The deformation process involves different stages. I was wondering how do you call the process where the materials return to their orginial state? Just as given in the bold text.
And, moreover, what is the formula which calculates the time it returns back to the orginal state for a random viscoelastic material?

The answer to your first question: "elastic," or what Nihilist said.

Viscoelastic materials exhibit energy losses and therefore are not "elastic." The Maxwell model is commonly used. In 1D, the "formula" contains one unknown material constant (in addition to Young's modulus) to be found experimentally.