msepostdoc-list Fwd: Midwest Mechanics Seminar April 4th ARMS 1010 4:30

[Donna Bystrom]

*Midwest Mechanics Seminar*

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                                                                  April 
4^th , 2012  4:30 ARMS Room 1010*

*Eliot Fried***

*D**epartment of Mechanical Engineering, McGill University*

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*Stability of a thin elastic film close to a rigid plate*

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*Abstract:*

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*We introduce and study a variational model for the formation of 
patterns induced by bringing the surface of a rigid plate into contact 
proximity with the surface of a polymeric film strongly bonded to a 
substrate. We treat the film as a homogeneous, isotropic, hyperelastic 
solid and account for both attractive and repulsive van der Waals 
interactions between the film surface and the proximate contractor.  
Aside from confiming the intuitive expectation that the presence of a 
repulsive contribution to the van der Waals potential should stabilize 
patterns that form on the film surface, we elucidate the role of 
repulsive interactions at the onset of instability. For a recently 
proposed van der Waals potential involving two parameters, the Hamaker 
constant **A **and the equilibrium spacing **d**e**, our results include 
estimates for the critical gap **d**c **at which undulations appear on 
the _lm surface, the corresponding wavenumber **k**c **of the 
undulations, and a lower bound **f **for the attractive force needed to 
induce the undulations. To leading order, **d**c **~ **(**Ah 
/**)****1**=**4**, **k**c **~ **1**=h**, and **f**m **~ 
**(**3**A=h**3**)**1**=**4**,  where **h **and ****denote the thickness 
and infinitesimal shear modulus of the film. Correction terms due to 
repulsive interactions indicate that, while **k**c **may be influenced 
by ****and **A**, **d**c **may also be influenced by **d**e**. Granted 
knowledge of ****and **A**, our results also suggest a simple 
experimental protocol for determining **d**e**.***

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*Bio:*

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*Eliot Fried obtained his Ph.D. in Applied Mechanics from the California 
Institute of Technology in 1991.  He received an NSF Mathematical 
Sciences Postdoctoral Fellowship, a Japan Society for the Promotion of 
Science Postdoctoral Research Fellowship, and an NSF Research Initiation 
Award. Currently he is a Professor of Mechanical Engineering and the 
Tier 1 Canada Research Chair in Interfacial and Defect Mechanics at 
McGill University. He previously held positions at Carnegie Mellon 
University, the Pennsylvania State University, College Park, the 
University of Illinois at Urbana-Champaign, and Washington University in 
St. Louis. At Illinois, he was a Fellow of the Center of Advanced Study 
and was awarded a Critical Research  Initiative Grant. His research 
focuses on the mechanics and thermodynamics of novel materials, 
including liquid crystals, surfactant solutions, hydrogels, and 
nanocrystalline alloys.***

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