An adhesive contact problem for a semi-plane with a surface elasticity in the Steigmann-Ogden form. (English) Zbl 1415.74008
Summary: The main goal of the present paper is to study a two-dimensional problem of adhesive contact of a rigid stamp with an elastic upper semi-plane. Surface elasticity in the Steigmann-Ogden form acts on the free boundary of the semi-plane. The mechanical problem is solved using integral representations of the stresses and the displacements. The resulting system of singular integro-differential equations is regularized using Fourier transform method. The numerical procedure of the solution of the system of singular integro-differential equations is presented, and the numerical results are obtained for different values of the mechanical parameters. The size-dependency of the solutions of the problem is studied. It can be seen that taking into account curvature-dependency of the surface energy is increasingly important at the very small scales (characteristic length of the contact interval is under 20 nm.
Keywords:
surface elasticity; surface energy; curvature-dependence; integral equations; contact problemsReferences:
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