The Elastic Field for Conical Indentation Including Sliding Friction for Transverse Isotropy

1992 ◽  
Vol 59 (2S) ◽  
pp. S123-S130 ◽  
Author(s):  
M. T. Hanson
Keyword(s):  
Shear Stress ◽  
Coulomb Friction ◽  
Sliding Friction ◽  
Contact Region ◽  
Transverse Isotropy ◽  
Elastic Field ◽  
Elementary Functions ◽  
Elastic Bodies ◽  
Title Problem ◽  
Conical Indentation

This paper gives closed-form expressions in terms of elementary functions for the title problem of conical indentation of elastic bodies possessing transverse isotropy. Traction in the contact region is also included in the form of Coulomb friction; thus, the shear stress is taken proportional to the contact pressure. The present expressions are derived here by integration of the point force Green’s functions.

The Elastic Field for Spherical Hertzian Contact Including Sliding Friction for Transverse Isotropy

1992 ◽  
Vol 114 (3) ◽  
pp. 606-611 ◽  
Author(s):  
M. T. Hanson
Keyword(s):  
Coulomb Friction ◽  
Sliding Friction ◽  
Contact Region ◽  
Transverse Isotropy ◽  
Elastic Field ◽  
Hertzian Contact ◽  
Elementary Functions ◽  
Elastic Bodies ◽  
Title Problem ◽  
Equivalent Expressions

This paper gives closed-form expressions in terms of elementary functions for the title problem of spherical Hertzian contact of elastic bodies possessing transverse isotropy. Traction in the contact region is also included in the form of Coulomb friction; thus the shear stress is proportional to the contact pressure. The present expressions derived here by integration of the point force Green’s functions are simpler and easier to apply than equivalent expressions which have previously been given.

The Elastic Field for Spherical Hertzian Contact of Isotropic Bodies Revisited: Some Alternative Expressions

1993 ◽  
Vol 115 (2) ◽  
pp. 327-332 ◽  
Author(s):  
M. T. Hanson ◽  
T. Johnson
Keyword(s):  
Coulomb Friction ◽  
Contact Region ◽  
Complete Solution ◽  
Elastic Field ◽  
Hertzian Contact ◽  
Hertz Contact ◽  
Elementary Functions ◽  
Present Solution ◽  
Coulomb Friction Law ◽  
Isotropic Bodies

Closed-form expressions in terms of elementary functions are derived for the elastic field resulting from spherical Hertz contact of isotropic bodies. Shear traction is also included using a Coulomb friction law; thus the shear stress in the contact region is equal to the contact pressure multiplied by a friction coefficient. This paper provides alternative expressions to those recently given by Hamilton (1983) and Sackfield and Hills (1983a). Two methods are outlined for obtaining the present solution and the complete solution for displacements and stresses are given for both normal and tangential loading in terms of just two distorted length parameters. The elastic field is written in a complex notation allowing the expressions to be put in a compact form. This also allows the expressions for sliding in two directions to be written as simply as for sliding in one direction.

The Elastic Potentials for Coplanar Interaction Between an Infinitesimal Prismatic Dislocation Loop and a Circular Crack for Transverse Isotropy

1992 ◽  
Vol 59 (2S) ◽  
pp. S72-S78 ◽  
Author(s):  
M. T. Hanson
Keyword(s):  
Isotropic Material ◽  
Transverse Isotropy ◽  
Circular Crack ◽  
Transversely Isotropic ◽  
Internal Crack ◽  
Elementary Functions ◽  
Elastic Potentials ◽  
Title Problem ◽  
Dislocation Crack ◽  
In The Beginning

This paper gives a closed-form evaluation in terms of elementary functions for the title problem of coplanar dislocation—crack interaction. The two cases of an external and internal crack are considered and the potential for each is found for an isotropic material. The similarity between isotropy and transverse isotropy is discussed in the beginning sections and is used to write the corresponding potential for a transversely isotropic material from the isotropic result.

Effect of Sliding Friction on Contact Stresses for Multi-Layered Elastic Bodies With Rough Surfaces

1997 ◽  
Vol 119 (3) ◽  
pp. 476-480 ◽  
Author(s):  
K. Mao ◽  
T. Bell ◽  
Y. Sun
Keyword(s):  
Sliding Friction ◽  
Rough Surfaces ◽  
Numerical Technique ◽  
Contact Region ◽  
Rolling Contact Fatigue ◽  
Contact Fatigue ◽  
Rolling Contact ◽  
Near Surface ◽  
Elastic Bodies ◽  
Contact Fatigue Life

The stress distributions associated with frictionless and smooth surfaces in contact are rarely experienced in practice. Factors such as layers, friction, surface roughness, lubricant films, and third body particulate are known to influence the state of stress and the resulting rolling contact fatigue life. A numerical technique for evaluating the subsurface stresses arising from the two-dimensional sliding contact of two elastic bodies with real rough surfaces has been developed, where an elastic body contacts with a multi-layer surface under both normal and tangential forces. The presence of friction and asperities within the contact region causes a large, highly stress region exposed to the surface. The significance of these near-surface stresses is related to modes of surface distress leading to surface eventual failure (Mao et al., 1997).

Coulomb Friction, Plasticity, and Limit Loads

1954 ◽  
Vol 21 (1) ◽  
pp. 71-74
Author(s):  
D. C. Drucker
Keyword(s):  
Plastic Deformation ◽  
Coulomb Friction ◽  
Limit Theorems ◽  
Sliding Friction ◽  
Cohesionless Soil ◽  
Limit Loads ◽  
Perfectly Plastic

Abstract Additional attention is given to the somewhat subtle but extremely important difference between Coulomb friction and the apparently corresponding resistance to plastic deformation. It is shown that the limit theorems previously proved for assemblages of perfectly plastic bodies do not always apply when there is finite sliding friction. Theorems are developed which relate the limit loads with finite Coulomb friction to the extreme cases of zero friction and of complete attachment, and also to the case where the frictional interfaces are “cemented” together with a cohesionless soil.

scholarly journals Ternary Logic of Motion to Resolve Kinematic Frictional Paradoxes

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 620 ◽  
Author(s):  
Michael Nosonovsky ◽  
Alexander D. Breki
Keyword(s):  
Dry Friction ◽  
Sliding Friction ◽  
Rigid Bodies ◽  
Newtonian Mechanics ◽  
Stability Criteria ◽  
Ternary Logic ◽  
Elastic Bodies ◽  
Logic Approach ◽  
Frictional System ◽  
Painlevé Paradoxes

Paradoxes of dry friction were discovered by Painlevé in 1895 and caused a controversy on whether the Coulomb–Amontons laws of dry friction are compatible with the Newtonian mechanics of the rigid bodies. Various resolutions of the paradoxes have been suggested including the abandonment of the model of rigid bodies and modifications of the law of friction. For compliant (elastic) bodies, the Painlevé paradoxes may correspond to the friction-induced instabilities. Here we investigate another possibility to resolve the paradoxes: the introduction of the three-value logic. We interpret the three states of a frictional system as either rest-motion-paradox or as rest-stable motion-unstable motion depending on whether a rigid or compliant system is investigated. We further relate the ternary logic approach with the entropic stability criteria for a frictional system and with the study of ultraslow sliding friction (intermediate between the rest and motion or between stick and slip).

scholarly journals Derivation of Ice Sliding Properties from The Numerical Modelling of Surging Ice Masses

1979 ◽  
Vol 23 (89) ◽  
pp. 420-421 ◽  
Author(s):  
W. F. Budd ◽  
B. J. McInnes ◽  
I. Smith
Keyword(s):  
Shear Stress ◽  
Numerical Modelling ◽  
Sliding Friction ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Flow Properties ◽  
Two Dimensional Model ◽  
Two Parameters ◽  
Basal Shear ◽  
Best Fit

Abstract It is difficult to deduce sliding properties from the numerical modelling of ordinary glaciers because the flow law of ice is still not known well enough to clearly differentiate sliding from internal deformation of the ice. For glaciers undergoing high-speed surges it appears that the majority of the total speed is due to sliding. Furthermore the average basal shear stress of the ice mass is lowered during the surge. This suggests that surging glaciers can be modelled by incorporating a sliding friction law which has the effective friction coefficient decreasing for high velocities. A relation of this type has been found for ice sliding on granite at −0.5°C by Barnes and others (1971) and has also been obtained for rough slabs with ice at the pressure-melting point by Budd and others (1979). A simple two-dimensional model was developed by Budd and McInnes (1974) and Budd (1975), which was found to exhibit the typical periodic surge-like characteristics of real ice masses. Since the sliding-stress relation for the low velocities and stresses was not known, and was not so important for the surges, it was decided to use the condition of gross equilibrium (i.e. that the ice mass as a whole does not accelerate) together with a single-parameter relation for the way in which the friction decreases with stress and velocity to prescribe the basal shear-stress distribution. The low-stress-velocity relation can thus be obtained as a result. This two-dimensional model has now been parameterized to take account of the three-dimensional aspects of real ice masses. A number of ice masses have since been closely matched by the model including three well-known surging ice masses: Lednik Medvezhiy, Variegated Glacier, and Bruarjökull. Since the flow properties of ice are so poorly known—especially for longitudinal stress and strain-rates—the model has been run with two unknown parameters: one a flow-law parameter (η) and the other a sliding parameter (ø). The model is run over a wide range of these two parameters to see if a good match can be made to the real ice masses and if so what the values of the parameters η and ø are for best fit. The matching of the three above ice masses gave very similar values for each of the two parameters η and ø, the value of η being within the range of values expected for the flow properties of temperate ice as determined by laboratory experiments. Using the same values of η and ø it is found that the ordinary glaciers modelled so far do not develop surging but that they could do if the value of ø were increased or if the mass-balance input were sufficiently increased. For Lednik Medvezhiy a detailed analysis of the friction coefficient with velocity was carried out and it was found that the values required for best fit showed a very close agreement to the sliding friction curve of Barnes and others (1971) at −0.5°C. It is concluded that this type of sliding relation can account for the major features of glacier surge phenomena. Finally it is apparent that the numerical modelling technique can be used very effectively to test any large-scale bulk sliding relation by the analysis of real surges of ice masses and in addition can provide further insight into the sliding relation in association with other stresses in the ice mass.

New Insights Into Slip-Stick Vibrations From Compact, Closed-Form Analysis

2017 ◽  
Author(s):  
Deborah Fowler ◽  
David Peters
Keyword(s):  
Closed Form ◽  
Coulomb Friction ◽  
Sliding Friction ◽  
Piecewise Linear ◽  
Limited Range ◽  
System Behavior ◽  
Form Analysis ◽  
Mass Damper ◽  
The Times ◽  
Sticking Point

A mechanical system sliding on a moving surface with Coulomb friction is a rich area for study. Despite much past work, there is still something to be gleaned by closed-form expressions for the system behavior. Consider a spring-mass-damper system (K, M, C) with deflection x, base moving in the +x direction at velocity V, sliding friction F, and sticking friction Fs. An initial condition of x0 at rest can be considered general because all possible motions will follow. Two dimensionless schemes are used. For the abstract, we focus on the scheme normalized by x0 with variable z = x/x0, τ = (ωnt, ωn = [K/M]1/2, ζ = c/[2(KM)1/2], ν̄ = V / (ωnx0), f = F/(Kx0), and fs = Fs/(Kx0). Since the solution is piecewise linear, this allows closed-form results. For this abstract, we consider C = 0, Fs = F. (Other cases are in the paper.) There are three critical ground speeds. The first, ν̄d, is when sticking first occurs (at z = f). At the second speed, ν̄c, sticking has moved to z = −f. Thereafter, the sticking point again increases, reaching z = f at the third speed, ν̄b. For higher ν̄, there is no sticking. In this paper, closed form expressions are presented for the three critical speeds:(1)ν¯d=[(1+3f)(1−5f)]12,ν¯c=[(1+f)(1−3f)]12,ν¯b=1−f These formulas are verified by numerical simulation. The insight is that there is a limited range of f for which certain critical points can be reached. Thus, 0 < f < 1/5 has different dynamics than 1/5 < f < 1/3. Formulas are also derived for the second maximum of z, which gives an indication of decay or growth of the system. For example, with f = fs and C = 0, the second maximum z with f < 1/5 is:(2)zmax=f+((1−f)2−ν¯2−4f)2+ν¯2ν¯d<ν¯<ν¯czmax=ν¯+fν¯c<ν¯<ν¯bzmax=1ν¯>ν¯c Formulas will also be given for the times at which the maximum occurs and the times at which a transition occurs from static to sliding for all cases.

Adhesion and Friction of Elastomers

1981 ◽  
Vol 54 (5) ◽  
pp. 944-962 ◽  
Author(s):  
A. D. Roberts
Keyword(s):  
Surface Energy ◽  
Liquid Film ◽  
Bearing Capacity ◽  
Electrical Double Layer ◽  
Sliding Friction ◽  
Contact Region ◽  
Rolling Resistance ◽  
Load Bearing Capacity ◽  
Dry Contact ◽  
Nonequilibrium Conditions

Abstract Use of mirror smooth spheres and cylinders of rubber allows the thickness and contour of a liquid film trapped between surfaces to be studied by optical interferometry. Close normal approach reveals the load bearing capacity of electrical double layer forces. In the absence of such forces, a liquid film collapses leading to areas of adhesion over most of the contact region. The adhesion can be interpreted in terms of surface energy. The force required to separate adhered surfaces is found to depend critically upon the rate of separation. Dry contact observations reveal that under nonequilibrium conditions the apparent surface energy may be very much greater than the equilibrium energy. The observations can be used, in certain circumstances, to predict tack, rolling resistance and sliding friction. Such prediction reflects a combination of surface properties and bulk viscoelasticity of the rubber. In particular, the approach has been applied to rolling on rough surfaces and to the friction of rubber on ice.

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