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CATEGORIES:Engineering Department Bio- and Micromechanics Sem
inars
SUMMARY:Method of reduction of dimensionality in contact m
echanics - Professor Valentin Popov\, TU Berlin
DTSTART;TZID=Europe/London:20120224T140000
DTEND;TZID=Europe/London:20120224T150000
UID:TALK35728AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/35728
DESCRIPTION:2007\, Geike and Popov have shown [1]\, that there
is a wide class of contacts between tree dimensio
nal bodes which can be mapped either exactly or wi
thout loss of essential information to one dimensi
onal systems (one-dimensional elastic or visco-ela
stic foundations). 2011\, Markus Heß proved many o
f the mapping theorems and have shown that the exa
ct mapping is always possible for any axis-symmetr
ical body\, both without and with adhesion [2]. Th
e equivalence of three dimensional systems to one
dimensional ones is valid for relations of relativ
e approach of the surfaces (or indentation depth)\
, the contact area and the contact force. Tangenti
al contact problem with and without creep is also
mapped exactly to one-dimensional system. Another
class of systems\, to which the mapping can be app
lied\, are bodies with randomly rough surfaces. It
can further be shown that the reduction method is
applicable to contacts of linear visco-elastic bo
dies as well as to thermal effects in contacts. \n
The method of reduction of dimensionality means a
huge reduction of computational time for simulatio
n of contact and friction between rough surfaces w
ith account of complicated rheology and adhesion.
Because of independence of single "springs" of equ
ivalent elastic foundations\, it is predestinated
for parallel calculation on graphic cards. The met
hod allows for the first time to combine microscop
ic contact mechanics with simulation of macroscopi
c system dynamics without determining the "law of
friction" as an intermediate step.\nUsing the poss
ibility to simulate both the frictional law and th
e macroscopic dynamics of a system in the framewor
k of the same numerical model we illustrate the me
thod on an example of a nano robot driven by oscil
lating spherical contacts both with smooth and rou
gh surface. \nReferences\n1. Geike T. and V.L. Pop
ov\, Mapping of three-dimensional contact problems
into one dimension. - Phys. Rev. E.\, 2007\, v. 7
6\, 036710 (5 pp.).\n2. Hess\, M.: Über die exakte
Abbildung ausgewählter dreidimensionaler Kontakte
auf Systeme mit niedrigerer räumlicher Dimension.
(About exact mapping of some contacts to systems
of lower spatial dimension)\, Cuvillier\, 172 p.\,
2011.
LOCATION:Oatley Seminar Room\, Department of Engineering
CONTACT:Ms Helen Gardner
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