Taking account of frictional forces in the contact region between a circular punch and an elastic half-space

1975 ◽  
Vol 11 (4) ◽  
pp. 432-434
Author(s):  
G. M. Nakashidze
Keyword(s):  
Half Space ◽  
Contact Region ◽  
Elastic Half Space ◽  
Circular Punch ◽  
Frictional Forces

Multiple Region Contact Solutions for a Flat Indenter on a Layered Elastic Half Space: Plane-Strain Case

1989 ◽  
Vol 56 (2) ◽  
pp. 251-262 ◽  
Author(s):  
T. W. Shield ◽  
D. B. Bogy
Keyword(s):  
Plane Strain ◽  
Half Space ◽  
Contact Region ◽  
Integral Transforms ◽  
Elastic Half Space ◽  
Geometrical Parameters ◽  
Restricted Range ◽  
Complete Contact ◽  
The One ◽  
Layered Half Space

The plane-strain problem of a smooth, flat rigid indenter contacting a layered elastic half space is examined. It is mathematically formulated using integral transforms to derive a singular integral equation for the contact pressure, which is solved by expansion in orthogonal polynomials. The solution predicts complete contact between the indenter and the surface of the layered half space only for a restricted range of the material and geometrical parameters. Outside of this range, solutions exist with two or three contact regions. The parameter space divisions between the one, two, or three contact region solutions depend on the material and geometrical parameters and they are found for both the one and two layer cases. As the modulus of the substrate decreases to zero, the two contact region solution predicts the expected result that contact occurs only at the corners of the indenter. The three contact region solution provides an explanation for the nonuniform approach to the half space solution as the layer thickness vanishes.

Contact Stress Analysis of a Layered Transversely Isotropic Half-Space

1992 ◽  
Vol 114 (2) ◽  
pp. 253-261 ◽  
Author(s):  
C. H. Kuo ◽  
L. M. Keer
Keyword(s):  
Half Space ◽  
Mixed Boundary ◽  
Contact Region ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Hankel Transform ◽  
Elastic Half Space ◽  
Contact Stresses ◽  
Stress Components ◽  
Contact Failure

The three-dimensional problem of contact between a spherical indenter and a multi-layered structure bonded to an elastic half-space is investigated. The layers and half-space are assumed to be composed of transversely isotropic materials. By the use of Hankel transforms, the mixed boundary value problem is reduced to an integral equation, which is solved numerically to determine the contact stresses and contact region. The interior displacement and stress fields in both the layer and half-space can be calculated from the inverse Hankel transform used with the solved contact stresses prescribed over the contact region. The stress components, which may be related to the contact failure of coatings, are discussed for various coating thicknesses.

A Unified Treatment of Axisymmetric Adhesive Contact on a Power-Law Graded Elastic Half-Space

2013 ◽  
Vol 80 (6) ◽  
Author(s):  
Fan Jin ◽  
Xu Guo ◽  
Wei Zhang
Keyword(s):  
Half Space ◽  
Power Law ◽  
Contact Region ◽  
Adhesive Contact ◽  
Elastic Half Space ◽  
Hertzian Contact ◽  
Contact Radius ◽  
Abel Transformation ◽  
Numerical Solution Methods ◽  
Special Cases

In the present paper, axisymmetric frictionless adhesive contact between a rigid punch and a power-law graded elastic half-space is analytically investigated with use of Betti's reciprocity theorem and the generalized Abel transformation, a set of general closed-form solutions are derived to the Hertzian contact and Johnson–Kendall–Roberts (JKR)-type adhesive contact problems for an arbitrary punch profile within a circular contact region. These solutions provide analytical expressions of the surface stress, deformation fields, and equilibrium relations among the applied load, indentation depth, and contact radius. Based on these results, we then examine the combined effects of material inhomogeneities and punch surface morphologies on the adhesion behaviors of the considered contact system. The analytical results obtained in this paper include the corresponding solutions for homogeneous isotropic materials and the Gibson soil as special cases and, therefore, can also serve as the benchmarks for checking the validity of the numerical solution methods.

A concave indenter on a piezoelectromagneto-elastic substrate or a layer elastically supported

2012 ◽  
Vol 47 (6) ◽  
pp. 362-378 ◽  
Author(s):  
Bogdan Rogowski
Keyword(s):  
Half Space ◽  
Elastic Foundation ◽  
Contact Region ◽  
Approximate Solutions ◽  
Elastic Half Space ◽  
Solution Technique ◽  
Elementary Functions ◽  
Full Field ◽  
Full Contact ◽  
Two Parameter

Indentation of piezoelectromagneto-elastic half-space or a layer on a two-parameter elastic foundation by a cylindrical indenter with a slightly concave base is considered. Full-field magnetoelectro-elastic solutions in elementary functions are obtained for the case of full contact and half-space. If the axial load is small, the contact area will be an annulus the outer circumference of which coincides with the edge of the punch. The inner circumference will shrink with increasing load and there will be a critical load above which the stratum makes contact with the entire punch base. The contact problem for high loads can therefore be treated by classical methods. The more interested case in which the load is less the critical value and the contact region is annulus remains. By use the methods of triple integral equations and series solution technique the solution for an indentured substrate over an annular contact region is also given. For parabolic and conical concave punches the exact or approximate solutions are obtained for full contact or annular contact region, respectively. For the layer on two-parameter elastic foundation and concave punch approximate solution is established.

The response of an anisotropic elastic half-space to a rolling cylinder

1971 ◽  
Vol 70 (3) ◽  
pp. 467-484 ◽  
Author(s):  
D. L. Clements
Keyword(s):  
Shear Stress ◽  
Half Space ◽  
Elastic Anisotropy ◽  
Contact Region ◽  
Steady Motion ◽  
Elastic Half Space ◽  
Infinite Length ◽  
Anisotropic Elastic ◽  
Similar Class ◽  
Basic Equations

The problem of the steady motion of a heavy cylinder, of infinite length, over the surface of an elastic half-space has been examined by Craggs and Roberts(1), Clements(2) and Roberts (3). In papers (1) and (2) the surfaces of both the cylinder and the half-space are assumed to be smooth so that the shear stress over the region of contact is zero. With this assumption Craggs and Roberts analysed the motion for an isotropic half-space while Clements considered the case of an anisotropic half-space. In the paper by Roberts (3) various problems concerning the rolling of rigid and non-rigid cylinders over an isotropic elastic half-space are discussed. In this paper we consider a similar class of rolling cylinder problems for an anisotropic half-space. We begin, in section 2, by deriving the relevant basic equations for the stress and displacement while in section 3 some properties of certain constants occurring in the equations of section 2 are derived for use in later sections. The problem of the steady motion of an inflated tyre is discussed in section 4 under the assumptions that the tyre exerts a constant pressure over the contact region which is instantaneously at rest. The solution shows that, with these assumptions, the shear stress is infinite near the ends of the region of contact. This indicates that there will be slipping of the tyre over the half-space at both ends of the contact region. If these zones of slip are large compared with the total contact area then the assumption of a contact region which is instantaneously at rest is invalidated so that the solution may only be regarded as being applicable when the zones of slip are small. An expression to determine the width of the zones of slip is derived and this expression is used, together with the numerical results of section 5, to obtain information about the influence of anisotropy on the width of the zones of slip. In section 6 the problem of the inflated tyre is discussed with allowance made for a zone of slip at both ends of the region of contact. The results of this section could be expected, particularly when the zones of slipping are wide, to more accurately predict the response of the anisotropic half-space to the rolling tyre than the results of section 4. Unfortunately, in order to satisfactorily complete the analysis, it is necessary to restrict the class of anisotropic materials for which the results are applicable. As a consequence, the work of section 4 is in many ways preferable to that of section 6 in indicating the influence which elastic anisotropy has upon the results.

The Interaction Between a System of Circular Punches on an Elastic Half Space

1982 ◽  
Vol 49 (2) ◽  
pp. 341-344 ◽  
Author(s):  
G. M. L. Gladwell ◽  
V. I. Fabrikant
Keyword(s):  
Half Space ◽  
Approximate Solutions ◽  
Elastic Half Space ◽  
Concentrated Load ◽  
Circular Punch

Galin derived an expression for the pressure produced under a rigid circular punch by the application of a concentrated load at another point of the half space. This result is used to derive approximate relationships among the forces, moments, and indentations for a system of punches on an elastic half space. The results are compared with a number of earlier approximate solutions.

Some Axisymmetric Problems for Layered Elastic Media: Part II—Solutions for Annular Indenters and Cracks

1989 ◽  
Vol 56 (4) ◽  
pp. 807-813 ◽  
Author(s):  
T. W. Shield ◽  
D. B. Bogy
Keyword(s):  
Half Space ◽  
Contact Region ◽  
Singular Integral Equations ◽  
Integral Transforms ◽  
Lower Surface ◽  
Elastic Half Space ◽  
Solution Technique ◽  
Physical Parameters ◽  
Annular Crack ◽  
Layered Half Space

In Part I, the multiple contact region solutions for an axisymmetric indenter were presented. The solution technique utilized integral transforms and singular integral equations. The emphasis there was the study of the conditions of contact as a function of the physical parameters of the indenter and the layered elastic half space. The method and results were similar to those for the analogous plane-strain problem that was studied in Shield and Bogy (1989). However, several differences in detail were required for the analysis of the axisymmetric geometry. In this Part II, the solution of Part I is used to study some related problems that have been considered previously in the literature for homogeneous half spaces. First we solve the problem of the axisymmetric annular indenter for the layered half space. Multiple contact region solutions are studied and the problem of an axisymmetric punch with internal pressure is solved for the layered half space and also for the special case of a layer with a traction-free lower surface. Finally, the problem of an annular crack in a homogeneous or layered structure is solved.

Unbonded Contact of a Square Plate on an Elastic Half-Space or a Winkler Foundation

1988 ◽  
Vol 55 (2) ◽  
pp. 430-436 ◽  
Author(s):  
Hui Li ◽  
J. P. Dempsey
Keyword(s):  
Contact Problem ◽  
Half Space ◽  
Contact Region ◽  
Elastic Half Space ◽  
Unilateral Contact ◽  
Winkler Foundation ◽  
Vertical Loading ◽  
Centrally Symmetric ◽  
Receding Contact ◽  
Square Plate

The unbonded frictionless receding contact problem of a thin plate placed under centrally symmetric vertical loading while resting on an elastic half-space or a Winkler foundation is solved in this paper. The problem is transformed into the solution of two-coupled integral-series equations over an unknown contact region. The problem is nonlinear by virtue of unilateral contact and therefore needs to be solved iteratively. Special attention is given to the edge and corner contact pressure singularities for the plate on the elastic half-space. Comparison is made with other relevant numerical results available.

scholarly journals Thermomechanical Slip in Elastic Contact Between Identical Materials

2021 ◽  
Vol 15 (4) ◽  
pp. 187-192
Author(s):  
Yurii Streliaiev ◽  
Rostyslav Martynyak ◽  
Kostyantyn Chumak
Keyword(s):  
Half Space ◽  
Contact Stress ◽  
Thermal Loading ◽  
Boundary Integral Equations ◽  
Contact Region ◽  
Elastic Half Space ◽  
Boundary Integral ◽  
Subsequent Stage ◽  
Relative Shear ◽  
Increasing Temperature

Abstract The contact problem for interaction between an elastic sphere and an elastic half-space is considered taking into account partial thermomechanical frictional slip induced by thermal expansion of the half-space. The elastic constants of the bodies are assumed to be identical. The Amontons–Coulomb law is used to account for friction. The problem is reduced to non-linear boundary integral equations that correspond to the initial stage of mechanical loading and the subsequent stage of thermal loading. The dependences of the contact stress distribution, relative displacements of the contacting surfaces, dimensions of the stick and slip zones on temperature of the half-space are studied numerically. It was revealed that an increase in temperature causes increases in the shear contact stress and the relative shear displacements of the contacting surfaces. The absolute values of the shear contact stress reach their maximum at the boundaries of the stick zones. The greatest value of the moduli of the relative shear displacements are reached at the boundary of the contact region. The stick zone radius decreases monotonically according to a nonlinear law with increasing temperature.

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