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Contact problems at nanoscale

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CATW02 - Complex analysis in mathematical physics and applications

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.

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

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