Traction Distribution Research Articles

On the role of friction and remodelling in cell–matrix interactions: A continuum mechanical model

We discuss a mathematical model addressing the mechanical interactions exchanged between living cells and the extra-cellular environment, by specialising our study to focal adhesions. Many biological functions, such as cell locomotion, proliferation or orientation, require living cells to establish stable connections with the extra-cellular matrix. In this respect, focal adhesions anchor cells to the extra-cellular matrix and regulate the transmission of signals in response to internal or external stimuli.Within the adopted mechanical setting, both the focal adhesion and the extra-cellular matrix are described as rectified elastic fibres, subjected to a system of elastic forces. Moreover, the proposed model relies upon two peculiar features. The former aspect concerns the characterisation of a friction-like interaction between the focal adhesion complex and the extra-cellular matrix. Friction does, indeed, play a role in determining stability and growth of focal adhesion. The latter phenomenon considered in the present model is remodelling. Here, remodelling is understood as the occurrence and development of irreversible, plastic-like distortions related to the internal structure of both the focal adhesion complex and the extra-cellular matrix.The obtained formulation encompasses and generalises a class of models formerly proposed in the literature to the case where friction-like interactions and remodelling of both focal adhesion and substratum are taken into account. The reported numerical results illustrate the influence of both friction and remodelling on the distribution of tractions, displacements and effective stiffness of the ensemble comprising focal adhesion, extra-cellular-matrix and interacting cells.

Effects of Near-Surface Composites on Frictional Rolling Contact Solved by a Semi-Analytical Model

Abstract A semi-analytical model (SAM) to tackle the steady-state elastic frictional rolling contact problem involving composites is presented. Specifically, the frictional rolling contact is categorized into two subtypes, namely, normal and tangential problems, and the conjugate gradient method (CGM) is used to figure out the normal pressure and tangential traction. In SAM, the equivalent inclusion method (EIM) is applied to analyze the influence of composites on the matrix, and the displacement disturbance resulting from such composites is added to the total surface displacement, which implements the coupling between surface contact and composites. The accuracy of the proposed model is verified by the finite element (FE) model. The effects of composites on the frictional rolling contact behavior are investigated. The results indicate that Young’s modulus, as well as the size and location of the composites, are correlated with the distributions of tangential traction, subsurface stresses, and the sizes of stick and sliding zones.

A Numerical Model for Solving Three-Dimensional Rolling Contact Problems with Elastic Coating Layers

In this work, a numerical model is proposed for three-dimensional rolling contact problems with one or two elastic layers, and the tangential contact solution is emphasized. Previous works on this topic have mostly been two-dimensional, in which only longitudinal creepage has been considered. With the three-dimensional model presented in this work, all possible creepages, such as the longitudinal, lateral and spin creepages are taken into account. In order to improve the calculation efficiency, the conjugate gradient method and the FFT technique are employed. The influence coefficients for displacement and stress are obtained from the corresponding frequency response functions. The numerical results are validated against existing results and good agreement can be found. The effects of the different layers’ thicknesses and elastic moduli under different creepage combinations on the traction distribution and stick/slip results are investigated. It can be seen that by adjusting the layer parameters the traction and stick/slip results can be modified significantly, and it may, therefore, be very useful information for improving the rolling contact fatigue and mitigating wear problems in various mechanical systems.Graphical

A sensorless traction strategy for all-wheel drive electric motorcycles

Motorcycle designers aim to enhance vehicle performance, stability, and safety, especially when the vehicle is approaching the tyres' friction limit. A strategy to achieve these purposes is to design All-Wheel Drive (AWD) vehicles with active torque distribution. Nowadays, effective technical solutions for powering the front wheel of a motorcycle have been proposed. The use of traction on both front and rear wheel is convenient when tyre friction is low, enhancing vehicle safety and performance. In this context, this paper presents a sensorless, open-loop traction strategy for AWD motorcycles that improves performance and stability both in straight running and in cornering, without requiring the knowledge of road-tyre adherence. This novel traction distribution strategy is based on the idea of maximising the area of the motorcycle performance envelope, also known as g-g diagram. A simplified mathematical model is used to find closed-form solution to this problem, then converted into a control algorithm for the front and rear driving torques. The performance of the proposed method is assessed with simulations: a detailed model of a light electric motorcycle is used for calculating the non-linear vehicle performance envelope, the acceleration response in straight running and cornering, and the response to road irregularities. Moreover, a comparison with feedback slip-based traction control system is conducted. Simulation results indicate that the AWD motorcycle outperforms the conventional rear wheel drive motorbike almost in all situations, especially when road-tyre adherence is low, and that no counter-indication for the adoption of the AWD architecture exists.

Contribution of the nucleation and recovery of disconnections to shear viscosity in diffusional creep

According to the principles of diffusional creep, the normal and tangent components of the velocity jumps between adjacent grains arise from, respectively, the climbing and sliding of disconnections along grain boundaries. Stationary deformation thus implies a balance between nucleation and recovery of moving disconnections. The model considers a periodic lattice of hexagonal grains with nucleation of disconnection multipoles at triple junctions. The strain energy coupled to the population of climbing disconnections is calculated by inferring that the internal strain field associated to disconnection pile-ups brings a distribution of tractions along GBs that is consistent with the field of diffusion potential gradient that drives disconnection climb. It follows that the distribution of the density of climbing disconnections is parabolic and that the dissipation due to the nucleation and recovery of climbing disconnections is equal to 50% of the dissipation arising from diffusion fluxes. These results hold for both Nabarro-Herring creep and Coble creep. The analysis of the disconnection nucleation process highlights the sources of non-Newtonian behaviour and the existence of a threshold stress as an intrinsic feature of diffusional creep.

Contribution of the Nucleation and Recovery of Disconnections to Shear Viscosity in Diffusional Creep

According to the principles of diffusional creep, the normal and tangent components of the velocity jumps between adjacent grains arise from, respectively, the climbing and sliding of disconnections along grain boundaries. Stationary deformation thus implies a balance between nucleation and recovery of moving disconnections. The model considers a periodic lattice of hexagonal grains with nucleation of disconnection multipoles at triple junctions. The strain energy coupled to the population of climbing disconnections is calculated by inferring that the internal strain field associated to disconnection pile-ups brings a distribution of tractions along GBs that is consistent with the field of diffusion potential gradient that drives disconnection climb. It follows that the distribution of the density of climbing disconnections is parabolic and that the contribution to dissipation is equal to 50% of the contribution arising from diffusion fluxes. These results hold for both Nabarro-Herring creep and Coble creep. The analysis of the disconnection nucleation process highlights the sources of non-Newtonian behaviour and the existence of a threshold stress as an intrinsic feature of diffusional creep.

Компоновка электропривода вагона метрополитена

Objective: Analysis of various layouts of the electric drive of wheelsets and the control traction con- verter on transistor modules. Methods: The assessment and comparison of the layout solutions of asynchronous electric drives with one inverter supplying two or four traction motors is carried out. A mathematical analysis of the influence of the difference in the diameters of wheelsets leading to an inequality of traction forces and causing sliding has been carried out. Results: It was revealed that the use of the layout one inverter — four asynchronous motors is the least efficient and leads to a greater extent to negative consequences during the operation of wheelsets. Practical importance: The use of an electric drive scheme for subway cars with one inverter feeding two traction motors is substantiated, which leads to a more even distribution of traction and braking forces and significantly reduces the risk of slipping and skidding. Thus, the wear of wheelsets and the rest of the kinematic chain is reduced and the resource of their nodes and elements increases to a large extent

Indentation of an elastic half-space by the cylindrical flat punch with a rounded edge under non-monotonic loading

The paper presents a novel approach to solving the contact problem for interaction with friction between a rigid cylindrical flat punch with rounded corners and a linearly elastic half-space. Increasing and decreasing normal loads act on the punch sequentially. Coulomb’s law is used to account for friction. The contact problem is reduced to nonlinear operator equations that must be solved at each step of the discrete loading process. The numerical method is applied. This method includes regularization of the equation, discretization of the regularized equations and the usage of an iterative process to obtain the approximate solution. The calculations were performed for different values of the relative radius of the flat area of the punch base. Distributions of contact traction and configuration of the stick and slip zones are studied at each monotonic stage of the loading process.

Coupler force reduction method for multiple-unit trains using a new hierarchical control system

During traction and braking of multiple-unit trains, substantial longitudinal dynamic forces might occur in couplers due to the non-optimal distribution of traction and braking forces generated by self-propelled carriages. These dynamic forces might create shocks affecting the reduction of endurance of the weakest train structural components primarily. Thus, the overall operational safety of the train is also lowered. The purpose of the paper is to develop a new control system to supervise the activities related to the longitudinal dynamics of each train carriage in a multiple-unit train to reduce the longitudinal coupler forces acting during train traction and braking. The hierarchical structure of the control system consists of two levels. The first master level of control works like standard cruise control. However, the reduction of longitudinal coupler forces is achieved by applying a second level of slave control systems with a control configuration of feedback compensation.

Feasibility on accurate measurement of non-uniform strain field through contact methods

When straight material filaments do not remain straight after deformation, the strain varies spatially. These spatially varying strain fields arise because of (1) non-uniform distribution of boundary traction, (2) presence of residual stress in the reference configuration, (3) the body being inhomogeneous. The strain measured using devices such as extensometer and strain gauge assumes that the strain is uniform over the gauge length, irrespective of the strains actual variation. Here the accuracy of the strain estimated using contact strain measurement techniques is investigated by assuming that the uniaxial strain (not stress) varies periodically along the measurement axis. A tight bound for the error in the measured strain is obtained and verified through numerical simulation. This study’s significant finding is that for gauge length of strain measurement about two times the periodicity of the strain variation, the measured strain’s value would be repeatable but with a significant error. Thus, one has to be cautious about the magnitude of the estimated non-uniform strain.

Numerical study on the ratcheting performance of rail flash butt welds in heavy haul operations

The ratcheting performance of a new R400HT rail flash butt weld was numerically evaluated under a typical heavy haul in-service condition. Due to varying mechanical properties across the rail weld, the weld region was divided into 23 zones in the numerical study. A dynamic finite element simulation of wheel–rail weld rolling contact was first carried out to obtain the total vertical contact force and its variation along rolling distance. Multiple quasi-static wheel–rail weld contact simulations were then performed by applying the total vertical contact force to determine the non-Hertzian contact pressure distribution when the wheel was located at different positions across the weld in the rolling direction. Based on each normal contact pressure distribution, the Haines and Ollerton's strip theory and Carter's theory were employed to estimate the corresponding longitudinal surface tangential traction distribution. Finally, a cyclic loading simulation was conducted to evaluate the ratcheting performance of the rail weld in terms of RCF initiation life by repeatedly translating these normal contact pressure and longitudinal tangential traction distributions on the running surface. The results reveal that the subzone with the lowest hardness in the softened zone has the shortest RCF initiation life among the weld region, followed by the region around the bond line. The parent rail provides the longest RCF initiation life and therefore has the best resistance to RCF. Additionally, the existence of the softened zone can shorten the RCF initiation life of the parent rail and the bond line section, particularly the regions located adjacent to the softened zone. The possible location of RCF initiation in the softened zone of the rail head can reach deeper than those in the parent rail and the region around the bond line. The results can help us understand the failure of flash butt rail welds in heavy haul operations and the numerical method can be applied to study different rail welds and rail welds under different conditions such as in a curved track.

Mixed boundary value problems in power-law functionally graded circular annulus

The present work proposes a semi-analytical technique for solution of mixed boundary value problem in functionally graded circular annulus wherein shear modulus varies radially in power-law form while Poisson’s ratio is constant. The technique relies on two main steps. In the first step, corresponding to terms in periodic Fourier series applied individually as traction along the annulus surface, stress and displacement field in the annulus is computed harnessing Airy stress functions approach. In the second step, leveraging the strain–displacement relations in polar co-ordinates, mixed boundary conditions are rendered in terms of displacement all along the annulus surface. Assuming the unknown traction along the annulus surface in terms of periodic Fourier series with finite terms, the modified displacement boundary condition, family of solution from the first step and orthogonality of sine and cosine functions is used to generate a system of simultaneous linear equations for the series coefficients. Knowing the coefficients of periodic Fourier series, stress and displacement field can be computed everywhere in the annulus. The first step is digitized in terms of MAPLE functions, exhaustively validated through traction distribution comprising of normal, shear traction on part of the boundary and pair of equal and diametrically opposite point load along the boundary. The second step is corroborated through a problem where the inner surface is subjected to a specified traction distribution and mixed boundary conditions exist along the outer surface in the form of complete constraint along a part and traction-free condition elsewhere.

Interlaminar fracture of asymmetrically delaminated specimens: Beam modelling and noteworthy characteristics

Despite providing interesting mode-mix ratios without elaborate test fixtures, asymmetrically delaminated specimens have been scarcely used for characterizing delamination resistance. This is mostly due to the elaborate analyses employed and the controversy about mode partitioning. This paper presents a beam model for asymmetrically delaminated unidirectional composite specimens. The physical meaning and underlying assumptions of the solutions obtained are clearly identified. Comparison with finite element analyses showed that the present beam model is accurate for a wide range of asymmetry and mode-mix ratios. Since it does not require complicated calculations, the beam model is well-suited for experimental data reduction. Furthermore, traction distributions near the crack-tip were found to differ from those of standard specimens, thereby increasing the interest in studying the fracture behaviour of asymmetrically delaminated specimens.

Effects of domain unfolding and catch-like dissociation on the collective behavior of integrin–fibronectin bond clusters

To gain more understanding of cell–matrix adhesion, we consider an idealized theoretical model of a cluster of integrin–fibronectin bonds at the cell–matrix interface subjected to a dynamic ramping. The distributions of bond traction and interfacial deformation are assumed to obey classical elastic equations, whereas the dissociation/association of individual bonds as well as unfolding/refolding of fibronectin domains are described by stochastic equations. Through stochastic-elasticity coupling, we perform Monte Carlo simulations to investigate how the collective behavior and adhesion performance of the integrin–fibronectin-mediated interface are influenced by two characteristics newly incorporated in the modeling, i.e., catch-like dissociation between integrin and fibronectin, and unfolding of repeated domains in fibronectin. The probable unfolding of fibronectin domains is found to have profound effects on the resultant adhesion energy of the integrin–fibronectin-mediated interface, and governs the failure model transiting between uniform decay and catastrophic crack-like rupture. Focal adhesions containing integrin–fibronectin bond clusters play a vital role in a wide variety of cellular processes or functions. We develop a stochastic-elasticity modeling framework for such specific interaction at cell–matrix interface, by unifying the elastic descriptions of force distribution and deformation, and the stochastic descriptions of bond dissociation/association and domain unfolding/folding. The present modeling reveals a rich array of out-of-equilibrium behaviors of the integrin–fibronectin-mediated interface, and may provide clues for the development of artificial domain-containing structures and functional surfaces to modulate the collective behavior of bond-mediated cell–matrix adhesion.

The role of bond strength in structural behaviors of UHPC-NC composite beams: Experimental investigation and finite element modeling

The booming application of UHPC-NC composite members renders the interfacial behavior a critical role in their macro-scale structural behaviors. Four composite beams were monotonically loaded to failure, with various thickness of the UHPC layer. The occurrence of UHPC-NC interface debonding demonstrated the role of bond strength. To this end, the standard slant shear test was improved and performed to quantify the bond strength in a realistic manner. For the computational aspects, reliable finite element (FE) models are constructed, which adopt the localizing gradient-enhanced model for the bulk region (UHPC and NC), the Menegotto-Pinto model for rebars, and a coupled cohesive-friction model for the interface. The meso-mechanical assumption is employed to smoothly integrate the cohesion with the friction. Viscous regularization is adopted to suppress the instability and the convergence problem. Identification of model parameters is well performed and presented. These FE models are verified with the tested composite beams, which offer a valuable insight to the evolution and distribution of normal and tangential tractions along the UHPC-NC interface. It is demonstrated that all the analyses are realized with the implicit incremental-iterative algorithm.

The two-dimensional fretting contact with a bulk stress. Part II – Loading history and dissimilar elastic materials

The contact model for similarly elastic materials advanced in the companion paper is enhanced to account for the more general case of contacting bodies with different elastic properties. The latter contact model, involving dissimilarly elastic bodies under partial slip, is particularly difficult to solve due to the mutual interaction between the normal and the shear tractions. As opposed to the contact of similar elastic materials, pressure is affected by the shear tractions and vice versa. Therefore, the contact submodels in the normal and in the tangential direction are not independent. The connection can only be overcome in an iterative manner, by adding a new external loop to the contact algorithm, in which the solutions of the systems in the normal and in the tangential directions are mutually adjusted by successively solving both systems until convergence is reached. Moreover, with friction being a dissipative process, any state depends upon the process path, i.e., on all previous states attained during the loading history. The contact model is solved as a series of quasi-static states that are expected to replicate the loading path. Two levels of iterations are added to the model of similarly elastic materials, described in the companion paper, to account for the dissimilarity in the elastic properties. The contact process is reproduced on a prolonged loading history, consisting in the first fretting loops. The distributions of contact tractions are obtained using a technique for the fast computation of convolutions involving the fast Fourier transform. The conducted simulations prove the method robustness and its application in the modelling of the fretting processes.

The torsional contact of coated bodies

This paper advances an algorithm for the simulation of the elastic contact undergoing a constant normal force and an oscillating torsional moment, under the assumption of partial slip. The solution of this type of contact can be achieved with a numerical formulation based on influence coefficients that express the contribution of elementary rectangular patches of uniform surface tractions, normal or tangential, to the displacement field induced in the elastic half-space. Summation of these elementary contributions allows for the calculation of the displacement field for arbitrary distributions of tractions, thus allowing for an iterative problem resolution that can handle arbitrary contact geometry, various frictional regimes and consideration of coated materials. The displacement response of multi-layered bodies is calculated based on the frequency response functions, and a previously advanced technique for calculation of convolution products in the Fourier transform domain is implemented for increased accuracy. The solution of the tangential contact problem is achieved by the treatment of the arising linear system of equations with the conjugate gradient method, which provides superior computational efficiency. The interaction between the normal and the tangential contact tractions is discussed. The influence of the Young modulus ratio between the coating and the substrate on the shear tractions in the partial slip torsional contact is investigated through numerical simulations.

Biomechanical study of different internal fixations in Pauwels type III femoral neck fracture - A finite elements analysis

ObjectiveTo evaluate biomechanical behavior of different internal fixation methods for the treatment of Pauwels Type III femoral neck fractures. MethodsThree internal fixators were developed to treat Pauwels Type III femoral neck fracture using finite elements: dynamic hip screw (DHS); DHS combined with anti-rotation screw; three cannulated screws in an inverted triangular configuration (ASNIS). Under the same conditions, vertical fracture displacement, and maximum and minimum principal, and Von Mises stresses were evaluated. ResultsThe vertical displacements evaluated were: 5.43 mm, 5.33 mm and 6.22 mm, rotational displacements values were 1.1 mm, 0.4 mm and 1.3 mm; maximum principle stress values obtained for the upper region of the femoral neck were 3.26 hPa, 2.77 hPa, and 4.5 hPa, minimum principal stress values obtained for the inferior region of the femoral neck were −1.97 hPa, −1.8 hPa and t −3.15 hPa; Von Mises peak stress values were 340.0 MPa, 315.5 MPa and 326.1 Mpa, for DHS, DHS with anti-rotation device, and ASNIS, respectively. Conclusion: The DHS combined with anti-rotation screw yielded better results in terms of rotational and vertical displacements, traction and compression distributions on fractures, and Von Mises stress, demonstrating mechanical superiority for Pauwels Type III fracture.

Comparison of two time-marching schemes for dynamic rupture simulation with a space-domain BIEM

The boundary integral equation method (BIEM) is one of the important numerical techniques used to simulate geophysical phenomena including dynamic propagation, nucleation, and sequence of earthquake ruptures. We studied the stability and convergence of two time-marching schemes numerically for 2-D problems in Mode I, II, and III conditions. One was a conventional method based on piecewise-constant spatiotemporal distribution of the rate of displacement gap V (CM), and the other was a slightly modified scheme from a predictor–corrector method previously applied to a spectral BIEM (NL). In the stability analysis, we simulated behavior of a traction-free fault under uncorrelated random distributions of initial traction. The growth rate of the perturbation is negative in a parameter regime of complex shape with CM, which has two numerical parameters, and the intersection for all the modes is very restricted as reported previously. In contrast, NL has only one parameter and yields simpler and a wide parameter regime of stability, conceivably allowing more flexible meshing on the fault. In the convergence analysis in which a smooth problem was solved, CM resulted in a numerical error scaled as Delta x^{1} while NL led to the scaling of Delta x^{2} typically or of Delta x^{1.5} under certain conditions in Mode II problems. NL requires negligible additional computational costs and modification of the code is quite straightforward relative to CM. Therefore, we conclude that NL is a useful time-marching scheme that has wide applicability in simulations of earthquake ruptures although the reason for the rather complicated convergence behavior and verification of the findings here to more general conditions deserve further study.

Effect of Surface Roughness on Adhesive Instabilities for the Elastic Layer

If an incompressible elastic layer bonded to a rigid plane is placed close to a second rigid plane, adhesive interactions between the surfaces can cause elastic instabilities. These lead to spatially non-uniform traction and gap distributions which exhibit a regular pattern with a characteristic wavenumber. However, real surfaces are never completely plane. In this paper, we consider the influence of surface roughness on the instability, with particular reference to the force-displacement relation. With random roughness profiles, the traction distributions are always spatially irregular, so the onset of instability is more difficult to define. One approach is to monitor the amplitude of the power spectrum of the distribution near the characteristic wavenumber. Since surface roughness generally reduces the mean adhesive traction, we might expect it to exert a stabilizing effect. Numerical results confirm this for moderate to large RMS amplitudes, but show that low RMS roughness can actually trigger the instability in ranges where the uniform layer would be stable. The resulting traction-displacement relation is then found to be approximately linear with a slope close to that at the point where the uniform solution loses stability.