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Contact problems at nanoscale

Presented by: 
Anna Zemlyanova
Thursday 31st October 2019 - 13:30 to 14:30
INI Seminar Room 1
In this talk, the surface elasticity in the form proposed by Steigmann and Ogden is applied to study plane problems of frictionless or adhesive contact of a rigid stamp with an elastic upper semi-plane. The results of the present work generalize the results for contact problems with Gurtin-Murdoch elasticity by including additional dependency on the curvature of the surface. The mechanical problem is reduced to a system of singular integro-differential equations which is regularized using Fourier transform method. The size-dependency of the solutions of the problem is highlighted. It is observed that the curvature-dependence of the surface energy is increasingly important at small scales. The numerical results are presented for different values of the mechanical parameters.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons