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CATEGORIES:Engineering Department Structures Research Seminar
 s
SUMMARY:New equations for inextensible sheets with applica
 tions to Moebius strips and helical nanoribbons - 
 Gert Van der Heijden (University College London)
DTSTART;TZID=Europe/London:20080502T150000
DTEND;TZID=Europe/London:20080502T160000
UID:TALK11523AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/11523
DESCRIPTION:We derive a new set of geometrically-exact equilib
 rium equations for the\ndeformation of thin inexte
 nsible strips of finite width. The equations are\n
 the Euler-Lagrange equations for a geometrical var
 iational problem with a\nfunctional in terms of th
 e curvature and torsion of the strip's axial curve
 \nas well as their derivatives with respect to arc
 length. The equations are\nused to solve the long-
 standing problem of finding the characteristic sha
 pe\nof a material Moebius strip. Solutions for inc
 reasing width-to-length ratio\nshow the formation 
 of creases bounding nearly flat triangular regions
 \, a\nfeature also familiar from fabric draping an
 d paper crumpling. This suggests\nthat our approac
 h could give new insight into energy localisation 
 phenomena\nin unstretchable elastic sheets\, which
  for instance could help to predict\npoints of ons
 et of tearing.\n   The technique for deriving equi
 librium equations can be generalised to\nintrinsic
 ally curved sheets (shells). In the second part of
  the talk we\nwill apply this to study the force-e
 xtension behaviour of helical ribbons.\nA complete
  analytical study of stretched/compressed exact he
 lical solutions\ncan be carried out. Unlike previo
 us rod models our strip model predicts\nhysteresis
  behaviour for low-pitch ribbons of arbitrary mate
 rial properties.\nAssociated with it is a first-or
 der transition between two different helical\nstat
 es\, a phenomenon observed in experiments with cho
 lesterol ribbons.\nNumerical solutions for non-hel
 ical solutions reveal a new non-uniform\nuncoiling
  scenario in which a ribbon of very low pitch shea
 rs under tension\nand successively releases a sequ
 ence of almost planar loops. Our results may\nbe r
 elevant for nanoscale devices such as force probes
 .\n\n
LOCATION:Engineering Department - LR6
CONTACT:Nami Norman
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