Method of reduction of dimensionality in contact and friction mechanics: A linkage between micro and macro scales View Full Text


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Article Info

DATE

2013-03

AUTHORS

Valentin L. Popov

ABSTRACT

Computer simulations have been an integral part of the technical development process for a long time now. Industrial tribology is one of the last fields in which computer simulations have, until now, played no significant role. This is primarily due to the fact that investigating tribological phenomena requires considering all spatial scales from the macroscopic shape of the contact system down to the micro-scales. In the present paper, we give an overview of the previous work on the so-called method of reduction of dimensionality (MRD), which in our opinion, gives a key for the linking of the micro- and macro-scales in tribological simulations. MRD in contact mechanics is based on the mapping of some classes of three-dimensional contact problems onto one-dimensional contacts with elastic foundations. The equivalence of three-dimensional systems to those of one-dimension is valid for relations of the indentation depth and the contact force and in some cases for the contact area. For arbitrary bodies of revolution, MRD is exact and provides a sort of “pocket edition” of contact mechanics, giving the possibility of deriving any result of classical contact mechanics with or without adhesion in a very simple way. A tangential contact problem with and without creep can also be mapped exactly to a one-dimensional system. It can be shown that the reduction method is applicable to contacts of linear visco-elastic bodies as well as to thermal effects in contacts. The method was further validated for randomly rough self-affine surfaces through comparison with direct 3D simulations. MRD means a huge reduction of computational time for the simulation of contact and friction between rough surfaces accounting for complicated rheology and adhesion. In MRD, not only is the dimension of the space reduced from three to one, but the resulting degrees of freedom are independent (like normal modes in the theory of oscillations). Because of this independence, the method is predestinated for parallel calculation on graphic cards, which brings further acceleration. The method opens completely new possibilities in combining microscopic contact mechanics with the simulation of macroscopic system dynamics without determining the “law of friction” as an intermediate step. More... »

PAGES

41-62

References to SciGraph publications

  • 2012-09. Modeling of the dynamic contact in stick-slip microdrives using the method of reduction of dimensionality in PHYSICAL MESOMECHANICS
  • 2012-09. Contact force resulting from rolling on a self-affine fractal rough surface in PHYSICAL MESOMECHANICS
  • 2012-09. Simulation of the influence of ultrasonic in-plane oscillations on dry friction accounting for stick and creep in PHYSICAL MESOMECHANICS
  • 2010-06. Force of friction between fractal rough surface and elastomer in TECHNICAL PHYSICS LETTERS
  • 2010. Contact Mechanics and Friction, Physical Principles and Applications in NONE
  • 1995-09. Axi-symmetric bodies of equal material in contact under torsion or shift in ARCHIVE OF APPLIED MECHANICS
  • 2012-09. On the reduction method of dimensionality: The exact mapping of axisymmetric contact problems with and without adhesion in PHYSICAL MESOMECHANICS
  • 2012-09. Adhesive properties of contacts between elastic bodies with randomly rough self-affine surfaces: A simulation with the method of reduction of dimensionality in PHYSICAL MESOMECHANICS
  • 1981-10. The stress on an elastic half-space due to sectionally smooth-ended punch in JOURNAL OF ELASTICITY
  • 2012-09. Dependence of the kinetic force of friction between a randomly rough surface and simple elastomer on the normal force in PHYSICAL MESOMECHANICS
  • 2012-09. Shakedown and induced microslip of an oscillating frictional contact in PHYSICAL MESOMECHANICS
  • 2012-09. Basic ideas and applications of the method of reduction of dimensionality in contact mechanics in PHYSICAL MESOMECHANICS
  • 2012-09. Mesoscopic nature of friction and numerical simulation methods in tribology in PHYSICAL MESOMECHANICS
  • 2000. Contact, Adhesion and Rupture of Elastic Solids in NONE
  • 2012-09. Multiscale simulation of friction with normal oscillations in the method of reduction of dimensionality in PHYSICAL MESOMECHANICS
  • 2011-01. Using hierarchical memory to calculate friction force between fractal rough solid surface and elastomer with arbitrary linear rheological properties in TECHNICAL PHYSICS LETTERS
  • 2012-09. Normal contact between a rigid surface and a viscous body: Verification of the method of reduction of dimensionality for viscous media in PHYSICAL MESOMECHANICS
  • 2012-09. On the dependence of the static friction force between a rigid, randomly rough fractal surface and a viscoelastic body on the normal force in PHYSICAL MESOMECHANICS
  • 2010-09. Adhesive Contribution to the Coefficient of Friction Between Rough Surfaces in TRIBOLOGY LETTERS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s40544-013-0005-3

    DOI

    http://dx.doi.org/10.1007/s40544-013-0005-3

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1051185420


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