Boundary element analysis of three dimensional nanoscale inhomogeneities

This work contains two parts, i.e. (1) the subdomain boundary element method (DBEM) and the Gurtin–Murdoch interface constitutive relation are used to investigate three dimensional (3D) nano-inhomogeneities; (2) under the condition of the same Poisson’s ratio for the inhomogeneities and the matrix, an integral equation formulation only containing the interface displacements, i.e. no interface tractions, is proposed to carry out the stress analysis of 3D nano-inhomogeneities. The proposed integral equation formulation (called as SBEM) can simply be implemented in the analysis of 3D nano-inhomogeneities compared to the DBEM. This paper presents the component form of 3D Gurtin–Murdoch interface constitutive relation which can easily be used in the numerical implementation. Nine-node quadrilateral elements are adopted to discretize the interfaces among the matrix and nano-inhomogeneities. The results from two kinds of methods, i.e. DBEM and SBEM, are in good agreement with each other.