On the significance of coherent interface effects for embedded nanoparticles

To extend classical micro and nanomechanics of inclusions and inhomogeneities from bulk phase only to interface-featured multi-phase, we formulated a solution procedure for evaluating the significance of interface stress on embedded nanoparticles. The methodology allows, for instance, analytical determination of the influential effects of interface stress on elastic fields of both nanoparticles and matrices within the general framework of continuum theory of bulk and interface elasticity. A thorough curvilinear analysis of a general Euclidean interface is performed with the aid of field theory and applied to facilitate the integration of displacement continuity and traction jump boundary conditions of interface elasticity into the classical formulation of displacement potentials. For illustration purposes, the solution methodology is applied to a spherical nanoparticle embedded in an infinite substrate subjected to most general far-field tension and eigenstrain loads. The developed model extends the solution limit of interface-induced length-scale effects on embedded ellipsoidal nanoparticles to the solution availability of their corresponding classical counterparts, provided that interface material properties are given.