  By using the updated improved Quantum Molecular Dynamics model in which a
surface-symmetry potential term has been introduced for the first time, the
excitation functions for fusion reactions of $^{40,48}$Ca+$^{90,96}$Zr at
energies around the Coulomb barrier have been studied. The experimental data of
the fusion cross sections for $^{40}$Ca+$^{90,96}$Zr have been reproduced
remarkably well without introducing any new parameters. The fusion cross
sections for the neutron-rich fusion reactions of $^{48}$Ca+$^{90,96}$Zr around
the Coulomb barrier are predicted to be enhanced compared with a
non-neutron-rich fusion reaction. In order to clarify the mechanism of the
enhancement of the fusion cross sections for neutron-rich nuclear fusions, we
pay a great attention to study the dynamic lowering of the Coulomb barrier
during a neck formation. The isospin effect on the barrier lowering is
investigated. It is interesting that the effect of the projectile and target
nuclear structure on fusion dynamics can be revealed to a certain extent in our
approach. The time evolution of the N/Z ratio at the neck region has been
firstly illustrated. A large enhancement of the N/Z ratio at neck region for
neutron-rich nuclear fusion reactions is found.
