Elasticity of nanometer-sized objects

We initiate the development of a theory of the elasticity of nanoscale objects based upon physical concepts which remain properly defined on the nanoscale. This theory provides a powerful way of understanding nanoscale elasticity in terms of local group contributions and gives insight into the breakdown of standard continuum relations. We also give two applications. In the first, we show how to use the theory to derive a relation between the bending and stretching properties of nanomechanical resonators and prove that it is much more accurate than the continuum-based relations currently employed in present experimental analyses. In the second, we link features of the underlining electronic structure to the elastic response of a silicon nanoresonator.