Abstract
Adhesive contacts of axially-symmetric bodies can also be exactly mapped to a one-dimensional equivalent model. The rule for this mapping was developed in 2011 by Markus Heß. It is based on the basic idea of Johnson, Kendall, and Roberts that the contact with adhesion arises from the contact without adhesion plus a rigid-body translation. Because both parts of the contact problem can be mapped to a one-dimensional equivalent model with a modified geometry, then this is true of the entire problem. To begin, we will formulate the simple rules of application for the adhesive normal contact and refrain from presenting the required evidence. Subsequently, these rules will be explained in more detail, which requires a certain understanding of the theoretical background on adhesion in three-dimensional contacts, which we will also provide. For those not satisfied with these short explanations, the entirety of the necessary evidence may be found in Chap. 17.
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Notes
- 1.
More specifically, Griffith investigated the stability of a crack in the middle of a disc loaded in tension.
- 2.
The opening mode (mode I crack) is the separation mode for which the tensile stress acts perpendicular to the plane of the crack.
- 3.
The equation is based on a fracture in a planar state of deformation; we may assume that locally in an axially-symmetric contact with adhesion, every point on the contact boundary exhibits this state.
- 4.
It is irrelevant if the superimposed profile is pressed into a planar elastic half-space or a parabolic body is pressed into an elastic half-space with the corresponding waveform.
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Heß, M., Popov, V.L. (2015). Normal Contact with Adhesion. In: Method of Dimensionality Reduction in Contact Mechanics and Friction. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-53876-6_4
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