By Valentin L. Popov, Markus Heß
This e-book describes for the 1st time a simulation procedure for the short calculation of touch houses and friction among tough surfaces in an entire shape. not like latest simulation tools, the tactic of dimensionality aid (MDR) is predicated at the precise mapping of assorted forms of third-dimensional touch difficulties onto contacts of one-dimensional foundations. in the confines of MDR, not just are 3 dimensional structures lowered to one-dimensional, but additionally the ensuing levels of freedom are self sufficient from one other. accordingly, MDR ends up in a huge relief of the advance time for the numerical implementation of touch difficulties in addition to the direct computation time and will eventually imagine an analogous function in tribology as FEM has in constitution mechanics or CFD tools, in hydrodynamics. moreover, it considerably simplifies analytical calculation and provides a kind of “pocket ebook version” of the whole lot touch mechanics. Measurements of the rheology of our bodies involved in addition to their floor topography and adhesive houses are the inputs of the calculations. specifically, it's attainable to seize the total dynamics of a process – starting with the macroscopic, dynamic touch calculation down to the impact of roughness – in one numerical simulation version. for that reason, MDR permits the unification of the tools of fixing touch difficulties on varied scales. The targets of this booklet are at the one hand, to turn out the applicability and reliability of the strategy and nevertheless, to provide an explanation for its very simple program to these interested.
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Additional resources for Method of Dimensionality Reduction in Contact Mechanics and Friction
A. a. 19) 8π E ∗ a3 �γ . 20) is in no way limited to the parabolic contact. They are generally valid for arbitrary axially-symmetric contacts with a simply connected contact area . No additional proof is needed to show that the results of the generalized JKR theory can be mapped to one-dimensional models. This is because if arbitrary axially-symmetric contacts without adhesion (for simply connected contact areas) satisfy the requirements of the reduction method (see Chap. 3), including the flat indenter, then this must also be true for their superposition.
In his dissertation from 2011, Heß  showed that a similar exact mapping is possible for an arbitrary axially-symmetric profile. In this chapter, we will apply the mapping rules determined by Heß without providing proof of their validity. A detailed derivation of these rules is provided in Chap. 17. The focus of the following investigation is the contact between axially- symmetric bodies and an elastic half-space. Let the axis of symmetry be z and the surface of the elastic half-space be given by z = 0.
Popov and M. 1007/978-3-642-53876-6_4 39 4 Normal Contact with Adhesion 40 of validity for various adhesion theories. Furthermore, they pointed out the fact that the JKR theory still provides good results outside of its actual area of validity. It is possible that this is the reason that the JKR theory is primarily used to describe adhesion. In this chapter, we will discuss how the leading adhesion theory from Johnson, Kendall, and Roberts is able to be exactly mapped using the method of dimensionality reduction.
Method of Dimensionality Reduction in Contact Mechanics and Friction by Valentin L. Popov, Markus Heß