Normal Contact of Elastic Spheres With Two Elastic Layers as a Model of Joint Articulation

1991 ◽  
Vol 113 (4) ◽  
pp. 410-417 ◽  
Author(s):  
A. W. Eberhardt ◽  
J. L. Lewis ◽  
L. M. Keer
Keyword(s):  
Surface Tension ◽  
Current Model ◽  
Middle Layer ◽  
Contact Radius ◽  
Shear Stresses ◽  
Normal Contact ◽  
Cartilage Layer ◽  
Calcified Cartilage ◽  
Substrate Properties ◽  
Elastic Layers

An analytical model of two elastic spheres with two elastic layers in normal, frictionless contact is developed which simulates contact of articulating joints, and allows for the calculation of stresses and displacements in the layered region of contact. Using various layer/layer/substrate combinations, the effects of variations in layer and substrate properties are determined in relation to the occurrence of tensile and shear stresses as the source of crack initiation in joint cartilage and bone. Vertical cracking at the cartilage surface and horizontal splitting at the tidemark have been observed in joints with primary osteoarthritis. Deep vertical cracks in the calcified cartilage and underlying bone have been observed in blunt trauma experiments. The current model shows that cartilage stresses for a particular system are a function of the ratio of contact radius to total layer thickness (a/h). Surface tension, which is observed for a/h small, is alleviated as a/h is increased due to increased load, softening and/or thinning of the cartilage layer. Decreases in a/h due to cartilage stiffening lead to increased global compressive stresses and increased incidence of surface tension, consistent with impact-induced surface cracks. Cartilage stresses are not significantly affected by variations in stiffness of the underlying material. Tensile radial strains in the cartilage layer approach one-third of the normal compressive strains, and increase significantly with cartilage softening. For cases where the middle layer stiffness exceeds that of the underlying substrate, tensile stresses occur at the base of the middle layer, consistent with impact induced cracks in the zone of calcified cartilage and subchondral bone. The presence of the superficial tangential zone appears to have little effect on underlying cartilage stresses.

An Analytical Model of Joint Contact

1990 ◽  
Vol 112 (4) ◽  
pp. 407-413 ◽  
Author(s):  
A. W. Eberhardt ◽  
L. M. Keer ◽  
J. L. Lewis ◽  
V. Vithoontien
Keyword(s):  
Stress Distribution ◽  
Normal Stress ◽  
Analytical Model ◽  
Contact Radius ◽  
Shear Stresses ◽  
Maximum Normal Stress ◽  
Calcified Cartilage ◽  
Joint Contact ◽  
Maximum Contact ◽  
Contact Parameters

The stress distribution in the region of contact between a layered elastic sphere and a layered elastic cavity is determined using an analytical model to simulate contact of articulating joints. The purpose is to use the solution to analyze the effects of cartilage thickness and stiffness, bone stiffness and joint curvature on the resulting stress field, and investigate the possibility of cracking of the material due to tensile and shear stresses. Vertical cracking of cartilage as well as horizontal splitting at the cartilage-calcified cartilage interface has been observed in osteoarthritic joints. The current results indicate that for a given system (material properties μ and ν constant), the stress distribution is a function of the ratio of contact radius to layer thickness (a/h), and while tensile stresses are seen to occur only when a/h is small, tensile strain is observed for all a/h values. Significant shear stresses are observed at the cartilage-bone interface. Softening of cartilage results in an increase in a/h, and a decrease in maximum normal stress. Cartilage thinning increases a/h and the maximum contact stress, while thickening has the opposite effect. A reduction in the indenting radius reduces a/h and increases the maximum normal stress. Bone softening is seen to have negligible effect on the resulting contact parameters and stress distribution.

Finite Element Analysis of Tire/Rim Interface Forces Under Braking and Cornering Loads

1992 ◽  
Vol 20 (2) ◽  
pp. 83-105 ◽  
Author(s):  
J. P. Jeusette ◽  
M. Theves
Keyword(s):  
Finite Element ◽  
Shear Stress ◽  
Contact Pressure ◽  
Element Model ◽  
Shear Stresses ◽  
Detailed Knowledge ◽  
Stress Distributions ◽  
Element Analysis ◽  
Plane Shear ◽  
Normal Contact

Abstract During vehicle braking and cornering, the tire's footprint region may see high normal contact pressures and in-plane shear stresses. The corresponding resultant forces and moments are transferred to the wheel. The optimal design of the tire bead area and the wheel requires a detailed knowledge of the contact pressure and shear stress distributions at the tire/rim interface. In this study, the forces and moments obtained from the simulation of a vehicle in stationary braking/cornering conditions are applied to a quasi-static braking/cornering tire finite element model. Detailed contact pressure and shear stress distributions at the tire/rim interface are computed for heavy braking and cornering maneuvers.

The Chorionic Plastron and its Role in the Eggs of the Muscinae (Diptera)

1960 ◽  
Vol s3-101 (55) ◽  
pp. 313-332
Author(s):  
H. E. HINTON
Keyword(s):  
Surface Tension ◽  
High Pressures ◽  
Middle Layer ◽  
Clean Water ◽  
Active Materials ◽  
Great Resistance ◽  
Plane Normal ◽  
Air Interface ◽  
Surface Active ◽  
Egg Shell

In flies of the subfamily Muscinae the egg-shell has both an outer and an inner meshwork layer, each of which holds a continuous film of air. Between these two meshwork layers there is a more or less thick middle layer to which the shell chiefly owes its mechanical strength. Holes or aeropyles through the middle layer effect the continuity of the outer and inner films of air. Both meshwork layers consist of struts that arise perpendicularly from the middle layer. In both layers the struts are branched at their apices in a plane normal to their long axes. These horizontal branches form a fine and open hydrofuge network that provides a large water-air interface when the egg is immersed. When it rains or when the egg is otherwise immersed in water, the film of air held in the outer meshwork layer of the shell funtions as a plastron. To be an efficient respiratory structure a plastron must resist wetting by both the hydrostatic pressures and the surface active materials to which it is normally exposed. The plastrons of all the Muscinae tested resist wetting in clean water by pressures far in excess of any they are likely to encounter in nature. The resistance of a plastron to hydrostatic pressures varies directly as the surface tension of the water, and the surface tension of water in contact with the decomposing materials in which the Muscinae lay their eggs is much lowered by surface active materials. These considerations seem to provide an explanation for the great resistance of the plastron of the Muscinae to wetting by excess pressures and for the paradox that the plastrons of these terrestrial eggs are more resistant to high pressures than are the plastrons of some aquatic insects that live in clean water.

scholarly journals Experimental study of the wake behind a surface-piercing cylinder for a clean and contaminated free surface

2000 ◽  
Vol 402 ◽  
pp. 109-136 ◽  
Author(s):  
AMY WARNCKE LANG ◽  
MORTEZA GHARIB
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Turbulent Flows ◽  
Cross Sections ◽  
Surface Deformation ◽  
Surface Condition ◽  
Free Surface Flows ◽  
Shear Stresses ◽  
Surface Contaminants ◽  
A New Technique

This experimental investigation into the nature of free-surface flows was to study the effects of surfactants on the wake of a surface-piercing cylinder. A better understanding of the process of vorticity generation and conversion at a free surface due to the absence or presence of surfactants has been gained. Surfactants, or surface contaminants, have the tendency to reduce the surface tension proportionally to the respective concentration at the free surface. Thus when surfactant concentration varies across a free surface, surface tension gradients occur and this results in shear stresses, thus altering the boundary condition at the free surface. A low Reynolds number wake behind a surface-piercing cylinder was chosen as the field of study, using digital particle image velocimetry (DPIV) to map the velocity and vorticity field for three orthogonal cross-sections of the flow. Reynolds numbers ranged from 350 to 460 and the Froude number was kept below 1.0. In addition, a new technique was used to simultaneously map the free surface deformation. Shadowgraph imaging of the free surface was also used to gain a better understanding of the flow. It was found that, depending on the surface condition, the connection of the shedding vortex filaments in the wake of the cylinder was greatly altered with the propensity for surface tension gradients to redirect the vorticity near the free surface to that of the surface-parallel component. This result has an impact on the understanding of turbulent flows in the vicinity of a free surface with varying surface conditions.

Precisely Controlling Assembly Angle of Surface Tension Powered Self-Assembly for MEMS Microstructures

2007 ◽  
Author(s):  
Kai-Lin Pan ◽  
Yi-Lin Yan ◽  
Bin Zhou
Keyword(s):  
Surface Tension ◽  
Surface Energy ◽  
Self Assembly ◽  
Current Model ◽  
Three Dimensional ◽  
Design Parameters ◽  
Solder Paste ◽  
Surface Evolver ◽  
Final Assembly ◽  
The Relationship

How to integrate the microstructures which are made by various micro manufacturing methods into a functional system or device is the key to the application of MEMS technology. Solder self-assembly is based on surface tension with the properties of “self-organization”, low cost, batch processes and the compatibility with surface mount technology, which makes it be a challenging alternate technique. Solder self-assembly is based on the principle of surface energy minimization of molten solder material. During the process of minimizing the surface energy, surface tension can pull the horizontal hinged or hingeless plate up to a particular angle to achieve the minimal system energy. Finite element method is applied in this paper. MEMS self-assembly three-dimensional dynamic simulation model is developed by SURFACE EVOLVER. First, the model in this paper dynamically simulate the angle change of hinged plate during the process of evolvement of solder; second, the comparisons among the results from the current model and those from analytical two-dimensional model and three-dimensional static model are carried out; third, through Design of Experiments (DoE) with the application of the current model, the influences of design parameters such as pad size, pad geometry, and solder paste volume to the assembly angle are compared and discussed. Through changing the pad size, pad geometry and solder paste volume in SURFACE EVOLVER model, the corresponding final assembly angel from dynamic three-dimensional models are obtained. The relationship between design parameters to the assembly angle is concluded by the application of statistical analyses. The final angle can be controlled more effectively through synthetically optimize these parameters. It can provide effective guidance to the practical manufacturing of MEMS. Further research should focuses on the MEMS self-assembly experiment to intensively understand the relationship between the pad sizes, pad position, solder paste volume, hinge position, lock position and intermetallic compounds and the final assembly angle.

An estimation of mechanical stress on alveolar walls during repetitive alveolar reopening and closure

2015 ◽  
Vol 119 (3) ◽  
pp. 190-201 ◽  
Author(s):  
Zheng-long Chen ◽  
Yuan-lin Song ◽  
Zhao-yan Hu ◽  
Su Zhang ◽  
Ya-zhu Chen
Keyword(s):  
Surface Tension ◽  
Respiratory Rate ◽  
Inflation Rate ◽  
Mechanical Stresses ◽  
Normal Lung ◽  
Shear Stresses ◽  
Fluid Viscosity ◽  
Small Airways ◽  
Protective Ventilation Strategy ◽  
Elevated Surface

Alveolar overdistension and mechanical stresses generated by repetitive opening and closing of small airways and alveoli have been widely recognized as two primary mechanistic factors that may contribute to the development of ventilator-induced lung injury. A long-duration exposure of alveolar epithelial cells to even small, shear stresses could lead to the changes in cytoskeleton and the production of inflammatory mediators. In this paper, we have made an attempt to estimate in situ the magnitudes of mechanical stresses exerted on the alveolar walls during repetitive alveolar reopening by using a tape-peeling model of McEwan and Taylor (35). To this end, we first speculate the possible ranges of capillary number ( Ca) ≡ μU/ γ (a dimensionless combination of surface tension γ, fluid viscosity μ, and alveolar opening velocity U) during in vivo alveolar opening. Subsequent calculations show that increasing respiratory rate or inflation rate serves to increase the values of mechanical stresses. For a normal lung, the predicted maximum shear stresses are <15 dyn/cm2 at all respiratory rates, whereas for a lung with elevated surface tension or viscosity, the maximum shear stress will notably increase, even at a slow respiratory rate. Similarly, the increased pressure gradients in the case of elevated surface or viscosity may lead to a pressure drop >300 dyn/cm2 across a cell, possibly inducing epithelial hydraulic cracks. In addition, we have conceived of a geometrical model of alveolar opening to make a prediction of the positive end-expiratory pressure (PEEP) required to splint open a collapsed alveolus, which as shown by our results, covers a wide range of pressures, from several centimeters to dozens of centimeters of water, strongly depending on the underlying pulmonary conditions. The establishment of adequate regional ventilation-to-perfusion ratios may prevent recruited alveoli from reabsorption atelectasis and accordingly, reduce the required levels of PEEP. The present study and several recent animal experiments likewise suggest that a lung-protective ventilation strategy should not only include small tidal volume and plateau pressure limitations but also consider such cofactors as ventilation frequency and inflation rate.

Cohesion and detachment in biofilm systems for different electron acceptor and donors

2007 ◽  
Vol 55 (8-9) ◽  
pp. 421-428 ◽  
Author(s):  
C. Coufort ◽  
N. Derlon ◽  
J. Ochoa-Chaves ◽  
A. Liné ◽  
E. Paul
Keyword(s):  
Basal Layer ◽  
Middle Layer ◽  
Electron Donors ◽  
Shear Stresses ◽  
Average Thickness ◽  
Low Shear Stress ◽  
Erosion Test ◽  
Biofilm Structure ◽  
Initial Biofilm ◽  
Low Shear

This work deals with the cohesion and detachment in biofilm systems for two electron acceptors and for two electron donors. Biofilms were developed on plates, under very low shear stress for one month and then subjected to an erosion test for two hours in a Couette-Taylor reactor. Biofilm was characterised in terms of average thickness and residual TOC mass. It was found that the biofilm structure is very heterogeneous and stratified. The top layer, which represents 60% of the biofilm mass, is very fragile and can be easily detached; the basal layer, which represents 20% of the biofilm mass, is very cohesive and can resist shear stresses up to 13 Pa. Between these two layers, a middle layer of intermediary cohesion represents 20% of the initial biofilm mass.

scholarly journals Sensitivity of Thermal Predictions to Uncertain Surface Tension Data in Laser Additive Manufacturing

2020 ◽  
Vol 142 (12) ◽  
Author(s):  
J. Coleman ◽  
A. Plotkowski ◽  
B. Stump ◽  
N. Raghavan ◽  
A. S. Sabau ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Surface Tension ◽  
Fluid Flow ◽  
Additive Manufacturing ◽  
Current Model ◽  
Surface Tension Gradient ◽  
Process Conditions ◽  
Conductive Heat ◽  
Melt Pool ◽  
Super Alloy

Abstract To understand the process-microstructure relationships in additive manufacturing (AM), it is necessary to predict the solidification characteristics in the melt pool. This study investigates the influence of Marangoni driven fluid flow on the predicted melt pool geometry and solidification conditions using a continuum finite volume model. A calibrated laser absorptivity was determined by comparing the model predictions (neglecting fluid flow) against melt pool dimensions obtained from single laser melt experiments on a nickel super alloy 625 (IN625) plate. Using this calibrated efficiency, predicted melt pool geometries agree well with experiments across a range of process conditions. When fluid mechanics is considered, a surface tension gradient recommended for IN625 tends to overpredict the influence of convective heat transfer, but the use of an intermediate value reported from experimental measurements of a similar nickel super alloy produces excellent experimental agreement. Despite its significant effect on the melt pool geometry predictions, fluid flow was found to have a small effect on the predicted solidification conditions compared to processing conditions. This result suggests that under certain circumstances, a model only considering conductive heat transfer is sufficient for approximating process-microstructure relationships in laser AM. Extending the model to multiple laser passes further showed that fluid flow also has a small effect on the solidification conditions compared to the transient variations in the process. Limitations of the current model and areas of improvement, including uncertainties associated with the phenomenological model inputs are discussed.

Revisiting the Anterior Glenoid: An Analysis of the Calcified Cartilage Layer, Capsulolabral Complex, and Glenoid Bone Density

2018 ◽  
Vol 34 (8) ◽  
pp. 2309-2318
Author(s):  
Michael R. Karns ◽  
R. Tyler Epperson ◽  
Sean Baran ◽  
Mattias B. Nielsen ◽  
Nicholas B. Taylor ◽  
...  
Keyword(s):  
Bone Density ◽  
Cartilage Layer ◽  
Calcified Cartilage ◽  
Anterior Glenoid
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