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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Dynamics of a regularized and bistable Ericksen ba
r using an extended Lagrangian approach - Bruno Lo
mbard (Laboratoire de Mécanique et d’Acoustique)
DTSTART;TZID=Europe/London:20220714T163000
DTEND;TZID=Europe/London:20220714T170000
UID:TALK175904AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/175904
DESCRIPTION:he motivation of this work is to better understand
the dynamic behaviour of bistable structures pres
enting an analogy with regularized Ericksen bars.
The archetype of such structures is the bistable t
ape spring\, which exhibits a particular scenario
of deployment\, from the stable coiled configurati
on to the straight stable configuration: at each t
ime of the deployment\, the geometry of the tape i
s similar to a twophase bar with a coiled part and
a straight part separated by a transition zone th
at moves along the tape. One goal of this work is
to show that a regularized and bistable Ericksen b
ar model contains all the properties to reproduce
such a dynamic behaviour. The mathematical structu
re of this model presents a locally non-convex pot
ential with two minima and a dependence of higher
order terms. Some similarities exist between this
model and the Euler-Korteweg system with a Van der
Waals equation. To study numerically the dynamic
behaviour of such models\, it is necessary to solv
e a dispersive and conditionally hyperbolic system
. For this purpose\, the Lagrangian of the regular
ized bistable Ericksen model is extended and penal
ized. Variable boundary conditions are deduced fro
m Hamilton&rsquo\;s principle and are used to cont
rol the evolution of the system. Dispersion analys
is allows to determine the numerical parameters of
the model. The obtained non&ndash\;homogeneous hy
perbolic system can be solved by standard splittin
g strategy and finite-volume methods. Numerical si
mulations illustrate how the parameters of the mod
el influence the width and the propagation speed o
f the transition zone. The effect of energy dissip
ation is also examined. Finally\, comparisons with
an exact kink wave solution indicate that the ext
ended Lagrangian solution reproduces well the dyna
mics of the original Lagrangian.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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