Tangential Traction Research Articles

A Theory of Macromolecular Chemotaxis

A macromolecule in a gradient of a cosolute that is preferentially (relative to the solvent) either attracted to or excluded from the domain of the macromolecule should experience a thermodynamic force and move, respectively, up or down the gradient. A theory of chemotactic forces arising from such preferential interactions, especially short-range ligand binding and excluded volume interactions, is developed via an extension of Kirkwood-Buff theory. The ligand binding result is confirmed for both non-ionic and ionic cosolutes by standard solution thermodynamics. The effect of increasing the electrolyte concentration to diminish the electrostatic free energy of a charged macromolecule is also treated formally via an electrostatic macromolecule-electrolyte preferential interaction coefficient. For short-range interactions, the induced chemotactic velocity is attributed entirely to tangential tractions at the interface between the macromolecule and its surrounding solution. The velocity of a spherical macromolecule driven by such tractions is derived by a hydrodynamic calculation for steady-state creepy flow with a partial slip boundary condition. Qualitative comparisons of theoretical predictions with experimental observations of Zheng and Pollack pertaining to charged microspheres near the surfaces of non-ionic gels suggest that the reported exclusion zones are due to chemotaxis induced by gradients of base (NaOH) (or acid (HCl)) and salt. With a single adjustable parameter, namely, the ratio of slip length to area per surface carboxyl (or amidine) group, this theory yields nearly quantitative agreement with many observations. The estimated slip length for the microspheres is comparable to that obtained for bovine serum albumen by fitting the chemotactic theory to two reported cross-diffusion coefficients. When a solution with a gradient of NaOH is placed in contact with a smooth glass wall, chemotactic surface tractions are predicted to cause convection of the solution toward the acidic end of the gradient, as observed in preliminary experiments.

Mechanics of Composite Layered Rough Medium in Contact

This study presents a first attempt to develop a numerical three-dimensional multilayered (more than 2 composite layered coatings) elasticperfectly plastic rough solids model to investigate the contact behavior under combined normal loading and tangential traction. Contact analyses are performed to study the effects composite thin film layers. Local contact pressure profiles, von Mises stresses, and shear stresses as a function of material properties and applied normal and tangential friction loads are calculated.

Pre-sliding Behaviour of Single Asperity Contact

The pre-sliding and static friction force behaviour at asperity level between a smooth ball and a smooth flat surface at different normal loads, as well as friction behaviour during full slip has been studied. The normal load dependence of the friction force and the preliminary displacement is discussed when the mean contact pressure is kept under 100 MPa. The theoretical model to calculate the shear stress and the preliminary displacement in the contact is discussed and the experimental data were used to verify the model. The results show that for low applied normal loads the adhesion force has an influence on the friction force measurements. Furthermore, the results for the friction force and preliminary displacement show good agreement with the theoretical trends. The experiments along with the model can be used to analyse the tangential traction in the contact and the behaviour of the stick–slip area. The measurement results along with the model were used to calculate the maximum shear stress at the point of sliding for different applied normal loads. It is also shown that at low applied normal loads the shear stress is not constant as compared to relatively high applied normal loads due to the presence of adhesion force.

Macular Pseudoholes With Lamellar Cleavage of Their Edge Remain Pseudoholes

To reappraise macular pseudohole characteristics using spectral-domain optical coherence tomography (OCT) and characteristics and postoperative outcomes of macular pseudoholes. Retrospective, observational case series. In this institutional study, 54 eyes with macular pseudohole were selected among 369 patients examined for an epiretinal membrane (ERM) by Cirrus spectral-domain OCT (Carl Zeiss Meditec) within a 2-year period. The diagnosis of macular pseudohole was based on the presence of a deep foveal pit, with verticalized edges and a macula thickened by the contraction of an ERM. All eyes underwent color fundus photography and spectral-domain OCT examination comprising a macular map, line raster scans, and en face images of the inner retinal surface. The main outcome measures were the morphologic description of the foveal profile in macular pseudoholes in relation to the pattern of the ERM contraction and the postoperative changes. In 24 eyes, the foveal pit had vertical, straight, smooth edges on the OCT scan corresponding to centripetal contraction of the ERM. Thirty other eyes exhibited some degree of stretching and cleavage of the foveal pit edge resulting from asymmetrical tangential traction of the ERM between multiple epicenters of contraction. Thirty-three patients underwent surgery, and their macular profile and visual acuity improved whatever their initial foveal profile. The OCT profile of macular pseudohole varies according to the pattern of the causal ERM contraction. Macular pseudoholes with a stretched foveal edge respond to ERM peeling as positively as other eyesand should not be confounded with macular lamellar holes.

Multibody modeling of non-planar ball bearings

This work presents the dynamic modeling of ball bearing which uses multibody dynamic for- malism. Such formalism allows immediate integration of the model in dynamic simulations of helicopter main gear boxes. Ball bearing is considered non-lubricated in order to predict its behavior in case of lubri- cation system failure. Rolling contacts are treated with the method proposed by Kalker. This approach is based on polynomial approximation of relative displacement on the contact ellipse. For low computational cost and without any spatial discretization, it gives a good estimation of tangential traction and creep. Also, a regularization of the Kalker linear creep theory is proposed. It is used here to facilitate the global convergence of the Newton iterative process. It is well suited for multibody dynamic simulations which do not need a very fine treatment of rolling contact. A numerical example of a ball bearing under thrust load is presented.

Material tailoring and moduli homogenization for finite twisting deformations of functionally graded Mooney-Rivlin hollow cylinders

We analytically analyze finite plane strain twisting deformations of a hollow cylinder made of an isotropicandinhomogeneousMooney-Rivlinmaterialwithmaterialmodulivaryingintheradialdirection.The cylinder is deformed by applying either tangential tractions on the inner surface and tangential displacements on the outer surface or vice versa. The radial variation of the moduli is found that will minimize the tangential displacement of the bounding surface where tangential traction is specified. Furthermore, the modulus of a homogeneous neo-Hookean cylinder is found that is energetically equivalent to the inhomogeneous cylinder.

A physics-based model to predict micro-pitting lives of lubricated point contacts

This paper proposes a physics-based model to predict the onset of micro-pit formation for lubricated point contacts of rough surfaces. A mixed elastohydrodynamic lubrication model is employed to predict the surface normal and tangential tractions for a stress prediction model to determine the resultant stress histories. The boundary element approach is used in the stress model to fully capture the measured three-dimensional topographies of the contacting rough surfaces, allowing an accurate prediction of the localized stress concentrations that dictate the occurrence of micro-pits. In the process, the method of coordinate transformation and the indirect approach of rigid body motion are devised to eliminate the kernel singularities. A novel numerical procedure is also developed to minimize any Gaussian quadrature numerical error in the integration of the near singular kernels. The fatigue damage is then evaluated employing a multi-axial fatigue criterion. The proposed micro-pitting life prediction methodology is demonstrated using an example ball-on-disk contact problem.

Non-linear analysis of pre-tensioned concrete planar beams

We have derived a one-dimensional mathematical model and a numerical procedure for the non-linear static analysis of pre-tensioned concrete planar beams, which intends to describe quantitatively the global behaviour as well as some local phenomena in the beam, such as the tangential slip and the traction between the tendon and concrete, with accuracy sufficient for engineering design. The advantage of such a model is its extreme computational efficiency compared to the two- and three-dimensional formulations. A shear-stiff, kinematically exact planar beam theory is used to model each component of the beam. The bending moment in the tendon is neglected. Cracking of concrete is accounted for using the smeared crack concept. Softening of material, and the related localisation of deformations, is in the numerical solution resolved by the combined use of the arc-length method and the constant strain crack band element, whose dimension is related to the fracture energy of concrete in tension. The tangential slip between the tendon and concrete is fully accounted for, yet the normal separation is not allowed. The model enables us to analyse the variation of slip and the tangential traction on tendons as well as softening of concrete in both tension and compression along the beam axis and in time. The validity of the present one-dimensional model is verified on two pre-stressed simply supported beams previously experimentally and computationally studied in literature (Rabczuk and Eibl, 2004 [2]; Rabczuk et al., 2005 [18]; Rabczuk and Belytschko, 2006 [20]). It is found out that the results of the present one-dimensional model are well in keeping with the experimental and numerical results from literature. Recalling the extreme computational efficiency of the present formulation compared to the 2D and 3D formulations it is concluded that the proposed method of analysis could be very convenient for engineering design.

Stage 1 macular holes of Gass classification illustrated by Optical Coherence Tomography scans: a review of 4 cases

AbstractPurpose Gaudric classification, stage 1 corresponds to intraretinal pseudocyst in the inner part of the foveola. The prolongation of the cyst laterally results in a split between the inner retina and the photoreceptor layer and a disruption of the outer retinal layers.Methods Four patients presented with a history of blurred vision and metamorphopsia. OCT examination showed a foveolar serous detachment between pigment epithelium and photoreceptor layer. Six months later, two patients presented lamellar holes and two patients evolved into stage 3 macular holes. In all cases we reported a complete resolution of the foveolar serous detachment . A surgical treatment was performed for three patients.Results OCT scans performed one month after surgery showed a total closure of the macular holes, an increase of visual acuity and a disappearance of the metamorphopsia. The main physiopathological theory formulated about macular holes formation concerns vitreo retinal tractions. As the posterior hyaloid remained attached to the center of the foveola and to the optic disc, displaying a convexity that may indicate the exertion of anteroposterior traction on its vitreous side, Gaudric admits that stage 1a macular hole is the result of antero posterior vitreo retinal tractions. Stage 1 as described by Gass is characterized by a serous foveolar detachment and is a consequence of tangential tractions of the pre foveolar vitreous cortex.Conclusion Our cases seem to be the tomographic illustration of the anatomic description of the stage 1 macular hole proposed by Gass and not mentioned in the tomographic classification proposed by Gaudric suggesting the implicationof tangential traction in macular holes formation.

Influence of wheel/rail tangential traction force on thermal cracking of railway wheels

In terms of the durability of carbon steel railway wheels, so-called tread thermal cracking, one of severe damages on the tread surface, was investigated to understand the dominating factor and the countermeasures against thereto. Based on the temperature conditions predicted by material investigation and numerical analysis, the residual stress state during tread braking and after cooling was estimated. On the basis of the analysis on the distribution morphology of the cracks, we have focused on the wheel/rail tangential traction force as a source of the sequential external force imposed on all circumferences of wheel tread. A series of full-scale experiments were carried out to clarify the influence of residual stress and tangential force on tread thermal cracking. The wheel/rail tangential force and the localized tensile residual stress caused by localized heating, rather than wheel weight, largely affect the thermal cracking.

Path-dependent analysis of elastic sphere contact subjected to tangential loading with varying directions

The Cattaneo–Mindlin solutions of contact between elastic spheres and their recent extensions do not consider the sequential application of arbitrarily directed shear forces in the contact tangential plane. For this loading condition, the contact tractions simultaneously undergo loading and unloading. This article presents a path-dependent analysis wherein we use superposition at each loading step to obtain the contact tangential traction, and, subsequently the tangential displacement and compliance. The methodology is illustrated by example calculation of contact shear force–displacement relationship, which shows the formation of hysteretic loop and the noncoaxiality of the shear forces and displacements.

An efficient approach for simulating seismoacoustic scattering due to an irregular fluid-solid interface in multilayered media

SUMMARY The seismoacoustic scattering due to an irregular fluid–solid interface must be considered when we model the seismic wave propagation in oceanic regions or gulf areas. In this paper, an efficient approach will be presented to treat this kind of problem. The approach can be viewed as an extension of the method originally developed for seismogram synthesis in multilayered solid media with irregular interfaces. In this method, we use the traditional boundary element method to discretize the boundary integral equation in each layer; then define the global matrix propagators by the boundary and continuity conditions in such way that they propagate the information of the element displacements and tractions ‘downwards’ for layers above the source while ‘upwards’ for layers below the source, finally solve the problem in the source layer. The main idea of the method is to use the global matrix propagators to suppress the tremendous increase in the memory requirement appearing in the traditional boundary element method when modelling wave propagation in multilayered media. As for the fluid–solid interface, the direct application of the above method is difficult since the global matrix propagators in fluid layers are much different from those defined in solid layers. By using the pressure as the variable inside the fluid layer, we can treat the acoustic wave propagation as a Helmoltz problem. The global matrix propagators can then be extended into the same size as those defined for solid layers by using the standard boundary conditions at the fluid–solid interface (i.e. normal traction continuity, zero tangential traction and normal displacement continuity). By the extended global matrix propagators we can thus propagate the information of the acoustic wave into the elastic wavefield and further obtain the results of the elastic wave propagation in arbitrary solid layers. To demonstrate the validity and feasibility of our method, we should compare our numerical results with the existing solutions. For problems of irregularly layered structures, however, we do not have exact (analytic) solutions. Therefore, it is important to compare the results calculated by completely different numerical methods to ensure validity. For such purpose, we calculate the cases of a plane P wave vertically incident onto two basin-like fluid–solid structures and an SV wave source located below a basin-like fluid–solid interface, of which the synthetic seismograms are accessible from the existing publications. Our results show almost complete agreement with those calculated by the reflection/transmission matrix method and those calculated by the discrete wavenumber method. Second, we calculate the synthetic time domain waveforms for a model with and without a basin-like fluid layer. Comparison observation clearly shows the effects of the fluid layer on the seismic ground motion at land in which seismologists or geophysicists may be of great and practical interests. Furthermore, we take into account the case when an explosive source is located in a fluid layer and illustrate that the method can simulate the water reverberation in the sea. That makes significant sense to deep ocean acoustic experiments.

Three Dimensional Traction Forces Exerted by Migrating Amoeboid Cells

There is still a lack of information regarding the mechanical aspects of cell migration and the quantification of the traction forces is essential to completely understand the migration process. Most of the methods developed to measure traction forces exerted by cells moving over flat substrates assume that the vertical forces exerted by the cells are negligible and they only exert tangential forces to the substrate. Now we have developed a method to determine the cellular traction forces exerted perpendicular to the substrate in addition to the in-plane forces. We measure the 3D substrate deformation by tracking the displacements of fluorescent marker beads embedded in the substrate. The traction forces exerted by the cells are obtained by solving analytically the elastostatic equation for a linearly elastic medium using the previously measured deformation of the substrate. In order to understand the role of specific cytoskeletal components in the organization of the three-dimensional stresses we are using Dictyostelium Discoideum cells, we study mutants with contractility and actin-crosslinking defects and compare these mutants with Wild type cells. We are looking at Myosin II null and Cortexillin null mutants to quantify the role that these proteins play in the mechanics of cell motility. We find that the three cell lines studied push on the substrate near the center of the cell and pull up near the periphery. The magnitude of the perpendicular forces is comparable to the magnitude of the tangential forces to the substrate; therefore this perpendicular component cannot be neglected. Our measurements indicate that the effects of mutations on the tangential and perpendicular traction forces to the substrate are different. Therefore, it suggests that the generation of the perpendicular and tangential traction forces is possibly controlled by two different mechanisms.

Deciphering Cellular Forces during Myoblast Fusion

The fusion of mammalian myoblast cells is an integral part of muscle growth and regeneration. Although the biochemical aspects of cell fusion have been extensively investigated, a quantitative description of the physical phenomena underlying this process has not yet been explored. This study aims to quantify and distinguish both the extracellular and intercellular forces generated by two myoblasts during fusion or the lack thereof. To achieve this goal, we fabricated a protein-patterned polyacrylamide hydrogel with embedded fluorescent particles to employ time-lapse traction force microscopy on isolated pairs of cells. Our results indicate the presence of large intracellular stresses due to the polarizing tangential traction vectors pointing away from the cell-cell interface in both fusing and non-fusing cells. For non-fusing cells, these polarizing stresses were maintained throughout the duration of the time-lapse microscopy as the cells shift to and fro on the protein patterns. However, for cells undergoing fusion, the polarization of the traction vectors ceases as the stresses generated by the cell injecting its nuclei dominates the other. In addition to the tangential forces, we also analyzed the particle displacement field for normal stresses, which are revealed to be negligible under all circumstances. The magnitudes of the normal stresses have been shown to exist at an order of magnitude lower than that of the tangential stresses.

Quasi-static analysis of thrust-loaded angular contact ball bearings part II: Results and discussion

Ball bearings are widely employed mechanical components characterized by high precision and quality, and usually play important roles in various rotary machines and mechanisms. Many advanced applications require a deep understanding of their various kinematic and tribological characteristics that are essential to predict the fatigue endurance, relieve the vibration and minimize the power dissipation of ball bearings in particular applications. An angular contact ball bearing under a specified operating condition is simulated with the quasi-static/creepage analytical model proposed in the preceding article. The results demonstrate that the ball bearing is a statically determinate system. That the balls spin on both inner and outer races means the ball is controlled by neither the inner nor the outer raceway. The friction between the ball and raceway renders the inner and outer contact angles unequal. The larger the coefficient of friction is, the larger the angle deviation. The tangential traction perpendicular to the rolling direction due to the spin induces a gyro-like rotation of the ball with respect to the raceway even if no inertial effects are considered. The tangential elastic compliance of contacting surfaces gives rise to locked areas within the contact patch and transforms the sliding lines from circles into spirals. The differential slip due to the close conformity of the ball and raceway makes the sliding and traction distributions asymmetric, which will influence the location of the spinning center of the ball with respect to the raceway. The quasi-static/creepage model can be used to reveal the operating behaviors of ball bearings running under steady conditions and to optimize the design of ball bearings for specific applications.

Quasi-static analysis of thrust-loaded angular contact ball bearings part I: theoretical formulation

Ball bearings play an important role in various rotating machineries, but the complicated kinematic and tribological features of ball bearings make many aspects of their operating behaviors still inconclusive. Most theoretical analyses of ball bearings up to date are based on either the hypothesis of race control or other empirical models to determine the ball motion of ball bearings, but none of these strategies can reveal and consequently employ the intrinsic coupling mechanism between the spin and the tangential traction of contacting bodies rolling upon one another. To remedy the deficiency of current analytical models for ball bearing analysis, the rolling contact theory is employed to establish an explicit link between motions and interactions within ball bearings. A differential slip model is established to precisely define the slip component due to the significant curvature of the common contact patches between the ball and inner/outer raceways. The creepage and the spin ratio are formulated to accurately define the relative rigid motion between the ball and the inner/outer raceway. Then a quasi-static analytical model is established that can accurately determine the motions of the balls and races of the ball bearing. It can also give a vivid description of the slip and traction distributions within the contact area. The analytical model can be effectively used to analyze the operational conditions and tribological features of solid-lubricated ball bearings. It can also be used optimize the construction of ball bearings for specific applications.

Lamellar macular hole following intravitreal pegaptanib sodium (Macugen) injection for diabetic macular edema

To report on a patient who developed a lamellar macular hole 1month after an intravitreal pegaptanib sodium injection. Interventional case report. A 66year old patient developed a lamellar macular hole 1month after an intravitreal pegaptanib sodium injection for diabetic macular edema (DME). The pathogenesis of the lamellar macular hole in our case can be attributed to the intravitreal injection that may have induced vitreous incarceration, causing vitreoretinal traction at the macula and development of a lamellar macular hole. Alternatively or in association, pegaptanib itself may have caused the lamellar macular hole by inducing sudden reduction of the DME and exacerbation of tangential traction of the posterior vitreous on the overlying macular retina. Lamellar macular hole seems to be a potential complication of pegaptanib injection even in patients without pretreatment clinically detectable vitreomacular traction.

A dynamic model to predict crack propagation in z-pinned composite structures

A dynamic model to predict crack growth phenomena in z-pinned reinforced composite structures is proposed. The formulation is based on a novel technique, which is able to couple Fracture Mechanics concepts with a strategy based on a moving mesh methodology. The former is utilized to predict the crack growth, whereas the latter defines the way to take into account the geometry changes on the basis of the invoked fracture parameters. The presence of the z-pins is simulated by means of a large-scale bridging approach, introducing along the delaminated interfaces normal and tangential traction forces depending on the dynamic characteristics of the pull-out mechanism. In order to evaluate the fracture parameters, which govern the crack evolution, the J-integral decomposition procedure is utilized, providing new expressions in the framework of a large-scale bridging crack growth. A numerical modeling based on the finite element procedure is implemented and comparisons with experimental results are reported to validate the proposed formulation. Moreover, a parametric study is developed to investigate the influence of z-pins on the crack growth mechanisms.

Frictional elastic contact with periodic loading

Quasi-static frictional contact problems for bodies of fairly general profile that can be represented as half planes can be solved using an extension of the methods of Ciavarella and Jäger. Here we consider the tangential traction distributions developed when such systems are subjected to loading that varies periodically in time. It is shown that the system reaches a steady state after the first loading cycle. In this state, part of the contact area (the permanent stick zone) experiences no further slip, whereas other points may experience periods of stick, slip and/or separation. We demonstrate that the extent of the permanent stick zone depends only on the periodic loading cycle and is independent of the initial conditions or of any initial transient loading phase. The exact traction distribution in this zone does depend on these factors, but the resultant of these tractions at any instant in the cycle does not. The tractions and slip velocities at all points outside the permanent stick zone are also independent of initial conditions, confirming an earlier conjecture that the frictional energy dissipation per cycle in such systems depends only on the periodic loading cycle. We also show that these parameters remain unchanged if the loading cycle is changed by a time-independent tangential force, provided this is not so large as to precipitate a period of gross slip (sliding).

The Effect of Poisson’s Ratio on the Contact Traction Distribution of a Functionally Graded Coating

This paper deals with the finite frictional contact of a functionally graded coating with considering the effect of Poisson’s ratio. We assume that a functionally graded coated half-space is indented by a rigid spherical punch and that the shear modulus of FGMs varies as exponential function. The whole contact region is divided into the central adhesion zone and the slip annulus. Within the slip annulus, the shear stress is limited by friction. By using the Hankel integral transform technique, the problem is reduced to a set of Cauchy singular integral equations. A numerical method is used to get the contact pressure and tangential tractions in the contact region for different Poisson’s ratio. The results show that the variation of Poisson’s ratio has obvious effect on both normal and tangential tractions. With the increase of ν, the peak value of the normal traction increases and that of the tangential traction decreases.