  We initiate the development of a theory of the elasticity of nanoscale
objects based upon new 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 new relation between the
bending and stretching properties of nanomechanical resonators and to prove
that it is much more accurate than the continuum-based relations currently
employed in present experimental analyses. In the second, we use the new
approach to link features of the underlining electronic structure to the
elastic response of a silicon nanoresonator.
