Size-dependent elastic properties of nanosized structural elements

Abstract

Effective stiffness properties (D) of nanosized structural elements such as plates and beams differ from those predicted by standard continuum mechanics (D c ). These differences (D − D c )/D c depend on the size of the structural element. A simple model is constructed to predict this size dependence of the effective properties. The important length scale in the problem is identified to be the ratio of the surface elastic modulus to the elastic modulus of the bulk. In general, the non-dimensional difference in the elastic properties from continuum predictions (D − D c )/D c is found to scale as αS/Eh, where α is a constant which depends on the geometry of the structural element considered, S is a surface elastic constant, E is a bulk elastic modulus and h a length defining the size of the structural element. Thus, the quantity S/E is identified as a material length scale for elasticity of nanosized structures. The model is compared with direct atomistic simulations of nanoscale structures using the embedded atom method for FCC Al and the Stillinger-Weber model of Si. Excellent agreement between the simulations and the model is found.

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.…”

Atomistic simulation on size-dependent yield strength and defects evolution of metal nanowires

“…As the scale is reduced to nanometer, the surface effects dramatically change the physical phenomena [10][11][12] and the yield strengths of the low-dimensional nanomaterials are different from the bulk materials [13][14][15][16][17][18]. Although, many efforts have been devoted to elucidate size effects in crystalline nanostructures [8,15,19], the size-dependent mechanical properties of nanostructure materials still need to be investigated further.…”

Size-dependent surface energy density of typically fcc metallic nanomaterials

“…A database of surface energy densities for various face-centered-cubic (fcc) and bodycentered-cubic (bcc) metals with differently oriented faces were established by Vitos [17] and Shenoy [18], based on the first-principle and MD calculations, respectively. Similar works were done by Miller and Shenoy [19], Mi et al [20] and Sheng et al [21]. However, the size dependence of the surface energy density was not considered in these simulations.…”