  Recent molecular dynamic simulations have found chiral single wall carbon
nanotubes (SWNTs) twist during stretching, which is similar to the motion of a
screw. Obviously this phenomenon, as a type of curvature-chirality effect, can
not be explained by usual isotropic elastic theory of SWNT. More interestingly,
with larger axial strains (before buckling), the axial strain induced torsion
(a-SIT) shows asymmetric behaviors for axial tensile and compressing strains,
which suggests anharmonic elasticity of SWNTs plays an important role in real
a-SIT responses. In order to study the a-SIT of chiral SWNTs with actual sizes,
and avoid possible deviations of computer simulation results due to the
finite-size effect, we propose a 2D analytical continuum model which can be
used to describe the the SWNTs of arbitrary chiralities, curvatures, and
lengths, with the concerning of anisotropic and anharmonic elasticity of SWNTs.
This elastic energy of present model comes from the continuum limit of lattice
energy based on Second Generation Reactive Empirical Bond Order potential
(REBO-II), a well-established empirical potential for solid carbons. Our model
has no adjustable parameters, except for those presented in REBO-II, and all
the coefficients in the model can be calculated analytically. Using our method,
we obtain a-SIT responses of chiral SWNTs with arbitrary radius, chiralities
and lengthes. Our results are in reasonable agreement with recent molecular
dynamic simulations. [Liang {\it et. al}, Phys. Rev. Lett, ${\bf 96}$, 165501
(2006).] Our approach can also be used to calculate other curvature-chirality
dependent anharmonic mechanic responses of SWNTs.
