By Markus Heß
This e-book describes for the 1st time a simulation approach for the quick calculation of touch homes and friction among tough surfaces in an entire shape. unlike present simulation tools, the tactic of dimensionality relief (MDR) is predicated at the targeted mapping of assorted sorts of 3-dimensional touch difficulties onto contacts of one-dimensional foundations. in the confines of MDR, not just are 3 dimensional platforms decreased to one-dimensional, but additionally the ensuing levels of freedom are self reliant from one other. accordingly, MDR leads to a major relief of the improvement time for the numerical implementation of touch difficulties in addition to the direct computation time and will finally imagine the same 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 variation” of everything touch mechanics. Measurements of the rheology of our bodies involved in addition to their floor topography and adhesive homes are the inputs of the calculations. specifically, it truly is attainable to seize the full dynamics of a approach – starting with the macroscopic, dynamic touch calculation down to the effect of roughness – in one numerical simulation version. as a result, MDR permits the unification of the tools of fixing touch difficulties on various scales. The ambitions of this booklet are at the one hand, to end up the applicability and reliability of the strategy and nevertheless, to provide an explanation for its very simple software to these interested.
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Extra info for Method of Dimensionality Reduction in Contact Mechanics and Friction
R. A. J. Ford, D. J. Thompson, Simplified touch filters in wheel/rail noise prediction. J. Sound Vibr. 293, 807–818 (2006)CrossRef 2. R. Pohrt, V. L. Popov, A. E. Filippov, general touch stiffness of elastic solids with fractal tough surfaces for one- and 3-dimensional structures. Phys. Rev. E 86, 026710 (2012)CrossRef � Springer-Verlag Berlin Heidelberg 2015 Valentin L. Popov and Markus HeßMethod of Dimensionality relief in touch Mechanics and Friction10. 1007/978-3-642-53876-6_15 15. Coupling to the Microscale Valentin L. Popov1 , Roman Pohrt1 and Markus Heß2 (1)Institute of Mechanics, Technische Universität Berlin, Berlin, Germany (2)Abt. IC Studienkolleg, Technische Universität Berlin, Berlin, Germany Valentin L. Popov (Corresponding writer) electronic mail: v. popov@tu-berlin. de Markus Heß e mail: markus. hess@tu-berlin. de 15. 1 creation the applying of the tactic of dimensionality relief is, in fact, constrained to the spatial scales for which continuum mechanics can be utilized. each functional software utilizing the strategy will lose its validity even past, as a result of finite spatial solution of the outside topography. consequently, it begs the query of even if the interactions on even smaller scales will be summarized right into a microscopic “contact legislation” or “law of friction,” in order that additionally the homes of the smallest attainable scale should be taken into consideration within the simulation. an entire process can in basic terms exist after the coupling to the macroscale in addition to to the microscale has been entire. during this bankruptcy, we clarify how the constraints of the finite spatial answer might be eradicated via the advent of a “microscopic” non-linear stiffness. 15. 2 Non-Linear Stiffness at the “Microscale” allow us to contemplate the classical Hertzian challenge: a inflexible sphere with the radius R is pressed into an elastic half-space with the powerful modulus of elasticity of E *. This challenge may be expressed by means of an similar one-dimensional touch among a inflexible sphere with the radius and the linearly elastic beginning with the stiffness in step with unit size The dependence of the strength at the indentation intensity is given by means of the Hertzian Eq. (3. 13). despite the fact that, this is often purely legitimate if the touch radius is far better than the discretization step dimension of the linearly elastic origin. once just one spring is involved, the stiffness is continuous and the end result deviates from that of the Hertzian equation. to ensure that the force-indentation intensity relation to stay right additionally at smaller forces, the discretization step dimension can continually be selected to be smaller. an alternate resolution relies at the concept that the one spring is assigned a non-linear stiffness. The creation of non-linear stiffness for the simulation of methods at the microscale isn't really a brand new proposal. for instance, this concept used to be utilized in  and  and is the basis of the concept that of “interfacial stiffness,” that's at the moment getting used actively via many specialists within the box of touch mechanics [3–5]. As defined in Sect.