We investigate the effect of surface/interface elasticity in the presence of nanoparticles, embedded in a semi-infinite elastic medium. The work is motivated by the technological significance of self-organization of strained islands in multilayered systems. Islands, adatom-clusters, or quantum dots are modeled as inhomogeneities, with properties that differ from the ones of the surrounding material. Within the framework of continuum elasticity theory, the Papkovitch-Neuber displacement methodology coupled with Gurtin's surface elasticity yields an analytical solution. The elastic field is expressed in terms of four sets of spherical and cylindrical harmonics. Surface elasticity introduces an additional length scale and results suggest that local stresses are significantly affected by the size of the nanoparticles.

The paper describes theoretical and computational studies associated with the interface elastic properties of noncoherent metallic bicrystals. Analytical forms of interface energy, interface stresses, and interface elastic constants are derived in terms of interatomic potential functions. Embedded-atom method potentials are then incorporated into the model to compute these excess thermodynamics variables, using energy minimization in a parallel computing environment. The proposed model is validated by calculating surface thermodynamic variables and comparing them with preexisting data. Next, the interface elastic properties of several fcc-fcc bicrystals are computed. The excess energies and stresses of interfaces are smaller than those on free surfaces of the same crystal orientations. In addition, no negative values of interface stresses are observed. Current results can be applied to various heterogeneous materials where interfaces assume a prominent role in the systems' mechanical behavior.

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.

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Elastic interactions of atomic steps can greatly impact surface morphology. Recent atomistic calculations and experimental observations find the standard dipole model of steps is valid only for very large step separations. In this Letter, a new model is presented that displays remarkable agreement with atomistic predictions for step separations larger than just a few step heights. It is shown that the interaction energy of steps exhibits a novel intermediate-ranged behavior and that, for particular systems, step interactions switch from repulsive to attractive as separation distance decreases.