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SUMMARY:A problem for a material surface attached to the boundary of an el
 astic semi-plane - Anna Zemlyanova (Kansas State University)
DTSTART:20230727T103000Z
DTEND:20230727T113000Z
UID:TALK202807@talks.cam.ac.uk
DESCRIPTION:A problem for a nano-sized material surface attached to the bo
 undary of an elastic isotropic semi-plane is considered. A normal external
  traction is applied to a boundary of the material surface. The material s
 urface is modeled using the Steigmann-Ogden form of surface energy. The pr
 oblem is solved by using integral representations of stresses and displace
 ments through certain unknown functions. With the help of these functions\
 , the problem can be reduced to either a system of two singular integral e
 quations or a single singular integral equation. Two types of material sur
 face tip boundary conditions are considered: free tip conditions and condi
 tions with compensated surface prestress term. The numerical solution of t
 he system of singular integral equations is obtained by expanding each unk
 nown function into a series based on Chebyshev polynomials. Then the appro
 ximations of the unknown functions can be obtained from a system of linear
  algebraic equations. Accuracy of the numerical procedure is studied. Vari
 ous numerical examples for different values of the surface energy paramete
 rs are considered. It is shown that both the surface parameters and the ty
 pe of tip conditions have significant influence on the behavior of the mat
 erial system.
LOCATION:Seminar Room 1\, Newton Institute
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