Finite element modelling of nanoscale inhomogeneities in an elastic matrix

Nanoscale inhomogeneities in elastic matrix materials are encountered in the development of nanocomposites and various nanoscale structures. The overall effective properties of nanocomposites and nanostructures are controlled by the elastic field of the inhomogeneity–matrix system. As an alternative to analytical solution approaches that are confined to the solution of a single inhomogeneity of ideal shape, this study presents a two-dimensional finite element formulation for the analysis of multiple arbitrary shaped anisotropic inhomogeneities in an anisotropic matrix material. The Gurtin–Murdoch surface/interface elasticity model is used in the analysis. Instabilities of the elastic field are found under certain conditions. Selected numerical results are presented to show the influence of inhomogeneity geometry, multiple inhomogeneities, inhomogeneity eigenstrain and anisotropy on the stress and displacement fields.