Effect of interface stresses on the elastic deformation of an elastic half-plane containing an elastic inclusion

The effect of the interface stresses is studied upon the size-dependent elastic deformation of an elastic half-plane having a cylindrical inclusion with distinct elastic properties. The elastic half-plane is subjected to either a uniaxial loading at infinity or a uniform non-shear eigenstrain in the inclusion. The straight edge of the half-plane is either traction-free, or rigid-slip, or motionless, which represents three practical situations of mechanical structures. Using two-dimensional Papkovich–Neuber potentials and the theory of surface/interface elasticity, the elastic field in the elastic half-plane is obtained. Comparable with classical result, the new formulation renders the significant effect of the interface stresses on the stress distribution in the half-plane when the radius of the inclusion is reduced to the nanometer scale. Numerical results show that the intensity of the influence depends on the surface/interface moduli, the stiffness ratio of the inclusion to the surrounding material, the boundary condition on the edge of the half-plane and the proximity of the inclusion to the edge.