Abstract

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 in two-dimensional setting. Introduction of surface energy leads to non-classical boundary conditions incorporating both stresses and derivatives of displacements. The mechanical problem will be 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 will be discussed. 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 based on B-splines is suggested, and the numerical results are presented for different values of the mechanical and the geometric parameters.