Surface/interface Effects On An Infinite Plane Containing Multiple Circular Nano-inhomogeneities

With the development of technology and productive forces science,the inhomogeneous elastomer with surface/interface effect was paid more and more attention.In order to consider the influence of surface effect on the mechanical behavior of nano materials,Gurtin and Murdoch developed surface elasticity based on continuum mechanics.However,in the preparation of nanocomposites,there are many defects,such as cracks,holes and inclusions.Therefore,the study of mechanical behavior of nonuniform media with surface/interface effect not only has the theoretical guidance for the design and processing of nanomaterials and nanometer components,but also enriches the classical elastic theory and has a great influence on the development of surface elastic mechanics.Based on the surface/interface theory of Gurtin and Murdoch,employing complex function,the problem of an isotropic elastic plane containing multiple circular nanoinhomogeneities was considered.Taking two circular inclusions as an example,the solution of any point at the nano-inhomogeneities and plane with surface/interface effects was obtained.The effect of existence of nano scale surface to the stress field of the whole plane structure was analyzed.