Boundary element analysis of an elastic half-plane containing nanoinhomogeneities

In this paper, the boundary element method (BEM) is used for the stress analysis of elastic half-plane containing nanoinhomogeneities with surface/interface effects. The boundary integral equations from the matrix and the nanoinhomogeneities are respectively discretized into a series of quadratic boundary elements. The related systems of equations which contain the interface displacements and tractions from the matrix side and the nanoinhomogeneities are established. By means of the Gurtin–Murdoch interface conditions, the resulting system of equations which contain only the interface displacements is obtained. Upon solving for the interface displacements, the interface tractions on the matrix side and on the boundary of each nanoinhomogeneity can be determined. Stresses at internal points can be calculated by using the internal point stress integral equations of the matrix and those for the nanoinhomogeneities. Under a remote loading/surface loading, the effects of the interface elastic parameters and the residual stresses of the elastic half-plane with nanoinhomogeneities are studied.