An axisymmetric problem for a nano-sized material surface on a boundary of an elastic semi-space

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• Anna Zemlyanova (Kansas State University)
• Friday 05 July 2024, 12:15-12:45
• Seminar Room 1, Newton Institute.

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WHTW02 - WHT Follow on: the applications, generalisation and implementation of the Wiener-Hopf Method

A problem for a nano-sized penny-shaped material surface attached to the boundary of an elastic isotropic semi-space is considered. An axisymmetric normal traction is applied to a material surface. The surface is modeled using the Steigmann-Ogden form of surface energy. The problem is solved by using the Boussinesq potentials represented by the Hankel transforms of certain unknown functions. With the help of these functions, the problem can be reduced to a system of two singular integral equations. Two 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 function into a series based on Chebyshev polynomials. Then the approximations of the unknown functions can be obtained from a system of linear algebraic equations. Accuracy of the numerical procedure is studied. Various numerical 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.   This is a joint work with Lauren M. White.

This talk is part of the Isaac Newton Institute Seminar Series series.

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