Size-dependent elastic properties of nanosized structural elements

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 alpha S/Eh, where alpha 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 A1 and the Stillinger-Weber model of Si. Excellent agreement between the simulations and the model is found.