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Surface energy approaches in modeling of nano-objects

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It is known that surface energy plays an increasingly important role in modeling of objects at nano-scales. In this talk, surface energy model proposed by Steigmann and Ogden will be applied to fracture problems and contact problems in two-dimensional setting. Introduction of surface energy leads to non-classical boundary conditions incorporating both stresses and derivatives of displacements. The mechanical problems are reduced to systems of singular integro-differential equations which are further reduced to systems of weakly-singular equations. The existence and uniqueness of the solution for almost all the values of the parameters is proved. It is shown that taking into account surface mechanics leads to the size-dependent solutions. A numerical scheme of the solution of the systems of singular integro-differential equations is suggested, and the numerical results are presented for different values of the mechanical and the geometric parameters.

This talk is part of the Engineering - Mechanics and Materials Seminar Series series.

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