## 3 Reference Numerical Modelling Approach
### Mechanical Interactions and CZM Properties  
The reliable mechanical performance of TTC numerical models is offered by an accurate calibration of material properties, but especially by the combination of multiple mechanical interactions between the involved load-bearing components (Figure 6).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & Elastic moduli & Longitudinal (screw axis) & MPa & 370 \\ \cline{3-5}
**Soft Layer** & \multirow{2}{*}{\begin{tabular}{c} Elastic moduli \\ (mean values) \\ \end{tabular} } & Tangential & MPa & 370 \\ \cline{3-5}  & & Shear & MPa & 720 \\ \cline{3-5}  & & Radial & MPa & 50 \\ \cline{3-5}  & & Maximum shear (MPa) & MPa & 5 \\ \cline{3-5}  & Failure & Damage evolution & - & Linear \\ \cline{3-5}  & & Failure displacement \(\delta_{\text{u}}\) (mm) & Mm & 4 \\ \hline \multirow{2}{*}{\
\begin{tabular}{c} **CZM Contact** \\ **Interaction** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} Resistance \\ (mean values) \\ \end{tabular} } & Longitudinal & MPa & 37.55 \\ \cline{3-5}  & Resistance & Transverse & MPa & 3.85 \\ \cline{3-5}  & & Shear & MPa & 3.85 \\ \cline{3-5}  & & Rolling shear & MPa & 3.5 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Input mechanical properties for the soft layer and for the CZM contact interaction (ABAQUS/Explicit).  
Figure 6: FE modelling TTC joints with inclined STSs under a standard PO setup. In evidence, the mechanical contact interactions for: (**a**) timber-to- timber, (**b**) base support and (**c,d**) STS details (hidden mesh pattern), with (**e**) traction-separation law.  
For the typical FE model in Figure 6a, tangential \"penalty\" and normal \"hard\" surface-to-surface behaviors are first defined for the timber surfaces (\(\mu_{\text{timber}}=0.5\)[28] the static friction coefficient). A second surface-to-surface contact interaction, see Figure 6b, is introduced between the bottom face of timber (lateral member) and the base steel support (\(\mu_{\text{base}}=0.2\)[28]). Finally, see Figure 6c,d, a double restraint is used in the region of the steel fasteners. Each screw is first rigidly connected with the surrounding soft layer via a distributed \"tie\" constraint, so that relative rotations and displacements among the interested surfaces could be avoided. The external surface of the soft layer and the timber elements are then interconnected by a surface-based CZM behaviour, that is conventionally defined in its basic features (linear elastic traction-separation model (Figure 6e), damage initiation criterion, damage evolution law). In this study, the \"default contact enforcement method\" of ABAQUS library is used for the definition of the interface stiffness parameters prior to damage onset. The \"Damage initiation\", in this regard, is set to coincide with timber failure, based on Tables 1 and 2. This limit condition is implemented in the form of a maximum nominal stress (MAXS) criterion:  
\[max\Bigg{\{}\frac{t_{n}}{t_{n}^{0}},\frac{t_{s}}{t_{s}^{0}},\frac{t_{t}}{t_{t}^ {0}}\Bigg{\}}=1 \tag{1}\]  
with \(t_{n}^{0}\), \(t_{s}^{0}\) and \(t_{t}^{0}\) representing the allowable nominal stress peaks corresponding to normal deformations (\(n\)) to the bonding interface or in the first (\(s\)) or second (\(t\)) shear directions (GL24h resistance values). For the examined PO setup, any kind of rate-dependent behaviour for the traction-separation elasticity law is disregarded in this study. The damage evolution is finally set as \"linear\", that is:  
\[t=(1-D)\overline{t} \tag{2}\]  
where \(D\) is a scalar damage variable (\(0\leq D\leq 1\)) that interrelates the contact stress value \(t\) (in any direction), compared to its value predicted by the elastic traction-separation behaviour for the separation without damage. A null residual CZM contact stiffness is thus achieved at the first attainment of an ultimate displacement equal to \(\delta_{\text{u}}=4\) mm (Table 2).