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SUMMARY:An axisymmetric problem for a nano-sized material surface on a bou
 ndary of an elastic semi-space - Anna Zemlyanova (Kansas State University)
DTSTART:20240705T111500Z
DTEND:20240705T114500Z
UID:TALK214990@talks.cam.ac.uk
DESCRIPTION:A problem for a nano-sized penny-shaped material surface attac
 hed to the boundary of an elastic isotropic semi-space is considered. An a
 xisymmetric normal traction is applied to a material surface. The surface 
 is modeled using the Steigmann-Ogden form of surface energy. The problem i
 s solved by using the Boussinesq potentials represented by the Hankel tran
 sforms of certain unknown functions. With the help of these functions\, th
 e problem can be reduced to a system of two singular integral equations. T
 wo types of material surface tip boundary conditions are considered: free 
 tip conditions and conditions with compensated surface prestress term. The
  numerical solution of this system is obtained by expanding each unknown f
 unction into a series based on Chebyshev polynomials. Then the approximati
 ons of the unknown functions can be obtained from a system of linear algeb
 raic equations. Accuracy of the numerical procedure is studied. Various nu
 merical examples for different values of the surface energy parameters are
  considered. It is shown that both the surface parameters and the type of 
 tip conditions have significant influence on the behavior of the material 
 system.\n&nbsp\;\nThis is a joint work with Lauren M. White.
LOCATION:Seminar Room 1\, Newton Institute
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