Consider a long rod made of metal, plastic, rubber, or some other homogeneous material. Hold the rod at the ends and twist one end clockwise and the other end counterclockwise. This torsion (twisting) causes stresses in the rod. If the force we apply is small enough, the rod behaves as an elastic body: when we release it, it will return to its original state. But if we apply a lot of twisting force, we will eventually change the rod's structure: some portion of it will behave plastically and will be permanently changed. If the whole rod behaves elastically, or if it all behaves plastically, then modeling is rather easy. More difficult cases occur when there is a mixture of elastic and plastic behavior. In this paper, we investigate the rod's behavior over a full range of torsion.