## 3 Results Analysis  
With the finite difference method, different influencing factors, including the strip width and the form and amplitude of the initial stress on the evolution of the stress distribution, are analyzed. To match the common stress distribution form in practice, the initial stress induced by the velocity distribution at the exit of the deformation zone is assumed to be a quartic polynomial, which can be expressed as Equation (8).  
\[\sigma_{y}(x)=a_{0}+a_{2}\bigg{(}\frac{x}{B/2}\bigg{)}^{2}+a_{4}\bigg{(}\frac{x }{B/2}\bigg{)}^{4} \tag{8}\]  
where \(a_{0}\), \(a_{2}\), and \(a_{4}\) are the coefficients of the quartic polynomial.  
First, when the strip width is 1000 mm, the effects of different initial stress forms on the stress evolution are shown in Figures 5-8. It can be seen that the stress tends to be zero after roughly one strip width among the four types of initial stress at the exit of the deformation zone, and the variation trends of the stress evolution of the different initial forms are different. In the case of \(a_{2}=-100\) MPa, \(a_{4}=0\) along direction \(y\), the stress along the edge of the strip tends to be steady, while the stress in the middle of the strip presents an \"S\"-shaped form. A similar law can be observed in the case of \(a_{2}=0,\ a_{4}=100\) MPa. In the case of \(a_{2}=-100\) MPa, \(a_{4}=100\) MPa, the stress in the middle of the strip presents an \"S\"-shaped form, but the change trend of the evolution of the stress along the edge of the strip is highly complex. That is, it decreases with distance, and then it increases to zero instead of decreasing to zero directly. The case of \(a_{2}=100\) MPa, \(a_{4}=-100\) MPa is similar to the case of \(a_{2}=-100\) MPa, \(a_{4}=100\) MPa. According to the theory of elasticity, the superposition principle can be used. That is, the case of \(a_{2}=-100\) MPa, \(a_{4}=100\) MPa can be treated as the superposition of \(a_{2}=-100\) MPa, \(a_{4}=0\) and \(a_{2}=0,\ a_{4}=100\) MPa. Thus, the case of \(a_{2}=-100\) MPa, \(a_{4}=0\) and \(a_{2}=0,\ a_{4}=100\) MPa can be considered as two basic modes, and any stress form combination at the exit of the deformation zone can be handled easily if the stress evolution regulation of the basic modes is known.  
Second, when the strip width is 1000 mm, and \(a_{4}=0\), the initial stress amplitude \(a_{2}\) will be 20, 40, 60, 80, or 100 MPa. The effect of the different initial stress amplitudes on the stress evolution is shown in Figure 9. It can be seen that the form of the stress distribution is similar to the different initial stress amplitudes on the same \(y\) coordinate, and the stress amplitude on the same \(y\) coordinate has a linear relationship with the amplitude of the initial stress. In addition, it can be seen that the stress amplitudes fall roughly 98.8% compared with the original stress on \(y=B\), whereas the stress on \(y=B/2\) is decaying.  
Finally, when \(a_{2}=-100\) MPa, \(a_{4}=0\), the strip width will be 1000, 1500, 2000, or 2500 mm, and the effect of the different strip widths on the stress evolution is shown in Figure 10. It can be seen that the different strip widths have a similar stress evolution regulation in the middle and along the edge of the strip. If the horizontal axis is \(y/B\), then all the curves will coincide with one another.  
Figure 8: Results of \(a_{2}=100\) MPa, \(a_{4}=-100\) MPa.  
Figure 7: Results of \(a_{2}=-100\) MPa, \(a_{4}=100\) MPa.  
Figure 9: Results of different initial stress amplitudes. (**a**) \(y=B\), (**b**) \(y=B/2\).  
From the above analysis, it can be determined that the initial stress amplitude and strip width have little effect on the change trend of the stress evolution, and the highly influential factor is the form of the initial stress, which can be broken down into two basic modes, namely, a unit quadratic or quartic coefficient. For example, the case of \(a_{2}=-100\) MPa, \(a_{4}=100\) MPa can be treated as the superposition of \(a_{2}=-100\) MPa, \(a_{4}=0\) and \(a_{2}=0,\ a_{4}=100\) MPa.