*3.3. 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).

**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.

 ቊ , ௦ ௦ , ௧ ௧ ቋ=1

For the typical FE model in Figure 6a, tangential "penalty" and normal "hard" surface-to-surface behaviors are first defined for the timber surfaces (µtimber = 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 (µbase = 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:

$$\max \left\{ \frac{t\_n}{t\_n^{0'}}, \frac{t\_s}{t\_s^{0'}}, \frac{t\_t}{t\_t^0} \right\} = 1 \tag{1}$$

with *t* 0 *n* , *t* 0 *<sup>s</sup>* and *t* 0 *t* 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:

$$t = (1 - D)\bar{t} \tag{2}$$

where *D* is a scalar damage variable (0 ≤ *D* ≤ 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 δ<sup>u</sup> = 4 mm (Table 2).

#### *3.4. Analysis of Force Contributions*

The derivation of relevant FE results is carried out on the basis of the collected numerical force-slip curves, for each one of the examined TTC configurations. More in detail, the attention of the post-processing stage is first focused on the shear force contributions that are sustained by the timber members and in the STSs. According to Figure 7, for an imposed vertical displacement, the total vertical reaction force *F* and the horizontal reaction force *H* at the base of each TTC joint are separately monitored. In the case of the vertical reaction *F*, moreover, the shear force terms sustained by the steel screws or at the timber-to-timber interface (by contact) are separately calculated, given that the overall load-bearing capacity of the TCC joint in the PO setup can be expressed as:

$$F = F\_{\text{screw}} + F\_{\text{timber}} \tag{3}$$

0 0 0

=௦௪ + ௧

= (1 − )̅

δ

≤ ≤

**Figure 7.** Monitored force contributions for the mechanical analysis and characterization of TTC joints with inclined STSs under a standard PO setup.

#### **4. Discussion of FE Results**

## *4.1. Force-Slip Curves*

α Generally, the FE modelling strategy herein presented proved to offer relatively good correlation with the selected literature data, both in quantitative and qualitative terms. For few configurations (especially for the TCC joints characterized by high α values), a major scatter was observed and justified by local damage phenomena that compromised the overall load-bearing performance of the FE assembled components.

Selected examples are shown in Figure 8 for S#1 specimens and different STS inclinations, while the corresponding test results are derived from [6].

α **Figure 8.** Force-slip curves of selected TTC joints with inclined STSs under a standard PO setup (ABAQUS/Explicit, S#1, α = var) and corresponding experimental results (data from [6]).

The typical PO analysis was thus stopped due to convergence issues, in the very late damaged stage. In most of the cases, see Figure 8, this ultimate collapse configuration was achieved for relatively small slip amplitudes (*s* < 10 mm), compared to the imposed displacement of 20 mm. For the FE

4 3 0.4 ௫

(ସ − ଵ)

α −

௦ =

predictions agreeing with Figure 8, the maximum resistance *Fmax* can be conventionally detected as the first condition between the attainment of the (a) actual maximum force or (b) a total force corresponding to a joint slip *s* = 15 mm (if any). The corresponding serviceability stiffness *Kser* is then given by [22,23]:

$$K\_{\rm ser} = \frac{0.4 \, F\_{\rm max}}{\frac{4}{3}(s\_{04} - s\_{01})} \tag{4}$$

with *s*<sup>04</sup> and *s*<sup>01</sup> the measured sliding amplitudes at the 40% and 10% part of the maximum resistance *Fmax*.
