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SUMMARY:Method of reduction of dimensionality in contact mechanics - Profe
 ssor Valentin Popov\, TU Berlin
DTSTART:20120224T140000Z
DTEND:20120224T150000Z
UID:TALK35728@talks.cam.ac.uk
CONTACT:Ms Helen Gardner
DESCRIPTION:2007\, Geike and Popov have shown [1]\, that there is a wide c
 lass of contacts between tree dimensional bodes which can be mapped either
  exactly or without loss of essential information to one dimensional syste
 ms (one-dimensional elastic or visco-elastic foundations). 2011\, Markus H
 eß proved many of the mapping theorems and have shown that the exact mapp
 ing is always possible for any axis-symmetrical body\, both without and wi
 th adhesion [2]. The equivalence of three dimensional systems to one dimen
 sional ones is valid for relations of relative approach of the surfaces (o
 r indentation depth)\, the contact area and the contact force. Tangential 
 contact problem with and without creep is also mapped exactly to one-dimen
 sional system. Another class of systems\, to which the mapping can be appl
 ied\, are bodies with randomly rough surfaces. It can further be shown tha
 t the reduction method is applicable to contacts of linear visco-elastic b
 odies as well as to thermal effects in contacts. \nThe method of reduction
  of dimensionality means a huge reduction of computational time for simula
 tion of contact and friction between rough surfaces with account of compli
 cated rheology and adhesion. Because of independence of single "springs" o
 f equivalent elastic foundations\, it is predestinated for parallel calcul
 ation on graphic cards. The method allows for the first time to combine mi
 croscopic contact mechanics with simulation of macroscopic system dynamics
  without determining the "law of friction" as an intermediate step.\nUsing
  the possibility to simulate both the frictional law and the macroscopic d
 ynamics of a system in the framework of the same numerical model we illust
 rate the method on an example of a nano robot driven by oscillating spheri
 cal contacts both with smooth and rough surface. \nReferences\n1.	Geike T.
  and V.L. Popov\, Mapping of three-dimensional contact problems into one d
 imension. - Phys. Rev. E.\, 2007\, v. 76\, 036710 (5 pp.).\n2.	Hess\, M.: 
 Über die exakte Abbildung ausgewählter dreidimensionaler Kontakte auf Sy
 steme mit niedrigerer räumlicher Dimension. (About exact mapping of some 
 contacts to systems of lower spatial dimension)\, Cuvillier\, 172 p.\, 201
 1.
LOCATION:Oatley Seminar Room\, Department of Engineering
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