  We develop and solve a continuum theory for the piezoelectric response of
nanotubes under applied uniaxial and torsional stresses. We find that the
piezoelectric response is controlled by the chiral angle, the aspect ratio, and
two dimensionless parameters specifying the ratio of the strengths of the
electrostatic and elastic energies. The model is solved in two limiting cases
and the solutions are discussed. These systems are found to have several
unexpected physical effects not seen in conventional bulk systems, including a
strong stretch-twist coupling and the development of a significant bound charge
density in addition to a surface charge density. The model is applied to
estimate the piezoelectric response of a boron-nitride nanotube under uniform
tensile stress.
