## 6 Evaluated Parameters  
### Parameter 1: Element Types  
Different element types have been developed for FEM, such as trusses, beams, planes, and solids, among others. As mentioned before, plane stress elements were chosen for the 2D FEM models. These elements can be either linear or quadratic, with full or reduced integration (see Figure 9). Quadratic elements can follow complex curves, but the computational cost is much higher than for linear elements. A similar situation occurs for full and reduced integration points, as more points require more computational effort. A more detailed discussion of the advantages and disadvantages of each formulation is provided in [20].  
Two numerical effects should be highlighted for plane (and solid) elements: shear locking and the hourglass effect. Quadrilateral elements with linear interpolation (four nodes in plane stress) and full integration (Figure 9a) are affected by shear locking. This spurious behaviour occurs when, under bending, the elements become stiffer than they should be since the linear shape function induces an unneal shear at the integration points [20] (Figure 10a). Increasing the number of elements may limit shear locking but not totally avoid it. On the other hand, quadrilateral elements (plane or solid) with linear interpolation and reduced integration have a single integration point located at the centroid (Figure 9b). The advantage of these elements is that shear locking disappears and the computational time reduces [89]. However, they exhibit a spurious behaviour, called the hourglass effect, that can easily propagate in coarse meshes, producing meaningless results. When the element is subjected to certain deformations, the neutral axes remain unchanged in length and rotation, so any variation in the stress-strain field is calculated at the integration point [20] (Figure 10b). As a result, the element is free to distort because no strain energy is produced to counteract such deformation. The hourglass effect can be minimized by mesh refinement, for example, using at least four elements through the thickness when structures carry bending loads [89]. Additionally, the software can introduce artificial stiffness to avoid large deformations. It is worth noting that shear locking and the hourglass effect occur in both explicit and implicit methods. Finally, quadratic elements, whether fully or reduced integrated (Figure 9c,d), do not exhibit these issues. However, their high computational cost becomes problematic when used for large models.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dilation Angle \(\mathbf{\psi}\)** & **Eccentricity \(\mathbf{e}\)** & \(\sigma_{\mathbf{\mathrm{tol}}}\)/\(\sigma_{\mathbf{\mathrm{c0}}}\) & \(K\) \\ \hline \(10^{\circ}\) & \(0.1\) & \(1.16\) & \(2/3\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Values for the yield surface and flow rule.  
Figure 10: Spurious behaviours (adapted from [20]): (**a**) shear locking; (**b**) hourglass effect.  
Figure 9: Plane elements [89]: linear with (**a**) full integration and (**b**) reduced integration; quadratic with (e) full integration and (**d**) reduced integration.  
For the implicit solution, the four types of elements were selected: linear (full and reduced integration) and quadratic (full and reduced integration). Regarding the explicit solution, Abaqus only provides linear elements with reduced integration.