Problems Involving a Receding Contact Between a Layer and a Half Space

Abstract

The work reconsiders the smooth receding contact between an elastic layer and a half space when the two bodies are pressed together. The analysis leads to a Fredholm integral equation of the second kind for an auxiliary function that is directly related to the contact pressure. An unexpected result is that the integral equation is homogeneous, and that finding the extent of contact can be viewed as an eigenvalue problem. The integral equation can be solved numerically to any required degree of accuracy, and the extent of contact and the contact pressure are computed for concentrated and uniformly distributed loads in both plane and axisymmetric problems. The present analysis confirms the results of Weitsman rather than Pu and Hussain over a wide range of mismatch in the elastic constants.

Numerical and Experimental Analysis of a Frictionless Receding Contact between Cylindrical Indenter, Layer and Substrate

“…Weitsman also analysed the plane case in [5] by treating the layer as an infinite beam resting on a half-space, but also failed to obtain good results. Keer, Dundurs and Tsai treated the problem in [6] by employing 2D elasticity theory equations for both the layer and the half-space and obtained results for the case of a symmetric distribution of load around the centre of the loading interval and then generalized their results in [7] to the cases when load distribution is not symmetrical; their result regarding the contact area width of approximately 0.85h is well below Filon's value. Gladwell also investigated the problem of an infinite beam pressed by a concentrated force in [8] and for small h obtained results in very good agreement with [6].…”

“…Keer, Dundurs and Tsai treated the problem in [6] by employing 2D elasticity theory equations for both the layer and the half-space and obtained results for the case of a symmetric distribution of load around the centre of the loading interval and then generalized their results in [7] to the cases when load distribution is not symmetrical; their result regarding the contact area width of approximately 0.85h is well below Filon's value. Gladwell also investigated the problem of an infinite beam pressed by a concentrated force in [8] and for small h obtained results in very good agreement with [6]. In [9], Ratwani and Erdogan extend the problem by introducing a rigid cylindrical indenter into the model (instead of an assumed pressure distribution), and in [10], Civelek and Erdogan for the first time take the elasticity of the indenter into account, however, they do not analyse explicitly the influence of load intensity on the contact width.…”

An efficient numerical method for the solution of sliding contact problems

“…For example, sometimes contacts are classified into stationary, on the one hand, and receding or advancing, on the other [1,2]. This classification is based on the consideration of the behaviour of contact patch under increasing applied load: stationary contact remains unchanged, advancing refers to the situation when the separation point moves out with respect to the contact, and receding to the situation when the opposite takes place.…”

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].…”