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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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