4. Analytical developments

The analytical formulation of clinch shear strength is the final stage of the research. The theoretical model is based on the following assumptions:

• the clinch is subjected to pure shear, with no other parasitic phenomena;

• Ruin occurs in the part of the clinch formed by the upper sheet in the section defined by h _cr (figure 12 );

• the part of the clinch formed by the bottom sheet is considered totally rigid.

These assumptions were validated by numerical simulations.

Based on these assumptions, an analytical shear strength model can be established: $R_{\text{c}}=\text{π}{t}_{\text{cr}}\left(t_{\text{cr}}+d\right)\frac{T_{\text{u}}}{\sqrt{3}}$