A contact problem for a circular cylindrical punch in adhesive contact with an elastic half-space: The case of rocking, and translation parallel to the plane

1969 ◽  
Vol 7 (3) ◽  
pp. 295-307 ◽  
Author(s):  
G.M.L. Gladwell
Keyword(s):  
Contact Problem ◽  
Half Space ◽  
Adhesive Contact ◽  
Elastic Half Space ◽  
Cylindrical Punch

scholarly journals Johnson–Kendall–Roberts adhesive contact for a toroidal indenter

2016 ◽  
Vol 472 (2191) ◽  
pp. 20160218 ◽  
Author(s):  
Ivan Argatov ◽  
Qiang Li ◽  
Roman Pohrt ◽  
Valentin L. Popov
Keyword(s):  
Asymptotic Solution ◽  
Contact Problem ◽  
Half Space ◽  
Elastic Properties ◽  
Contact Area ◽  
Adhesive Contact ◽  
Elastic Half Space ◽  
The Other ◽  
Leading Order

The unilateral axisymmetric frictionless adhesive contact problem for a toroidal indenter and an elastic half-space is considered in the framework of the Johnson–Kendall–Roberts theory. In the case of a semi-fixed annular contact area, when one of the contact radii is fixed, while the other varies during indentation, we obtain the asymptotic solution of the adhesive contact problem based on the solution of the corresponding unilateral non-adhesive contact problem. In particular, the adhesive contact problem for Barber’s concave indenter is considered in detail. In the case when both contact radii are variable, we construct the leading-order asymptotic solution for a narrow annular contact area. It is found that for a v-shaped generalized toroidal indenter, the pull-off force is independent of the elastic properties of the indented solid.

scholarly journals An Axisymmetric Contact Problem of an Elastic Half-Space with a Spherical Cavity.

1991 ◽  
Vol 57 (543) ◽  
pp. 2664-2671
Author(s):  
Takao AKIYAMA ◽  
Toshiaki HARA ◽  
Toshikazu SHIBUYA ◽  
Takashi KOIZUMI
Keyword(s):  
Contact Problem ◽  
Half Space ◽  
Spherical Cavity ◽  
Elastic Half Space ◽  
Axisymmetric Contact Problem

Axisymmetric contact with friction of a rigid sphere with an elastic half-space

2009 ◽  
Vol 465 (2108) ◽  
pp. 2565-2588 ◽  
Author(s):  
O. I. Zhupanska
Keyword(s):  
Contact Problem ◽  
Half Space ◽  
Integral Transform ◽  
Elastic Half Space ◽  
Rigid Sphere ◽  
Analytical Treatment ◽  
Normal Contact ◽  
Exact Analytical Solutions ◽  
Single Integral ◽  
Toroidal Coordinates

The problem of normal contact with friction of a rigid sphere with an elastic half-space is considered. An analytical treatment of the problem is presented, with the corresponding boundary-value problem formulated in the toroidal coordinates. A general solution in the form of Papkovich–Neuber functions and the Mehler–Fock integral transform is used to reduce the problem to a single integral equation with respect to the unknown contact pressure in the slip zone. An analysis of contact stresses is carried out, and exact analytical solutions are obtained in limiting cases, including a full stick contact problem and a contact problem for an incompressible half-space.

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.

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