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SUMMARY:Dynamics of a regularized and bistable Ericksen bar using an exten
 ded Lagrangian approach - Bruno Lombard (Laboratoire de Mécanique et d’
 Acoustique)
DTSTART:20220714T153000Z
DTEND:20220714T160000Z
UID:TALK175904@talks.cam.ac.uk
DESCRIPTION:he motivation of this work is to better understand the dynamic
  behaviour of bistable structures presenting an analogy with regularized E
 ricksen bars. The archetype of such structures is the bistable tape spring
 \, which exhibits a particular scenario of deployment\, from the stable co
 iled configuration to the straight stable configuration: at each time of t
 he deployment\, the geometry of the tape is similar to a twophase bar with
  a coiled part and a straight part separated by a transition zone that mov
 es along the tape. One goal of this work is to show that a regularized and
  bistable Ericksen bar model contains all the properties to reproduce such
  a dynamic behaviour. The mathematical structure of this model presents a 
 locally non-convex potential with two minima and a dependence of higher or
 der terms. Some similarities exist between this model and the Euler-Kortew
 eg system with a Van der Waals equation. To study numerically the dynamic 
 behaviour of such models\, it is necessary to solve a dispersive and condi
 tionally hyperbolic system. For this purpose\, the Lagrangian of the regul
 arized bistable Ericksen model is extended and penalized. Variable boundar
 y conditions are deduced from Hamilton&rsquo\;s principle and are used to 
 control the evolution of the system. Dispersion analysis allows to determi
 ne the numerical parameters of the model. The obtained non&ndash\;homogene
 ous hyperbolic system can be solved by standard splitting strategy and fin
 ite-volume methods. Numerical simulations illustrate how the parameters of
  the model influence the width and the propagation speed of the transition
  zone. The effect of energy dissipation is also examined. Finally\, compar
 isons with an exact kink wave solution indicate that the extended Lagrangi
 an solution reproduces well the dynamics of the original Lagrangian.
LOCATION:Seminar Room 1\, Newton Institute
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