## 3 A Post-Processing Algorithm to Enforce Traction Continuity along the Interface
### The Effects of the Geometrical Parameters of the Polynomial
The stresses calculated with the “fill boundary” algorithm of Vic-2D without the traction continuity algorithm are also shown, where the black diamonds correspond to the centers of the subsets above and below the interface. In all the cases shown in this figure, \(n_{x2,inter}=10\) and \(n_{x2,cent}=11\). were observed also when \(n_{x2,cnt}\) was fixed at a moderate value (e.g., \(n_{x2,cnt}\) = 11), especially for the shear stress. A small value of \(n_{x2,inter}\) (e.g., \(n_{x2,inter}\) = 6) led to large gradients in the normal stresses near the interface, as well as to small discontinuities at the pixels located \(n_{x2}\) pixels above and below the interface (Figure 6a,b). A large value of \(n_{x2,inter}\) (e.g., \(n_{x2,inter}\) = 16) resulted in an artificial increase or decrease of stresses at localized regions around the interface compared with the domains above and below (Figure 6c,d). For example, the normal stress decreased locally at the interface at \(x_{1}\) = 370 pixels (Figure 6c), while the shear stress increased locally at \(x_{1}\) = 170 and 370 pixels (Figure 6d). Some issues are illustrated further in plots of the normal and shear stresses vs position along two lines perpendicular to the interface at \(x_{1}\) = 170 and 220 pixels (Figure 6e-h). The value of normal stress on the interface was similar for \(n_{x2,inter}\) \(\leq\) 14, but diverged for higher values, with a difference of about 1 MPa for \(n_{x2,inter}\) = 20. For \(n_{x2,inter}\) \(\leq\) 6, the TC enforcement resulted in a poor agreement between the stresses obtained by the polynomial and the original stresses also at the pixels closer to the center of the subset. The shear stress at the interface also diverged, with an increase of about 1 MPa for \(n_{x2,inter}\) = 16, at \(x_{1}\) = 170 pixels (Figure 6f). The effect of \(n_{x2,cnt}\) was generally smaller than that of \(n_{x2,inter}\). Full-field maps of stresses obtained with \(n_{x2,cnt}\) = 7 and \(n_{x2,inter}\) = 10 (Figure 7a,b), were similar to those in Figure 2c,d. However, large value of \(n_{x2,cnt}\) = 19 resulted in small discontinuities in normal stress at the pixels located \(n_{x2}\) pixels  
Figure 6: The effect of parameter \(n_{x2,inter}\) on the stress field. (**a–d**) Full-field maps of normal (left) and shear (right) stresses for \(n_{x2,inter}\) = 6 and 16. (**e–h**) Normal (left) and shear (right) stresses vs position along paths perpendicular to the interface at \(x_{1}\) = 170 and 220 pixels (grey lines in (**c**)) for different values of \(n_{x2,inter}\). The circles on the curves correspond to \(n_{x2,inter}\), while the filled diamonds correspond to \(n_{x2}\). The stresses calculated with the “fill boundary” algorithm of Vic-2D without the traction continuity algorithm are also shown, where the black diamonds correspond to the centers of the subsets above and below the interface. In all the cases shown in this figure \(n_{x1}\) = 7 and \(n_{x2,cnt}\) = 11.  
above and below the interface (Figure 7c,d). Both at \(x_{1}=170\) and 220 pixels there was a very small effect of \(n_{x2,cnt}\) on the normal stress at the interface (Figure 7e,g). However, for \(n_{x2,cnt}\geq 17\), the fit between the stresses obtained by the polynomial and the original stresses was poor also for the pixels closer to the center of the subset. Similarly to \(n_{x2,inter}\), the shear stress at the interface may significantly have differed for large values of \(n_{x2,cnt}\) (Figure 7f).