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By Markus Heß

This ebook describes for the 1st time a simulation procedure for the short calculation of touch homes and friction among tough surfaces in a whole shape. unlike current simulation tools, the tactic of dimensionality aid (MDR) is predicated at the designated mapping of varied kinds of three-d touch difficulties onto contacts of one-dimensional foundations. in the confines of MDR, not just are 3 dimensional structures diminished to one-dimensional, but in addition the ensuing levels of freedom are self sustaining from one other. consequently, MDR leads to a tremendous aid of the advance time for the numerical implementation of touch difficulties in addition to the direct computation time and will finally think the same position in tribology as FEM has in constitution mechanics or CFD equipment, in hydrodynamics. additionally, it considerably simplifies analytical calculation and provides a kind of “pocket booklet variation” of the whole lot touch mechanics. Measurements of the rheology of our bodies in touch in addition to their floor topography and adhesive houses are the inputs of the calculations. particularly, it's attainable to catch the full dynamics of a method – starting with the macroscopic, dynamic touch calculation right down to the impact of roughness – in one numerical simulation version. as a result, MDR enables the unification of the equipment of fixing touch difficulties on assorted scales. The targets of this booklet are at the one hand, to end up the applicability and reliability of the strategy and nevertheless, to give an explanation for its very simple software to these interested.

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R. M. Radok, Quart. Appl. Math. 15, 198 (1957)MATHMathSciNet 2. S. Kürschner, A. E. Filippov, Phys. Mesomech. 15, 270–274 (2012)CrossRef three. L. D. Landau, E. M. Lifschitz, Lehrbuch der Theoretischen Physik, Band VII Elastizitätstheorie, 1st edn. (Akademie, Berlin, 1965) four. L. D. Landau, E. M. Lifschitz, Lehrbuch Der Theoretischen Physik, Band VI Hydrodynamik, five. überarb. Aufl. (Akademie Verlag, 1991) five. I. N. Bronstein, ok. A. Semendjajew, G. Musiol, H. Mühlig, Taschenbuch Der Mathematik, five. überarb. u. erw. Aufl. (Harri Deutsch, 2000) 6. W. Yang, J. Appl. Mech. 33, 395 (1966)CrossRef 7. R. M. Christensen, thought of Viscoelasticity: An advent (Academic Press, manhattan, 1971) eight. E. H. Lee, J. R. M. Radok, J. Appl. Mech. 27, 438 (1960)CrossRefMATHMathSciNet nine. B. Gross, Mathematical constitution of the Theories of Viscoelasticity (Hermann, Paris, 1953)MATH 10. A. C. Pipkin, Lectures on Viscoelasticity concept (Springer, Berlin, 1972)CrossRefMATH eleven. D. R. Bland, thought of Linear Viscoelasticity (Pergamon, Oxford, 1960)MATH 12. M. Vandamme, F. J. Ulm, Int. J. Solids Struct. forty three, 3142 (2006)CrossRefMATH Footnotes 1The mathematically sound approach involves taking the incompressibility into consideration in Eq. (19. 29) and in simple terms then, taking the Laplace transformation. it truly is, even if, effortless to determine that this method ends up in a similar consequence. � Springer-Verlag Berlin Heidelberg 2015 Valentin L. Popov and Markus HeßMethod of Dimensionality relief involved Mechanics and Friction10. 1007/978-3-642-53876-6_20 20. Appendix four: identifying Two-Dimensional energy Spectrums from One-Dimensional Scans Valentin L. Popov1   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) e mail: v. popov@tu-berlin. de Markus Heß electronic mail: markus. hess@tu-berlin. de 20. 1 advent the facility spectra of tough surfaces are invaluable “input parameters” for the calculation of touch and frictional houses. the facility spectrum of a randomly tough floor should be decided utilizing the Fourier remodel of a measured two-dimensional floor topography. The experimental selection of the full floor topography, for example, with an atomic strength microscope can, although, be very time extensive. as a result, it begs the query, even if it's attainable to figure out the total two-dimensional strength spectrum from a constrained variety of one-dimensional scans. For isotropically randomly tough surfaces, the entire helpful details is, in reality, already inside the one-dimensional scans of the outside. those can be utilized to acquire the mandatory floor details extra speedy and with much less difficulty. 20. 2 Definitions The two-dimensional energy spectrum of a floor is outlined as (20. 1) the place is the two-dimensional radius vector. is the outside profile outlined over the oblong region with the discretization step sizes and with an average of 0, in order that ; the following, denotes the typical over the statistical ensemble.

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