Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities

Abstract

The effect of surface energies, strains, and stresses on the size-dependent elastic state of embedded inhomogeneities are investigated. At nanolength scales, due to the increasing surface-to-volume ratio, surface effects become important and induce a size dependency in the otherwise size-independent classical elasticity solutions. In this letter, closed-form expressions are derived for the elastic state of eigenstrained spherical inhomogeneities with surface effects using a variational formulation. Our results indicate that surface elasticity can significantly alter the fundamental nature of stress state at nanometer length scales. Additional applications of our work on nanostructures such as quantum dots, composites, etc. are implied.

Electrospun polymer nanofibers: Mechanical and thermodynamic perspectives

“…Mechanistic models have attributed such behavior, for both two-dimensional and one-dimensional nanosystems, to surface effects. 19,[60][61][62][63] Although surface phenomena clearly play a role in the final properties of materials of reduced sizes, detailed analyses shows that surface effect alone cannot adequately explain the experimental observations. In the following sections, we first review the mechanical properties of several electrospun fibers and describe the related testing methods.…”

“…Thus, Sharma et al 61 calculated the stress concentration of a spherical aluminum cavity under hydrostatic tension, as a function of the cavity radius R 0 (see Fig. 24).…”

“…9 Surface Influence on the Elastic Properties of Nanoobjects Theoretical models incorporating the free surface energy into the continuum theory of mechanics have been suggested 61,75 for explaining the size-dependent elastic behavior of the nanoscale objects (i.e., particles, wires, and films). In traditional continuum mechanics, such surface free surface energy is typically neglected, as it is associated with only a few layers of atoms near the surface, which occupy a minor percentage of the total volume of material of interest.…”

Displacement field of a screw dislocation in a〈011〉Cu nanowire: An atomistic study

“…These questions have received lots of attention during these last decades since the pioneering mathematical works of Gurtin and Murdoch. [23][24][25] Using, for instance, the Chen et al 26 approach, the surface stress is described as symmetric 2×2 tensor σ S in the tangent plane of the curved surface. This latter is seen as a vanishingly thin membrane which can sustain in-plane stresses but offers no resistance for bending.…”

A unified computational framework for bulk and surface elasticity theory: a curvilinear-coordinate-based finite element methodology

“…Sharma et al, 2003;Sharma and Ganti, 2004;Sharma and Wheeler, 2007;Duan et al, 2005;Duan and Karihaloo, 2007;Benveniste and Miloh, 2001;Huang and Sun, 2007;Yvonnet et al, 2008;Fischer and Svoboda, 2010;Weissmüller et al, 2010;Levitas, 2013). This resurgence of interest in the mechanics of solid surfaces can be largely attributed to the increasing number of applications involving nanoscale structures.…”