Nanoparticles and the influence of interface elasticity

Abstract

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.Razmatra se uticaj napona na povrsi i interfejsu na elasticno polje nanocestice potopljene u konacni sferni substrat. Ovde se ima u vidu aksijalno zatezno polje koje deluje na spoljnu granicu supstrata i nesmicuce uniformno polje usadne deformacije unutar cestice. Kao rezultat osne simetrije dve potencijalne funkcije pomeranja Papkovic-Nojbera su dovoljne da reprezentuju resenje elasticnosti. Naponski efekti na povrsi i interfejsu su potpuno reprezentovani Gurtinovom i Mardokovom teorijom elasticnosti povrsi i interfejsa. Ovi efekti modifikuju granicne uslove pridruzene klasicnoj kontinualnoj teoriji elasticnosti. Kompletna metodologija rezultuje u elastostatickom resenju Navijeovih jednacina. U suprotnosti od klasicnog resenja, modifikovana verzija uvodi dodatne zavisnosti od velicine nanocestica kao i materijalne osobine povrsi i interfejsa.