**3. Reference Numerical Modelling Approach**

A key aspect of the full three dimensional (3D) solid models discussed in this paper is represented by the use of mechanical properties derived from [20,21]. Among others, a "soft layer" with CZM damage interactions is introduced at the interface between the steel STSs and the surrounding timber members. It was shown in [20,21] that the CZM damage modelling technique is particularly suitable for TTC joints with inclined STSs, where the region of fasteners can be sensitive to localized damage phenomena, with consequent relevant effects on the collected load-bearing responses. Compared to other modelling approaches, the CZM technique has well-known intrinsic advantages, since it does not need to pre-define potential cracks, or to introduce complex and computationally expensive adaptive mesh techniques, nor to define a very dense mesh pattern where cracks are expected.

## *3.1. Solving Strategy and Model Assembly*

The numerical simulations are carried out with the ABAQUS/Explicit computer software [18,19], in the form of displacement-controlled, dynamic analyses with quasi-static deformations. All the FE assemblies are subjected to a linearly increasing vertical displacement, on the top face of the central member. The imposed vertical displacement is set in 20 mm, for all the examined configurations. Force-slip characteristic curves, as well as stress distributions and damage mechanisms in the TTC joint components are then monitored throughout the numerical investigation, a set of fixed FE assumptions is repeated for all the TTC joints under a standard PO setup, with major variations represented by trivial geometrical details.

The major simplification regards some basic symmetry considerations, thus 1/4th or 1/2nd the nominal geometry of each TTC specimen is taken into account. 8-node three-dimensional (3D) solid elements, (C3D8R-type) stress-strain bricks with reduced integration from the ABAQUS library are used for all the joint components. The reference FE model of TTC joint includes also a rigid base support made of steel, to allocate the lateral timber member in a standard PO setup. A swept (advancing font) meshing technique is then used to optimize the computational cost of simulations. The average edge size is minimized in the region of the STSs (0.3 mm-to-0.5 mm), and then maximized for the steel rigid base and the lateral portions of timber elements (5 mm-to-8 mm). Figure 4 shows an example of S#1 joint (α = −15◦ ). Based on [20,21], major efforts are then spent for the description of STSs and their mechanical interaction with the surrounding timber elements (Figure 5).

To this aim, each screw consists of an equivalent, circular cross-section with uniform diameter (D<sup>2</sup> = 6.3 mm from Figure 3d) and total length L.

A "soft layer" representative of STSs threads and timber fibers is then interposed between each screw and the surrounding timber (D<sup>1</sup> = 8.1 mm from Figure 3d). α −

α − **Figure 4.** Reference FE numerical model for TTC joints with inclined STSs under a standard PO setup (S#1, α = −15◦ ).

−

α −

α −

**Figure 5.** Example of (**a**) typical FE assembly (1/4th the S#1 geometry, with = −−15◦ ) and (**b**) detail of the STS region (ABAQUS/Explicit, hidden mesh pattern). Reproduced from [21] with permission from Elsevier®, Copyright license number 4895820420991, August 2020.
