scholarly journals A Paradox in Sliding Contact Problems With Friction

2003 ◽  
Vol 72 (3) ◽  
pp. 450-452 ◽  
Author(s):  
G. G. Adams ◽  
J. R. Barber ◽  
M. Ciavarella ◽  
J. R. Rice
Keyword(s):  
Half Plane ◽  
Slip Velocity ◽  
Finite Strain ◽  
Applied Pressure ◽  
Strain Analysis ◽  
Contact Problems ◽  
Rigid Punch ◽  
Flat Punch ◽  
Relative Slip ◽  
Velocity Changes

In problems involving the relative sliding to two bodies, the frictional force is taken to oppose the direction of the local relative slip velocity. For a rigid flat punch sliding over a half-plane at any speed, it is shown that the velocities of the half-plane particles near the edges of the punch seem to grow without limit in the same direction as the punch motion. Thus the local relative slip velocity changes sign. This phenomenon leads to a paradox in friction, in the sense that the assumed direction of sliding used for Coulomb friction is opposite that of the resulting slip velocity in the region sufficiently close to each of the edges of the punch. This paradox is not restricted to the case of a rigid punch, as it is due to the deformations in the half-plane over which the pressure is moving. It would therefore occur for any punch shape and elastic constants (including an elastic wedge) for which the applied pressure, moving along the free surface of the half-plane, is singular. The paradox is resolved by using a finite strain analysis of the kinematics for the rigid punch problem and it is expected that finite strain theory would resolve the paradox for a more general contact problem.

A Rigid Punch Bonded to a Half Plane

1979 ◽  
Vol 46 (4) ◽  
pp. 844-848 ◽  
Author(s):  
G. G. Adams
Keyword(s):  
Shear Stress ◽  
Free Surface ◽  
Normal Stress ◽  
Half Plane ◽  
Square Root ◽  
Rigid Punch ◽  
Flat Punch ◽  
Logarithmic Singularities

The well-known solution for a rigid punch bonded to an elastic half plane has oscillatory singularities at the corners of the punch. It is shown here that the resulting displacement of the free surface of the half plane actually spirals in upon itself and is therefore physically inadmissible. The problem of a flat punch with sloped sides is then formulated and a solution obtained which does not have an oscillatory singularity. The limit is taken as the punch sides become perpendicular with its base. This leads to square root singularities in the shear stress and to logarithmic singularities in the normal stress along the bond.

Thermal Distortion of an Anisotropic Elastic Half-Plane and its Application in Contact Problems Including Frictional Heating

2005 ◽  
Vol 128 (1) ◽  
pp. 32-39 ◽  
Author(s):  
Yuan Lin ◽  
Timothy C. Ovaert
Keyword(s):  
Heat Flux ◽  
Half Plane ◽  
Frictional Heating ◽  
Contact Problems ◽  
Local Heat ◽  
Extended Version ◽  
Parabolic Profile ◽  
Local Heat Flux ◽  
Anisotropic Elastic ◽  
Thermoelastic Contact Problem

The thermal surface distortion of an anisotropic elastic half-plane is studied using the extended version of Stroh’s formalism. In general, the curvature of the surface depends both on the local heat flux into the half-plane and the local temperature variation along the surface. However, if the material is orthotropic, the curvature of the surface depends only on the local heat flux into the half-plane. As a direct application, the two-dimensional thermoelastic contact problem of an indenter sliding against an orthotropic half-plane is considered. Two cases, where the indenter has either a flat or a parabolic profile, are studied in detail. Comparisons with other available results in the literature show that the present method is correct and accurate.

Constitutive inequalities for isotropic elastic solids under finite strain

1970 ◽  
Vol 314 (1519) ◽  
pp. 457-472 ◽  
Keyword(s):  
Scalar Product ◽  
Finite Strain ◽  
Strain Analysis ◽  
Stress And Strain ◽  
Elastic Solids ◽  
Intrinsic Interest ◽  
Typical Member ◽  
Rates Of Change ◽  
Constitutive Inequalities ◽  
Strain Measures

Possible restrictions on isotropic constitutive laws for finitely deformed elastic solids are examined from the standpoint of Hill (1968). This introduced the notion of conjugate pairs of stress and strain measures, whereby families of contending inequalities can be generated. A typical member inequality stipulates that the scalar product of the rates of change of certain conjugate variables is positive in all circumstances. Interrelations between the various inequalities are explored, and some statical implications are established. The discussion depends on several ancillary theorems which are apparently new; these have, in addition, an intrinsic interest in the broad field of basic stress—strain analysis.

Structural, electronic and elastic properties of Ti2TlC, Zr2TlC and Hf2TlC

Open Physics ◽  
2009 ◽  
Vol 7 (4) ◽  
Author(s):  
Abdelmadjid Bouhemadou
Keyword(s):  
Elastic Properties ◽  
Finite Strain ◽  
High Pressures ◽  
Applied Pressure ◽  
First Principle ◽  
Shear Moduli ◽  
Lattice Constants ◽  
First Principle Calculations ◽  
Electrical Conductors ◽  
Good Agreement

AbstractUsing First-principle calculations, we have studied the structural, electronic and elastic properties of M2TlC, with M = Ti, Zr and Hf. Geometrical optimization of the unit cell is in good agreement with the available experimental data. The effect of high pressures, up to 20 GPa, on the lattice constants shows that the contractions are higher along the c-axis than along the a axis. We have observed a quadratic dependence of the lattice parameters versus the applied pressure. The band structures show that all three materials are electrical conductors. The analysis of the site and momentum projected densities shows that bonding is due to M d-C p and M d-Tl p hybridizations. The M d-C p bonds are lower in energy and stiffer than M d-Tl p bonds. The elastic constants are calculated using the static finite strain technique. We derived the bulk and shear moduli, Young’s modulus and Poisson’s ratio for ideal polycrystalline M2TlC aggregates. We estimated the Debye temperature of M2TlC from the average sound velocity. This is the first quantitative theoretical prediction of the elastic properties of Ti2TlC, Zr2TlC, and Hf2TlC compounds that requires experimental confirmation.

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