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SUMMARY:Surface energy approaches in modeling of nano-objects - Prof Anna 
 Zemlyanova\, Department of Mathematics\, Kansas State University
DTSTART:20191025T130000Z
DTEND:20191025T140000Z
UID:TALK129349@talks.cam.ac.uk
CONTACT:Hilde Hambro
DESCRIPTION:It is known that surface energy plays an increasingly importan
 t role in modeling of objects at nano-scales. In this talk\, surface energ
 y model proposed by Steigmann and Ogden will be applied to fracture proble
 ms and contact problems in two-dimensional setting. Introduction of surfac
 e energy leads to non-classical boundary conditions incorporating both str
 esses and derivatives of displacements. The mechanical problems are reduce
 d to systems of singular integro-differential equations which are further 
 reduced to systems of weakly-singular equations. The existence and uniquen
 ess of the solution for almost all the values of the parameters is proved.
  It is shown that taking into account surface mechanics leads to the size-
 dependent solutions. A numerical scheme of the solution of the systems of 
 singular integro-differential  equations is suggested\, and the numerical 
 results are presented for different values of the mechanical and the geome
 tric parameters. 
LOCATION:Oatley Seminar Room\, Department of Engineering
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