengths for an extended period, downstream of the piers. The upstream turbulent kinetic energy production was similar for both piers, while the upstream dissipation rate was higher for the CP. The length scales were greater at the upstream for the case of the SP while, downstream, they were greater for the CP. The findings of this work demonstrate the importance of a pile cap in restricting downward-moving flow by showing a lower magnitude of scour-inducing turbulence parameters for the CP as compared with the SP.

Leakage Threshold of a Saddle Point

The threshold condition for leakage inception is of great interest to many engineering applications, and it is essential for seal design. In the current study, the leakage threshold is studied by means of a numerical method for a mechanical contact problem between an elastic bi-sinusoidal surface and a rigid flat surface. The coalesce process of the contact patches is first investigated, and a generalized form of solution for the relation between the contact area ratio and the average applied pressure is acquired. The current study shows that the critical value of the average applied pressure and the corresponding contact area required to close the percolation path can be represented as a power law of a shape parameter, if the effect of the hydrostatic load from the pressurized fluid is ignored. With contact patches merged under a constant applied load, the contact breakup process is investigated with elevated sealed fluid pressure condition, and it is shown that the leakage threshold is a function of the excess pressure, which is defined as a ratio between the average applied pressure and the critical pressure under dry contact conditions.Graphical abstract

Pressure fields produced by single-bubble collapse near a corner

Damage from repeated bubble collapse to neighboring rigid objects is a consequence of cavitation. Few studies exist on the dynamics of bubbles collapsing near a corner, i.e., two flat rigid surfaces making a right angle. Here we solve the three-dimensional compressible Navier-Stokes equations for gas and liquid flows to quantify the pressure fields. The second wall affects the collapse by (i) causing the re-entrant jet to no longer point in the direction normal to the closest wall but at an angle toward the corner and (ii) causing the maximum wall pressure to be observed in the corner when the bubble is sufficiently close to equidistant from each boundary due to shock reflections.

Fabrication and Characterization Techniques of In Vitro 3D Tissue Models.

The culturing of cells in the laboratory under controlled conditions has always been crucial for the advancement of scientific research. Cell-based assays have played an important role in providing simple, fast, accurate, and cost-effective methods in drug discovery, disease modeling, and tissue engineering while mitigating reliance on cost-intensive and ethically challenging animal studies. The techniques involved in culturing cells are critical as results are based on cellular response to drugs, cellular cues, external stimuli, and human physiology. In order to establish in vitro cultures, cells are either isolated from normal or diseased tissue and allowed to grow in two or three dimensions. Two-dimensional (2D) cell culture methods involve the proliferation of cells on flat rigid surfaces resulting in a monolayer culture, while in three-dimensional (3D) cell cultures, the additional dimension provides a more accurate representation of the tissue milieu. In this review, we discuss the various methods involved in the development of 3D cell culture systems emphasizing the differences between 2D and 3D systems and methods involved in the recapitulation of the organ-specific 3D microenvironment. In addition, we discuss the latest developments in 3D tissue model fabrication techniques, microfluidics-based organ-on-a-chip, and imaging as a characterization technique for 3D tissue models.

Junction flow inside and around three-row cylindrical group on rigid flat surface

Groups of bluff bodies are widespread in nature and technology. These are the supports of bridge crossings, high-rise buildings in cities, offshore drilling and wind platforms, algae and vegetation in the seas and rivers, forests and other objects. The flow of air or water around such structures has a complex vortex and jet character and requires significant efforts in the process of scientific research to improve the environmental situation and reduce material and technical costs in the process of operating such structures. The purpose of the research is study the features of the generation and evolution of vortex and jet flows near and inside the three-row group of cylinders, which are installed on the rigid flat surface. The results of experimental studies showed that the flow around the group of cylinders had a complex unsteady nature, which is due to the interaction of vortex and jet flows typical flow elements with the three-row cylindrical group, which was located installed on the rigid flat surface. The three-row cylindrical group (31 piles with a diameter of 0.027 m) is a model of a bridge support, which was streamlined at a velocity of 0.06 m/s to 0.5 m/s (Reynolds number Red=(1600–6700) and Froude number Fr=(0.04–0.18)). Visual investigations and measurements of the velocity field were carried out inside and around the three-row structure. The features of the formation and evolution of vortex and jet flows inside and near the cylindrical group were established. Integral, spectral and correlation characteristics of the velocity fluctuation field were obtained. Mean, root-mean-square values of velocity and probability density functions of velocity fluctuations integrally displayed the changes in the velocity field in the spatial and temporal domain in the junction area of grillage and plate. The power spectral densities of velocity fluctuations and mutual correlation functions made it possible to study the features of the generation of the velocity fluctuation field in the frequency domain and its interrelationships in space. It was revealed that the velocity field inside the horseshoe vortex structures was multimodal. The spectral levels of velocity fluctuations at the periphery of the quasistable horseshoe vortex structures were higher than in the cores of these structures. The highest levels of the velocity fluctuation spectra were observed in front of the second lateral cylinder where the interaction of the vortex and jet flows took place. Discrete peaks in the spectral levels of velocity fluctuations are found at the frequencies of formation of large-scale wake vortices and the frequencies of formation of small-scale vortex structures of the shear layer, which are due to the Kelvin-Helmholtz instability. It has been established that the frequency of formation of shear layer vortices is (10–40) times higher than the frequency of formation of wake vortices.

A three-dimensional discrete model for approximating the deformation of a viral capsid subjected to lying over a flat surface in the static and time-dependent case

In this paper, we present a three-dimensional discrete model governing the deformation of a viral capsid, modelled as a regular icosahedron and subjected not to cross a given flat rigid surface on which it initially lies in correspondence of one vertex only. First, we set up the model in the form of a set of variational inequalities posed over a non-empty, closed and convex subset of a suitable space. Second, we show the existence and uniqueness of the solution for the proposed model. Third, we numerically test this model and we observe that the outputs of the numerical experiments comply with physics. Finally, we establish the existence of solutions for the corresponding time-dependent version of the obstacle problem under consideration.

Traveling Wave Solutions to the Free Boundary Incompressible Navier‐Stokes Equations

AbstractIn this paper we study a finite‐depth layer of viscous incompressible fluid in dimension , modeled by the Navier‐Stokes equations. The fluid is assumed to be bounded below by a flat rigid surface and above by a free, moving interface. A uniform gravitational field acts perpendicularly to the flat surface, and we consider the cases with and without surface tension acting on the free interface. In addition to these gravity‐capillary effects, we allow for a second force field in the bulk and an external stress tensor on the free interface, both of which are posited to be in traveling wave form, i.e., time‐independent when viewed in a coordinate system moving at a constant velocity parallel to the rigid lower boundary. We prove that, with surface tension in dimension and without surface tension in dimension , for every nontrivial traveling velocity there exists a nonempty open set of force and stress data that give rise to traveling wave solutions. While the existence of inviscid traveling waves is well‐known, to the best of our knowledge this is the first construction of viscous traveling wave solutions.Our proof involves a number of novel analytic ingredients, including: the study of an overdetermined Stokes problem and its underdetermined adjoint problem, a delicate asymptotic development of the symbol for a normal‐stress to normal‐Dirichlet map defined via the Stokes operator, a new scale of specialized anisotropic Sobolev spaces, and the study of a pseudodifferential operator that synthesizes the various operators acting on the free surface functions. © 2022 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.

Rough surface contact under creep conditions

A pressing concern in superplastic forming (SPF) is the ability to quantitatively model to effectively design tooling and assess process viability. Current finite element method simulations for SPF generally do not include the evolutionary nature of friction under creep conditions. The presence of creep strain leads to junction growth and saturated contact areas at longer time scales than conventional metal forming; therefore, friction models that ignore creep-induced strains will underpredict asperity contact and friction levels. In this work, a new micro-contact model of a rough surface in contact with a rigid flat surface is created to predict asperity flattening under creep behavior. A semi-empirical equation of the real contact area and friction at different SPF conditions is established.

An asperity-based statistical model for the adhesive friction of elastic nominally flat rough contact interfaces

Contact mechanics-based models for the friction of nominally flat rough surfaces have not been able to adequately capture certain key experimentally observed phenomena, such as the transition from a static friction peak to a lower level of sliding friction and the shear-induced contact area reduction that has been observed in the pre-sliding regime especially for soft materials. Here, we propose a statistical model based on physically-rooted contact mechanics laws describing the micromechanics of individual junctions. The model considers the quasi-static tangential loading, up to full sliding, of the contact between a smooth rigid flat surface and a nominally flat linear elastic rough surface comprising random independent spherical asperities, and accounts for the coupling between adhesion and friction at the micro-junction level. The model qualitatively reproduces both the macroscopic shear-induced contact area reduction and, remarkably, the static friction peak without the need to explicitly introduce two different friction levels. It also demonstrates how the static friction peak and contact area evolution depend on the normal load and certain key microscale interface properties such as surface energy, mode mixity and frictional shear strength. “Tougher” interfaces (i.e. with larger surface energy and smaller mode mixity parameter) are shown to result in a larger real contact area and a more pronounced static friction peak. Overall, this work provides important insights about how key microscale properties operating at the asperity level can combine with the surface statistics to reproduce important macroscopic responses observed in rough frictional soft contact experiments.

Modelling virus contact mechanics under atomic force imaging conditions

In this paper, we present a discrete model governing the deformation of a convex regular polygon subjected not to cross a given flat rigid surface, on which it initially lies in correspondence of one point only. First, we set up the model in the form of a set of variational inequalities posed over a non-empty, closed and convex subset of a suitable Euclidean space. Second, we show the existence and uniqueness of the solution. The model provides a simplified illustration of processes involved in virus imaging by atomic force microscopy: adhesion to a surface, distributed strain, relaxation to a shape that balances adhesion and elastic forces. The analysis of numerical simulations results based on this model opens a new way of estimating the contact area and elastic parameters in virus contact mechanics studies.

Effects of Including a Penetration Test in Motorcyclist Helmet Standards: Influence on Helmet Stiffness and Impact Performance

Regulation ECE-22.05/06 does not require a helmet penetration test. Penetration testing is controversial since it has been shown that it may cause the helmet to behave in a non-desirable stiff way in real-world crashes. This study aimed to assess the effect of the penetration test in the impact performance of helmets. Twenty full-face motorcycle helmets were penetration tested at multiple locations of the helmet shell. Then, 10 helmets were selected and split into two groups (hard shell and soft shell) depending on the results of the penetration tests. These 10 helmets were then drop tested at front, lateral, and top areas at two different impact speeds (5 m/s and 8.2 m/s) to assess their impact performance against head injuries. The statistical analyses did not show any significant difference between the two groups (hard/soft shell) at 5 m/s. Similar results were observed at 8.2 m/s, except for the top area of the helmet in which the peak linear acceleration was significantly higher for the soft shell group than for the hard shell group (230 ± 12 g vs. 211 ± 11 g; p-value = 0.038). The results of this study suggest that a stiffer shell does not necessarily cause helmets to behave in a stiffer way when striking rigid flat surfaces. These experiments also showed that hard shell helmets can provide better protection at higher impact speeds without damaging helmet performance at lower impact speeds.

Junction Flow About Cylindrical Group on Rigid Flat Surface

Junction Flow About Cylindrical Group on Rigid Flat Surface

Investigation of Shape Transformations of Vesicles, Induced by Their Adhesion to Flat Substrates Characterized by Different Adhesion Strength.

The adhesion of lipid vesicles to a rigid flat surface is investigated. We examine the influence of the membrane spontaneous curvature, adhesion strength, and the reduced volume on the stability and shape transformations of adhered vesicles. The minimal strength of the adhesion necessary to stabilize the shapes of adhered vesicles belonging to different shape classes is determined. It is shown that the budding of an adhered vesicle may be induced by the change of the adhesion strength. The importance of the free vesicle shape for its susceptibility to adhesion is discussed.

On the kinematics of a concave sidecut line deformed on a flat surface

The present paper investigates the static equilibrium of a thin elastic structure with concave sidecut pressed against a flat rigid surface, as an idealization of a ski or snowboard undergoing the conditions of a carved turn. An analytical model is derived to represent the contact behaviour and provide an explanation for concentrated loads occurring at the sidecut extremities. The deformations are prescribed assuming tied contact along the sidecut line and neglecting torsional deformations. The loading conditions leading to this ideal deformed state are then sought, in order to better understand the mechanics of the turn. The results are illustrated with different sidecut geometries and compared with finite element computations for validation purposes. Depending on the function describing the sidecut line, concentrated force and moment are found to take place at the sidecut extremities.

Numerical Simulation of Tensile Residual Stresses in SWCNT-Reinforced Polymer Composites

Abstract The residual stresses play a significant role in the mechanical properties and strengthening capability of nanocomposites. The present research aims to numerically investigate the residual stress relaxation in nanotube-reinforced polymers in response to mechanical tensile loading. The systems under study consist of the armchair and zigzag single-walled carbon nanotubes (SWCNT) embedded in a polymer matrix. The nanotubes and polymer matrix are assumed to be bonded by van der Waals interactions based on the Lennard-Jones (L-J) potential at the interface. The interactions between carbon atoms in the nanotube and nodes in the polymer matrix are modelled by equivalent springs. In order to evaluate the analysis of elastic-perfectly plastic using finite element (FE) modelling, first, relaxation of the plastic residual stresses on steel hemisphere in contact with a rigid flat surface was examined in a loading-unloading cycle and verified with available data. Afterwards, the residual stress relaxation in nanotubes with different space-frame structures was computed due to displacement-controlled loading. Finally, the stress state and the plastic residual stresses in the nanocomposite for different carbon nanotube content were analyzed and discussed during loading and unloading. Regarding the effect of tensile stress, it was revealed that nanotube structures have significant effects on the residual stresses created in the nanocomposite.

Flattening analysis of plastically graded cylindrical contact under plane stress condition

The present work deals with finite element based flattening analysis of a functionally graded cylindrical contact against a rigid flat surface under plane stress condition. The yield strength of the semi-cylinder is varied radially according to an exponential function. The contact between the semi-cylinder and the rigid flat is considered to be perfect-slip type in nature. To reduce the computational time, a 2D quarter circle is used to model the cylinder and rigid flat surface is modelled using a straight line. The effect of the gradation parameter on contact behaviours e.g. contact area, contact force, contact pressure etc. of the semi-cylinder are presented and discussed.