By Valentin L. Popov, Markus Heß
This publication describes for the 1st time a simulation process for the short calculation of touch houses and friction among tough surfaces in an entire shape. not like current simulation equipment, the tactic of dimensionality aid (MDR) relies at the specific mapping of assorted different types of 3-dimensional touch difficulties onto contacts of one-dimensional foundations. in the confines of MDR, not just are 3 dimensional structures decreased to one-dimensional, but in addition the ensuing levels of freedom are self sufficient from one other. for that reason, MDR leads to a big aid of the improvement time for the numerical implementation of touch difficulties in addition to the direct computation time and will finally suppose the same function in tribology as FEM has in constitution mechanics or CFD tools, in hydrodynamics. moreover, it considerably simplifies analytical calculation and offers a type of “pocket booklet variation” of everything touch mechanics. Measurements of the rheology of our bodies in touch in addition to their floor topography and adhesive homes are the inputs of the calculations. specifically, it's attainable to seize the whole dynamics of a procedure – starting with the macroscopic, dynamic touch calculation right down to the impact of roughness – in one numerical simulation version. hence, MDR enables the unification of the equipment of fixing touch difficulties on varied scales. The objectives of this publication are at the one hand, to end up the applicability and reliability of the tactic and nevertheless, to give an explanation for its very simple software to these interested.
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Extra resources for Method of Dimensionality Reduction in Contact Mechanics and Friction
75), the contact force is finally obtained as a function of contact radius: FN (a) = E ∗ R2 + a2 ln 2 R+a R−a − E ∗ Ra. 78) correspond exactly to the three-dimensional contacts based on the solutions of Segedin , which are obtained using the Area-functions. Finally, let it be known that we could have just as well developed the spherical profile as a series. 74) would have been given in the form of a power series. 27) is not known, we have, in fact, no choice but to use this strategy. L. Johnson, Contact Mechanics, Nachdruck der 1.
28) ⇒ g(x) = 2R R The surface displacement in the equivalent model, according to Eq. 25). 21) into account, we obtain uz (x) = d(a) = a2 − R 2πa �γ . 30) The normal force is the sum of the spring forces a a FN (a) = E uz (x)dx = 2E ∗ d− ∗ 4 a3 x2 dx = E ∗ − R 3 R 8π a3 E ∗ �γ . 31) will seem familiar to the reader, for they are exactly those developed by Johnson, Kendall, and Roberts using the minimum in the total energy. 23). For this, let k not be fixed for the time being. The slope of the equivalent profile at the point x = a is 2a ∂g(a) a2 = .
4 Full Reduction of the Adhesive… 49 indenters with the radius of curvature must first be determined. According to the rule of Popov, we must simply divide the radius of curvature by two: x2 r2 . 28) ⇒ g(x) = 2R R The surface displacement in the equivalent model, according to Eq. 25). 21) into account, we obtain uz (x) = d(a) = a2 − R 2πa �γ . 30) The normal force is the sum of the spring forces a a FN (a) = E uz (x)dx = 2E ∗ d− ∗ 4 a3 x2 dx = E ∗ − R 3 R 8π a3 E ∗ �γ . 31) will seem familiar to the reader, for they are exactly those developed by Johnson, Kendall, and Roberts using the minimum in the total energy.
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