# Product Design Analysis with Regard to Recycling and Selected Mechanical Properties
## 2 Materials and Methods
### Finite Element Models  
FEM calculations were carried out using Midas NFX 2023 R1 software (MIDASoft, Inc., New York, NY, USA). The parts of the models were assigned the materials indicated in Section 2.1, the properties of which are summarised in Table 3.  
Hybrid Mesher was used to build the meshes of the individual models. To improve the quality of the contact connections between the parts to be connected, a mesh of different densities was used for the individual parts. However, in no case was the side length of the finite element greater than 7 mm. Mesh parameters for the adopted connection variants are shown in Table 4.  
As the subject of the research in this article was not a detailed analysis of the changes in bolt and rivet forces during connection preloading and in the operating condition, no fastener preload was introduced in the models. In addition, the exact value of the clamping stresses in riveted connections is usually unknown [64], and experimental tests would have to be performed to find it out [65]. However, it should be emphasised that the clamping stresses in rivets are not as significant as in the case of preloaded bolts. The clamping of the bolts was modelled by adding contact connections between the bolt heads and the top plate and between the nuts and the bottom plate to the models. Similarly, rivet clamping was modelled by adding contact connections between the respective rivet heads and plates (top and bottom) to the models.  
'General' contact elements were used between the top plate and the bottom plate, while 'Welded' contact elements were used between the other pairs of parts to be connected [66]. These other pairs of parts include the following ones: top plate--top base; bottom plate--bottom base; bolt head--top plate; nut--bottom plate; bolt--nut; rivet head--top plate; rivet head--bottom plate; and rivet shanks--connected plates.  
The following values of the 'General' contact layer parameters were adopted [67,68]:  
* Normal stiffness factor equal to 10;
* Tangential stiffness factor equal to 1;
* Coefficient of static friction equal to 0.14.  
Due to the use of 'Welded' contact elements, it was possible to prevent the parts from moving relative to each other in any direction [68].  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Variant** & **Number of Nodes** & **Number of Finite Elements** \\ \hline
1a & 32,837 & 47,225 \\
1b & 29,762 & 42,201 \\
1c & 26,312 & 36,494 \\
2a & 23,504 & 30,780 \\
2b & 21,590 & 27,776 \\
2c & 19,762 & 25,150 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Mesh parameters for the adopted connection variants.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Part Name** & **Material** & \begin{tabular}{c} **Elastic Modulus** \\ **[GPa]** \\ \end{tabular} & \
\begin{tabular}{c} **Poisson’s Ratio** \\ **[–]** \\ \end{tabular} &
\begin{tabular}{c} **Tensile Strength** \\ **[MPa]** \\ \end{tabular} \\ \hline Top plate & A356.0-T6 & 72 & 0.33 & 200 \\ Bottom plate & A992 & 200 & 0.3 & 450 \\ Top base & A356.0-T6 & 72 & 0.33 & 200 \\ Bottom base & A992 & 200 & 0.3 & 450 \\ Bolt & 440C & 200 & 0.28 & 758 \\ Nut & 440C & 200 & 0.28 & 758 \\ Rivet & 440C & 200 & 0.28 & 758 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Material properties of the connection models.  
The selected discrete models of the connection according to Variant 1a and Variant 1b are shown in Figure 7a and 7b, respectively. The figures also show how the models were restrained and loaded. In all cases, the models were restrained by taking all degrees of freedom from the underside of the bottom plate and loaded from the top with a uniform pressure \(p\) of 0.2 MPa applied in 2 steps, which for a pressure area of 156 cm\({}^{2}\) corresponds to a working load of 3.12 kN. The Nonlinear Static Analysis module with the geometric non-linearity option [66] was used to perform the calculations.