Interface tension-induced stress field around periodic nano-inclusions of arbitrary shape

Abstract

This paper investigates the plane deformation of periodic nano-inclusions of arbitrary shape embedded in a homogeneous isotropic material. A representative unit cell (RUC) with periodic boundary conditions imposed on its edges is used to represent the periodicity of the structure. Residual interface tension is incorporated into the deformation model so that the normal and tangential stresses have to jump across the matrix–inclusion interface, despite that the displacement can generally be treated as continuous across that interface. The stress field in the entire RUC is obtained by using the complex variable methods with the assistance of conformal mapping, series expansion, and collocation techniques. Numerical examples are presented for three different inclusion shapes. The results show that the interface tension-induced stress field can be greatly influenced by the shape, elastic modulus, and volume fraction of the inclusions.