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In this manuscript, we discuss the influence of surface and interface
stress on the elastic field of a nanoparticle, embedded in a finite
spherical substrate. We consider an axially symmetric traction field
acting along the outer boundary of the substrate and a non-shear uniform
eigenstrain field inside the particle. As a result of axial symmetry,
two Papkovitch-Neuber displacement potential functions are sufficient to
represent the elastic solution. The surface and interface stress effects
are fully represented utilizing Gurtin and Murdoch's theory of surface
and interface elasticity. These effects modify the traction-continuity
boundary conditions associated with the classical continuum elasticity
theory. A complete methodology is presented resulting in the solution of
the elastostatic Navier's equations. In contrast to the classical
solution, the modified version introduces additional dependencies on the
size of the nanoparticles as well as the surface and interface material
properties. |
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