Finite frictional contact

Sprensen et al. [63] also examined the effect of incommensurability. The tip was made incommensurate by rotating it about the axis perpendicular to the substrate by an angle 0. The amount of friction and wear depended sensitively on the size of the contact, the load, and 0. The friction between large slabs exhibited the behavior expected for incommensurate surfaces There was no wear, and the kinetic friction was zero within computational accuracy. The friction on small tips was also zero until a threshold load was exceeded. Then elastic instabilities were observed leading to a finite friction. Even larger loads lead to wear like that found for commensurate surfaces. 

In this expression Y = Yi + Y2 12 where Yj and Y2 are the surface tensions of the sphere and flat, respectively, and Yj2 is the surface tension of the interface between them. The JKR expression recognizes the fact that even in the absence of a normal force (N = 0) siuface tension will cause some elastic deformation of the surfaces producing a finite contact area. This fact alone renders the concept of a coefficient of friction meaningless since it implies that there is some finite friction force between solids even under zero normal force. 

Oscillations may exert a strong effect on adsorption processes in the frictional contact. Adsorption of particles on the electrode with a certain potential is known [23] to occur at a finite speed. Under low oscillation frequencies the adsorption manages to follow the potential and participate in the variation of the interfacial layer structure. At high frequencies the adsorption mechanism does not work, giving place to electrostatic charging of the layer as a condenser, i.e. the generation of the double electric layer (DEL). A mechanical model of the interfacial DEL has been elaborated by Shepenkov [24]. It follows from the model that, if a periodic mechanical force acts on the double layer from the side of the liquid or electrode, the electrode potential will vary periodically with the same excitation frequency. 

Ju JW, Taylrjr RL. A perturbed Lagrangian formulation for the finite element solution of nonlinear frictional contact problems. J. De Mechanique Theorique et Appliquee 1988 7(S1) 1-14. 

A finite element model of the rivet and pin system was developed to analyze rivet deployment and optimize the design of the system. The model includes the rivet body and pin and a cylindrical portion of bone. A finite sliding contact analysis with friction (Abaqus Version 5.8) was conducted in two steps placement of the rivet body into a hole in bone and insertion of the pin into the rivet body. The material properties were as follows Bone E=2 GPa, Poisson s ratio=0.3 and polymer E=2.5 GPA, Poisson s ratio=0.45. The friction coefficient on all surfaces was 0.1. 

Contact conditions add even more difficulty and complexity to an already very complex and difficult analysis of rubber products and tires. Contact conditions are unilateral and need to be constantly checked during the incremental nonlinear analysis. In addition, they are not smooth, thus degrading the performance of nonlinear solvers. A number of numerical regularization parameters need to be introduced to prevent chattering and ensure robustness of a finite element analysis (FEA) with frictional contact. 

It may come as a surprise to some that two commensurate surfaces withstand finite shear forces even if they are separated by a fluid.31 But one has to keep in mind that breaking translational invariance automatically induces a potential of mean force T. From the symmetry breaking, commensurate walls can be pinned even by an ideal gas embedded between them.32 The reason is that T scales linearly with the area of contact. In the thermodynamic limit, the energy barrier for the slider to move by one lattice constant becomes infinitely high so that the motion cannot be thermally activated, and hence, static friction becomes finite. No such argument applies when the surfaces do not share a common period. 

Introduction. In the absence of all contact with an external solid, a prime mover placed in a fluid of finite or even zero density can propel itself by ejecting a fluid or solid mass toward the rear. By convention we say that this mover is propelled by jet propulsion, although the propulsive thrust really results from the effects of pressure and friction exerted on the wall of the hollow interior of the mover by the solids or fluids moving in the interior toward the exhaust nozzle ... 

Ideally, that is for infinitely hard solids, a rolling sphere or cylinder makes contact with the underlying surface at only one point or a single line, respectively. In this cases, rolling friction would in fact be zero as there is no relative movement of the contacting surfaces. In real systems, there is always a finite contact area, as we have seen in Section 6.8. As a result, there are different sources of energy dissipation and thus rolling friction ... 

In analogy to indentation experiments, measurements of the lateral contact stiffness were used for determining the contact radius [114]. For achieving this, the finite stiffness of tip and cantilever have to be taken into account, which imposes considerable calibration issues. The lateral stiffness of the tip was determined by means of a finite element simulation [143]. As noted by Dedkov [95], the agreement of the experimental friction-load curves of Carpick et al. [115] with the JKR model is rather unexpected when considering the low value of the transition parameter A(0.2Further work seems to be necessary in order to clarify the limits of validity of the particular contact mechanics models, especially with regard to nanoscale contacts. 

Indeed, the shear stress at the solid surface is txz=T (S 8z)z=q (where T (, is the melt viscosity and (8USz)z=0 the shear rate at the interface). If there is a finite slip velocity Vs at the interface, the shear stress at the solid surface can also be evaluated as txz=P Fs, where 3 is the friction coefficient between the fluid molecules in contact with the surface and the solid surface [139]. Introducing the extrapolation length b of the velocity profile to zero (b=Vs/(8vy8z)z=0, see Fig. 18), one obtains (3=r bA). Thus, any determination of b will yield (3, the friction coefficient between the surface and the fluid. This friction coefficient is a crucial characteristics of the interface it is obviously directly related to the molecular interactions between the fluid and the solid surface, and it connects these interactions at the molecular level to the rheological properties of the system. 

Shear in an epoxy-bonded film. The results, in Figure 5.2, show that there is a linear relationship between compressive stress and shear stress, but that there is a finite shear stress in the uncompressed state. As a result, the coefficient of friction decreases as the contact pressure increases as shown in Figure 5.3. 

We begin by considering the blade-ice contact area. We then formulate the ploughing and shear stress forces, which together comprise the ice friction. Next, we posit the lubrication equation and solve it using finite-differences. Finally, we validate the model results against experimental data and show some additional model predictions. 

Cheek plates (for design and more detailed descriptions see below), the heart-shaped pieces sealing the side of the nip between the rollers, can not be in rubbing contact with the rollers as excessive wear would take place and the constant friction, which is aggravated by the presence of fine powder particles, causes the rollers and the cheek plates to quickly become red hot. Rather, well adjusted cheek plates have a finite clearance which is selected such that the leakage of fine material is minimized. In this... 

The dispersive stress evidently contributes an additional term to the force balance. This stress is strongly dependent on solids concentration. According to Hanes and Inman (100), this stress requires a finite interparticle shear strain rate and would not exist in a sliding bed of solids. In the latter case, the immersed weight of the particles would be transmitted to the pipe wall by interparticle Coulombic friction. The stress resulting from this type of contact was denoted the supported load (94). 

The finite element model described in Section 11.2 was used here to model the friction experiments described above. However, to simulate the 16 Nm torque, a bolt pre-stress of 227 MPa was applied. This value was obtained experimentally from the axial gauges in the shank of a specially manufactured instmmented bolt, as discussed previously. For comparison, both the continuous and stick-slip [25] fiiction models (available in MSC Marc finite element code) was used to account for fiiction between the contacting interfaces. The fiiction coefficients were chosen to be 0.1, 0.3 and 0.45 between the bolt/laminate, washer/laminate and laminate/laminate interfaces, respectively. More details on fiiction coefficient selection can be found in [17]. 

The indentation process has been analyzed by the finite element method. It has been used the implicit methodology. The studied models have been analyzed under axisymmetric conditions. It has been demonstrated that apparently the forces do not depend on the friction between the contact surfaces of the punch and workpiece. The forces in axisymmetric models are influenced by the width of the workpiece while the height is not so relevant. 

When two solid objects are in contact under a normal load W, a certain finite amount of force will be required to initiate and maintain tangential movement with respect to one another. When at rest, no recoverable energy is stored at the interface between the two, so that when force is applied and work is done, most of that work is dissipated as heat. The force which must be overcome in order to make the two objects move is known generally as friction. In general, one finds that two frictional forces will be involved in such a process the force necessary to initiate movement or that to overcome static friction, and that necessary to maintain movement or kinetic friction. 

For this example, we will initially assume that the tip of the manipulator is already in motion relative to the contact surface (slipping). The coefficient of friction is finite. In this case, we may assume that the contact forces applied in the directions of motion are already laige enough to overcome static friction. We will also examine the same ccxitact when the coefficient of friction is negligible (frictionless surface), and when the manipulatcx tip is not slipping on the surface. 

O Bradaigh and Pipes originally studied the plane stress flows of ideal fiber reinforced fluids (IFRF) and have used a penalty method to impose the fiber inextensibility constraint with biquadratic velocity/bilinear discontinuous tension elements. A linear and quasistatic scheme has been used to calculate instantaneous velocities which are multiplied by the time step to displace the mesh. Such an approach involves the buildup of considerable error unless time steps are extraordinarily small. Recently, this model has been improved by developing a mesh updating scheme that incorporates finite incompressibility and inextensibility constraints [8]. The new model also uses large displacement contact/friction elements to model tool contact and interply slip between layers of IFRF, in plane strain. 

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