Is it possible that the refractive index of a material could change?if so,what are those factors and what kind of variation could they bring?
Yes. The refractive index of water changes with temperature. It falls slightly as the temperature rises.
The refractive index of a dielectric material with nonlinear behavior can also be changed by an application of an external DC electric field. This is called the electro-optic effect (or Kerr effect) and it has applications in nonlinear optics. For example you can use it in optical phase modulators.
Let me share an interesting example with you that you see in your daily life but still don't notice. Our own atmosphere is composed of various layers of varying densities ( both physical and optical ) hence due to a light ray follows a unique path in accordance the variation of the refractive index with the height hence we can't see beyond a particular distance on the road. Next we can discuss the fact that not even all components of the white light have similar refractive index for the same material due to difference in wavelegths of the different components. Also one can do some research upon the physical factors that determine the cauchy's coefficient .