Axisymmetric contact problem for a semiinfinite cylinder and a half space

Adhesion and pull-off force of an elastic indenter from an elastic half-space

“…(b) Axisymmetric problem Agarwal [10] investigated the axisymmetric problem of a flat-ended elastic cylinder pressed against an elastic half-space, but did not obtain numerical results. This problem was later solved by Gecit [11] who included a graph of the generalized stress intensity factor as a function of and g 3 (α) is shown in figure 7. It is emphasized that these numerical results and the curve-fit given by equation (5.3) were obtained from the graphical results presented by Gecit [11] along with knowledge of the expected behaviour at α = ±1 which helped to reduce the maximum error at the endpoints to 4.9% at α = −1 to 1.6% at α = 1.…”

“…An asymptotic analysis of this separation zone using Mellin transforms is then performed and determines the critical value of the generalized stress intensity factor in terms of the material parameter α, the work of adhesion and the cohesive stress. This relationship is combined with the results of the contact problems [9,11] in order to determine the relations for the pull-off force of the finite width/radius elastic punch on a half-space.…”

“…It is emphasized that unlike the Hertz problem it is not possible to generalize the results of a rigid indenter to that of an elastic one. Furthermore, because the order of the singularity is not one-half, it is not at all obvious how the stress distributions determined by Adams & Bogy [9] and Gecit [11] can inform the determination of the pull-off force. The normal stress acting on the symmetry plane can be written as…”

“…Subsequently, Adams & Bogy [9] used that solution along with an elastic half-plane solution in order to determine the stress distribution along the interface between the strip and half-plane. Similarly, Agarwal [10] and Gecit [11] investigated the corresponding axisymmetric problem. It was Gecit who was able to obtain a solution to this problem in terms of a singular integral equation with a generalized Cauchy kernel.…”

Effect of nonhomogeneity on the contact of an isotropic half-space and a rigid base with an axially symmetric recess

“…If the contact area diminishes as the load is applied, the contact is called receding. The analytical studies involving receding contact in homogeneous and graded media can be found in [Hussain et al 1968;Noble and Hussain 1969;Weitsman 1969;Pu and Hussain 1970;Keer et al 1972;Gecit 1986;Nowell and Hills 1988;Chaudhuri and Ray 1998;Birinci and Erdol 1999;Chaudhuri and Ray 2003;Comez et al 2004;El-Borgi et al 2006]. Numerical studies based either on the finite element method or on the boundary element method can be found in [Jing and Liao 1990;Garrido et al 1991;Paris et al 1995;Satish Kumar et al 1996;Garrido and Lorenzana 1998].…”