Shear Stress Equation Research Articles

Dynamic Reissner–Sagoci problem for a transversely isotropic half-space containing finite length cylindrical cavity

A transversely isotropic linear elastic half-space containing a circular cylindrical cavity of finite length with a depth-wise axis of material symmetry is considered to be under the effect of a mono-harmonic torsional motion applied on a rigid circular disc with the same radius of the cavity and welded at the bottom of the cavity. With the aid of Fourier sine and cosine integral transforms, the mixed boundary value problem is reduced to a generalized Cauchy singular integral equation for the unknown shear stress. The Cauchy integral equation involved in this paper is analytically investigated such that the solution is written in the form of a known singular function multiplied by an unknown regular function. The regular part of the shear stress is numerically determined with the use of Gauss–Jacobi integration formula. Series representation of the stress and displacement are obtained, and it is shown that their degenerated form to the static problem of isotropic material is coincide with the existing solutions in the literature. To investigate the effects of material anisotropy and the length of cavity, the tangential displacement and the shear stress in between the rigid disc and the bottom of cavity are numerically evaluated and illustrated, where some differences are distinguished. With the differences illustrated in this paper for different length of cavity, it is recognized that the effect of length of cavity cannot be neglected in analysis and design. Different results for different degrees of anisotropy shows that the anisotropy of the material is a normal behavior, which should be considered in this kind of medium.

Microscopic bio‐corrosion evaluations of magnesium surfaces in static and dynamic conditions

Biodegradable materials including biodegradable metals are continuously being investigated for the development of next generation cardiovascular stents. Predictive in vitro tests are needed that could evaluate potential materials while simulating in vivo conditions. In this manuscript we report the microscopic bio-corrosion evaluations of magnesium surfaces in static and dynamic conditions. A corrosion test bench was designed and fabricated and static and dynamic corrosion tests were carried out with samples of magnesium alloy. The fluid wall shear stress equation and the Churchill's friction factor equation were used to calculate the fluid velocity required to generate the desired shear stress on samples in the test bench. Static and dynamic corrosion tests at 24 and 72 h were carried out at 0.88 Pa shear stress mimicking the in vivo shear stress. Microscopic evaluations of the corroded surfaces were carried out by optical, scanning electron microscopy and energy dispersive X-ray spectroscopy to evaluate the corrosion behaviour and surface properties of the test samples. The surface and interface analysis of magnesium samples post test indicated that dynamic conditions prevented the build-up of corrosion by-products on the sample surface and the corrosion mechanism was uniform as compared to static conditions. The use of a masking element to restrict the exposed area of the sample didn't result in increased corrosion at the boundary. Thus, we have demonstrated the feasibility of the designed test bench as a viable method for bio-corrosion surface analysis under dynamic corrosion conditions for potential biodegradable cardiovascular stent materials.

First Exact Solutions for Flows of Rate Type Fluids in a Circular Duct that Applies a Constant Couple to the Fluid

Rotational flow of an Oldroyd-B fluid induced by an infinite circular cylinder that applies a constant couple to the fluid is studied by means of integral transforms. Such a problem is not solved in the existing literature for rate type fluids and the present solutions are based on a simple but important remark regarding the governing equation for the non-trivial shear stress. The solutions that have been obtained satisfy all imposed initial and boundary conditions and can easy be reduced to the similar solutions corresponding to Maxwell, second-grade, and Newtonian fluids performing the same motion. Finally, the influence of material parameters on the velocity and shear stress distributions is graphically underlined.

A new dual-plate slipometer for measuring slip between molten polymers and extrusion die materials.

In this work, we study the slip behaviors common to plastics die extrusion metals or platings using a new instrument called a dual-plate slipometer. By dual-plate, we mean that whereas the stationary plate incorporates a local shear stress transducer, the moving plate does not. The stationary plate and transducer are made of one stainless steel, but the moving plate is made from, or plated with, different extrusion die materials under study. This new instrument allows slip velocity to be measured without having to build a new shear stress transducer from each extrusion metal or plating under study. We explore the effect of extrusion die composition and die metal surface morphology on the slip properties of polyolefins using a sliding plate rheometer. In this work, we studied the slip behaviors of polyolefins on four common plastics die extrusion metals or platings, without having to build a new shear stress transducer from each. Specifically, our new method replaces the moving plate; with each of the four die metals or platings under study without changing the stainless steel material of the shear stress transducer and its stationary plate. Our experiments include high-density polyethylene, low-density polyethylene, and polypropylene (PP) on four different die metals or platings. We use steady simple shear to obtain shear stress versus nominal shear rate for different gaps, from which we can then deduce the slip velocity using the Mooney analysis. We then fit four slip models to our experimental measurements, and we find the Hatzikiriakos hyperbolic sine model to be accurate, even for the measured inflections in the slip velocity as a function of shear stress curves. Our analysis includes detailed characterization of the die metal plating surfaces, including measurements of the composition of the sliding plates by energy dispersive spectroscopy, surface energy by contact angle goniometry, and surface roughness by both white light interference and stylus profilometries. We use our slip measurements to evaluate the Allal-Vergnes equation for the critical shear stress for slip [A. Allal and B. Vergnes, "Effect of die surface on the onset of stick-slip transition in the flow of molten linear polymers," J. Non-Newtonian Fluid Mech. 167-168, 46-49 (2012)]. We conclude our analysis by dedimensionalizing slip, and we then use these dimensionless groups to analyze slip. This paper provides a set of reference data for extrusion die designers for polyolefins.

Investigating the Effect of Blood Sample Volume in the Chandler Loop Model: Theoretical and Experimental Analysis

Although the Chandler loop model has been used in various in vitro flow studies, there is a lack of guidance on the selection of the appropriate sample volume. The questions of how to determine the appropriate sample volume and its effect on blood activation have not been fully addressed. This study proposes a new criterion for determining sample volume and defines a time-averaged wall shear stress equation for this model. In vitro experiments were performed to investigate the implications of sample volume on blood cell activation in the presence of model stent. Experimental results indicated that in the absence of a stent and for shear stress up to about 56 dyn/cm2, platelet activation was independent of volume and shear. On the other hand, the formation of platelet–leukocyte aggregates was affected by volume as well as the presence of a stent. Doubling blood volume for the same stent resulted in a twofold decrease in platelet microparticle formation and platelet–leukocyte aggregation. These results demonstrate the importance of selecting appropriate sample volume for the Chandler loop model, since it influences blood activation parameters, especially platelet–leukocyte aggregation formation, which can play an important role in material-induced thrombosis. These results have significance for in vitro screening of materials for biocompatibility.

A Scour Depth Approach for Deriving Erodibility Parameters from Jet Erosion Tests

Abstract. Typically the erosion rate of cohesive soils is modeled using the excess shear stress equation, which includes two soil parameters: the erodibility coefficient (k d ) and the critical shear stress (I„ c ). A jet erosion test (JET) is a standardized method available for deriving the erodibility of cohesive soils. The JET data are typically analyzed using a Blaisdell solution approach. A second solution approach based on direct parameter optimization to the measured scour depth data has recently been proposed but with limited evaluation. Therefore, the objectives of this research were to: (1) develop a new spreadsheet tool that simultaneously solves for the erodibility parameters using both solution approaches, (2) evaluate the solutions in terms of their ability to predict the observed scour depth data, and (3) quantify differences in the predicted erodibility parameters from the two approaches. A series of JETs conducted across the Illinois River watershed in eastern Oklahoma were used to evaluate the performance of the spreadsheet and the solution methodologies. The new scour depth solution provided improved fits to the original scour depth data along with being more stable in converging to a solution as a function of the initial parameter estimates. The automated spreadsheet provides an easy-to-use tool for deriving erodibility parameters from JETs.

Shear Stress Distribution and Deflection of Preflex I-Girder with Corrugated Steel Web

A new type of preflex I-girder with corrugated steel web has been proposed to provide better solution for urban elevated bridge. The purpose of this study is to explore shear stress distribution and deflection of such preflex I-girder. Shear stress distribution in section of steel-concrete composite girder was analyzed by shearing stress integral equation and piecewise function, and a quarter-scale preflex I-girder with corrugated steel web was fabricated and tested. Experimental and analytical results show that the shear stiffness is only depends on corrugated steel web, and the shear stress is uniformly distributed along the height of corrugated web. It is found that the proposed shear stress equation is consistent with the experimental result and the deflection integral equation is agreed well with the FEA result. The result suggests that the shear deflection is as larger as 25.8% of the total deflection, and should take shearing deflection into consideration.

Measuring Soil Erodibility Using a Laboratory “Mini” JET

Abstract. Typically soil erodibility is quantified using an excess shear stress equation, dependent on two major soil parameters: the critical shear stress (I„ c ) and the erodibility coefficient (k d ). A submerged jet test (JET, Jet Erosion Test) is one method that has been developed and methodology of use established in the literature for measuring these parameters. In this study, a new miniature version of the JET device (“mini” JET), with the advantage of being easier to use in the field, was used to measure I„ c and k d for two soils (silty sand and clayey sand), and results were compared to the larger original laboratory JET. The objective of this research was to determine if the “mini” JET measured equivalent values for I„ c and k d compared to the original JET device. In-order to compare the performance and repeatability of both JET devices, tests were performed on paired samples prepared in the same way and tested at the same time. Samples of the soils tested were prepared at different water contents with a standard compaction effort of 600 kN-m/m 3 (ASTM). Some variability in measuring I„ c and k d was observed between paired samples due to variability in the soil texture of the soil samples and differences in soil moisture levels. The k d values measured by the two JET devices for both soils were not significantly different. The I„ c values measured by the “mini” JET were consistently lower than those measured by the original JET. This was hypothesized to be due to the structure of the soil sample due to the compaction method and the procedure utilized to determine I„ c . Adjustment of the equilibrium depth of the “mini” JET resulted in small differences in the estimated I„ c between both JET devices. Both JET devices also demonstrated consistent performance in measuring I„ c -k d relationships, which were compared with those observed in previous field research.

Intraventricular Flow Velocity Vector Visualization Based on the Continuity Equation and Measurements of Vorticity and Wall Shear Stress

We have developed a system to estimate velocity vector fields inside the cardiac ventricle by echocardiography and to evaluate several flow dynamical parameters to assess the pathophysiology of cardiovascular diseases. A two-dimensional continuity equation was applied to color Doppler data using speckle tracking data as boundary conditions, and the velocity component perpendicular to the echo beam line was obtained. We determined the optimal smoothing method of the color Doppler data, and the 8-pixel standard deviation of the Gaussian filter provided vorticity without nonphysiological stripe shape noise. We also determined the weight function at the bilateral boundaries given by the speckle tracking data of the ventricle or vascular wall motion, and the weight function linear to the distance from the boundary provided accurate flow velocities not only inside the vortex flow but also around near-wall regions on the basis of the results of the validation of a digital phantom of a pipe flow model.

Continuous Membrane Emulsification with Pulsed (Oscillatory) Flow

Tubular micrometer pore sized sieve type membranes with internal diameter of 14 mm and length of 60 mm containing uniform pores of diameter 10 and 20 μm were used to generate emulsions of sunflower oil dispersed in water and stabilized by Tween 20 using oscillatory flow of the continuous phase. Drop diameters between 30 and 300 μm could be produced, in a controllable way and with span values of down to 0.4. By using pulsed flow it was possible to provide dispersed phase concentrations of up to 45% v/v in a single pass over the membrane, that is, without the need to recirculate the continuous phase through the membrane tube. It was possible to correlate the drop size produced with the shear conditions at the membrane surface using the wave shear stress equation. The oscillatory Reynolds number indicated flow varying from laminar to substantially turbulent, but the change in flow conditions did not show a notable influence on the drop diameters produced, over what is predicted by the varying wall shear stress applied to the wave equation. However, the 20 μm pore sized sieve type membrane appeared to allow the passage of the pressure pulse through the membrane pores, under certain operating conditions, which did lead to finer drop sizes produced than would be predicted. These through-membrane pulsations could be suppressed by changes in operating conditions: a higher dispersed phase injection rate or more viscous continuous phase, and they did not occur under similar operating conditions used with the 10 μm pore sized sieve type of membrane. Generating emulsions of this size using pulsed continuous phase flow provides opportunities for combining drop generation at high dispersed phase concentration, by membrane emulsification, with downstream processing such as reaction in plug flow reactors.

Internal Erosion during Soil Pipeflow: State of the Science for Experimental and Numerical Analysis

Keywords: Ephemeral gully erosion Erodibility Internal erosion Landslides Pipeflow Soil pipes. Abstract. Many field observations have led to speculation on the role of piping in embankment failures, landslides, and gully erosion. However, there has not been a consensus on the subsurface flow and erosion processes involved, and inconsistent use of terms have exacerbated the problem. One such piping process that has been the focus in numerous field observations, but with very limited mechanistic experimental work, is flow through a discrete macropore or soil pipe. Questions exist as to the conditions under which preferential flow through soil pipes results in internal erosion, stabilizes hillslopes by acting as drains, destabilizes hillslopes via pore-pressure buildups, and results in gully formation or reformation of filled-in ephemeral gullies. The objectives of this article are to review discrepancies in terminology in order to represent the piping processes better, to highlight past experimental work on the specific processes of soil pipeflow and internal erosion, and to assess the state-of-the-art modeling of pipeflow and internal erosion. The studies reviewed include those that examined the process of slope stability as affected by the clogging of soil pipes, the process of gullies forming due to mass failures caused by flow into discontinuous soil pipes, and the process of gully initiation by tunnel collapse due to pipes enlarging by internal erosion. In some of these studies, the soil pipes were simulated with perforated tubes placed in the soil, while in others the soil pipes were formed from the soil itself. Analytical solutions of the excess shear stress equation have been applied to experimental data of internal erosion of soil pipes to calculate critical shear stress and erodibility properties of soils. The most common numerical models for pipeflow have been based on Richards’ equation, with the soil pipe treated as a highly conductive porous medium instead of a void. Incorporating internal erosion into such models has proven complicated due to enlargement of the pipe with time, turbulent flow, and episodic clogging of soil pipes. These studies and modeling approaches are described, and gaps in our understanding of pipeflow and internal erosion processes and our ability to model these processes are identified, along with recommendations for future research.

Investigation of Vorticity Effects on Local Scouring

This paper describes a numerical model developed to simulate flow and bed deformation around hydraulic structures. The model uses an improved formula for the bed shear stress by applying vorticity effect and solves the full three-dimensional Reynolds-averaged Navier–Stokes equations to calculate the flow field. The capability for numerical models to predict local scour is severely restricted by the sediment transport formula. Up to now, the scour computations were developed based on general sedimentation formula through a straight unobstructed flow path. The new sedimentation formula introduced in this paper can take into account vortices that affect the local scour process. To verify the model, a bridge pier and a groyne, which are considered as typical river-engineering structures, were simulated in different hydraulic conditions by applying both the ordinary bed shear stress equation and the new one. Comparisons show that the new equation could predict the scour more accurately than the ordinary one.

Reply to the Discussion by H. Jiang and B. Fu of “Prediction of energy absorption capacity of un-cracked and cracked concrete elements through three-point bending tests”1Appears in the Canadian Journal of Civil Engineering, 39(10): 1161–1162 [doi: 10.1139.l2012-089

In the discussion, the discussers are concerned about the applicability of the suggested model in the paper for the cases of torsional loading and reinforced concrete. The authors want to mention that the above paper provides a general methodology to calculate the total energy absorption capacity of concrete elements, which includes typical beams and columns. For concrete elements subjected to torsion, the torsional shear stress equations in Mechanics of Solids or Elasticity textbook could be adopted without much effort, for the cases of pure torsion and combined torsion, axial loading, and bending. Prediction of the energy absorption capacity of reinforced concrete elements could be also conducted with inclusion of the perfect elastic-plastic behavior of steel rebar. All the stress calculations in classical reinforced concrete can be used to sketch the complete load displacement of the element and further predict its energy absorption capacity.

Finding the elastic strain limit at the tip region of a physical cut with arbitrarily loaded faces

A model describing the stress-strain state in the neighborhood of a physical cut with an arbitrary distribution of external load along its faces is presented. The stress-strain state of a material layer bounded by the continuations of the cut faces is considered. The interaction between the layer and the external half-planes leads to a closed system of integrodifferential equations for the mean stress components in the layer, which splits into two equations for the mean normal stresses and an equation for the mean shear stress. Numerical solutions of the system for the cases of symmetric and antisymmetric loading of the faces by concentrated forces are given. Conditions for the transition of the tip region of the cut to the state of plasticity and fracture are considered.

A modified nonlinear sub-grid scale model for large eddy simulation with application to rotating turbulent channel flows

In this paper, a dynamic subgrid scale (SGS) stress model is proposed by modifying the existing quadratic nonlinear model. Unlike the conventional eddy viscosity models, the nonlinear model suggests an anisotropic tensorial polynomial relation between the SGS stress and the resolved strain rate tensor. Examined in the rotating turbulent channel flow, the previous nonlinear model is found unable to successfully predict the turbulent kinetic energy and the Reynolds shear stress. In the previous nonlinear model, an excessive backward energy transfer from the SGS to the resolved scale is found, so it is removed in the new model to provide sufficient SGS dissipation. The dynamic method is reconsidered, based on the analysis of the transport equation of the resolved Reynolds shear stress. The new dynamic nonlinear model is examined in the rotating turbulent channel flow at Re = 7000 and various rotation numbers (Ro), ranging from 0.0 to 0.6. The new dynamic procedure determines a more proper model coefficient for the nonlinear term, so the modified nonlinear model predicts superior results to the previous nonlinear models. The Vreman's approach of the eddy viscosity is implemented into the nonlinear model, to compare with the conventional dynamic Smagorinsky type nonlinear model in the rotating turbulent channel flow.

2E5-3 Intraventricular Flow Velocity Vector Visualization Based on the Continuity Equation and Measurements of Vorticity and Wall Shear Stress(Biomedical Ultrasound)

2E5-3 Intraventricular Flow Velocity Vector Visualization Based on the Continuity Equation and Measurements of Vorticity and Wall Shear Stress(Biomedical Ultrasound)

Lubricated sliding dynamics: Flow factors and Stribeck curve

We study the fluid flow at the interface between elastic solids with randomly rough surfaces. We derive (approximate) analytical expressions for the fluid flow factors which enter in the equation describing the fluid flow, and for the frictional shear stress factors which enter in the equation for the frictional shear stress. Numerical results for a rubber cylinder with surface roughness sliding on a flat lubricated substrate, under "low" and "high" pressure conditions, are presented and discussed. Finally we discuss the role of the fluid-induced elastic deformations of the surface roughness profile.

A STUDY ON PROLONGATION OF THE LIFETIME OF SEISMIC ISOLATED BUILDING WITH LEAD RUBBER BEARING

In order to prolong the lifetime of seismic isolated building with lead rubber bearing (LRB), we investigate the relationship between the seismic response of the LRB-isolated building and the aging of LRB by a non-linear response analysis. For the non-linear response analysis, the restoring-force model of LRB taking in account the aged deterioration over 100 years old is developed from the experimental data. The experimental equation of the failure shear stress of LRB is also proposed. From the seismic response analyses, the aged deterioration of the failure shear stress of LRB is found to be important in the life-prolongation of LRB-isolated building.

A Study of Frictional Property of the Human Fingertip Using Three-Dimensional Finite Element Analysis

Since the tactile perception detects skin deformation due to the contact of an object, it is important to understand contact mechanics, especially, frictional behavior of the human fingertip. The coefficient of friction is recently modeled as a function of the applied normal load in which case the traditional Coulomb's law does not provide a description for the skin surface. When a surface is a rubber-like material, the frictional behavior follows the frictional law of the rubber-like material. Therefore, we developed a three-dimensional Finite Element model of the fingertip and analyzed frictional behavior based on the frictional law of rubber-like material. We proposed a combined technique using both experimental and Finite Element analyses in order to investigate the frictional property of the fingertip. A three-dimensional Finite Element model of the fingertip was developed using MRI images. We hypothesized a frictional equation of the critical shear stress. Squared differences between equivalent coefficient of friction of the FE analysis and the coefficient of kinetic friction of the experiment while sliding was decreased and the Finite Element analysis iterated until the error was minimized, and thus the frictional equation was determined. We obtained the equation of the critical shear stress and simulated kinetic friction of the fingertip while sliding under arbitrary normal loading condition by using the Finite Element analysis. We think this study is an appropriate method for understanding the frictional property of the human fingertip using the Finite Element analysis.

Experimental Study on the Modeling of Condensation Heat Transfer Coefficients in High Mass Flux Region of Refrigerant HFC-134a Inside the Vertical Smooth Tube in Annular Flow Regime

This article presents an experimental investigation on the co-current downward condensation of R134a in a vertical smooth copper tube having inner diameter of 8.1 mm and a length of 500 mm. Condensation experiments are done at mass fluxes varying between 260 and 515 kg/m2-s. The condensing temperatures are 40°C and 50°C; heat fluxes are between 10.16 and 66.61 kW/m2. The quality of the refrigerant in the test section is calculated considering the temperature and pressure obtained from the experiment. The pressure drop across the test section is directly measured by a differential pressure transducer. The average experimental heat transfer coefficient of the refrigerant is calculated by applying an energy balance based on the energy transferred from the test section. The average predicted heat transfer coefficient of the refrigerant is determined by means of the model of Kosky and Staub, and Von Karman universal velocity distribution correlations using different interfacial shear stress equations valid for annular flow in horizontal and vertical tubes to investigate the Chen et al. annular flow theory. The effects of heat flux, mass flux, and condensation temperature on the pressure drop are also discussed. A new correlation using a large number of data points for the turbulent condensation heat transfer coefficient is proposed.