*3.2. Finite-Element Results*

#### 3.2.1. Single Strut Simulations

Figure 9 shows the results of the FE simulations of single struts under axial compression. For both the base strut and the corroded strut, the axial reaction force *RF*1 shows nearly equal values and the difference lies under 0.02%. In Figure 10 the comparison for the bending loaded struts is presented. In both cases the results of the beam model and the solid model are in good agreement. For the base struts, the difference regarding reaction force *RF* and reaction moment *RM* lies at around 1%. For the corroded struts, the difference is lower than 0.03%. Furthermore, especially in the case of the corroded strut, the calculation time can be massively decreased using a beam modeling approach.

**Figure 9.** Reaction force (RF) comparison of modeling approaches for base and corroded strut under axial compression; (**left**) beam elements, (**right**) solid elements.

**Figure 10.** Reaction force (RF) and reaction moment (RM ) comparison of modeling approaches for base and corroded strut under bending; (**left**) beam elements, (**right**) solid elements.

#### 3.2.2. Whole Scaffold Modeling

Figure 11 shows the results of the FE Scaffold parametric study. Shown is the resulting smeared Young's modulus *E* of the scaffold, which results from dividing the axial reaction forces by the projected cross section of the whole scaffold *A*, as a function of the base strut radius *rs* for different thicknesses of the substrate layer *tsub* and (a) a compound Young's modulus of the substrate layer of *Esub* = 19 GPa (equal to *EZn*<sup>1</sup>*Mg*), (b) *Esub* = 38 GPa, (c) *Esub* = 57 GPa and (d) *Esub* = 76 GPa. The stiffness grows exponentially as a function of the strut diameter and is clearly more pronounced the higher the Young's modulus of the compound of the substrate. A significant increase in the axial stiffness of the scaffolds can be observed from all hypothetical Young's moduli of the substrate. Table 2 sums the quantitative results for the respective Young's moduli. It can be seen that already for a base materials equivalent Young's modulus of the substrate, small substrate thicknesses of a few microns and small strut radii lead to an increase in stiffness of 22–85%. The effect increases significantly when considering higher layer thicknesses and higher stiffnesses of the substrate layer.


**Table 2.** Percentage increase of the smeared Young's modulus *E* for varying substrate Young's moduli *Esub* and layer thicknesses *tsub*.

**Figure 11.** Results of the FE simulations of corroded scaffolds for varying parameters.

#### *3.3. Confirmation by Physical Evaluation*

Figure 12 shows the results of the two tested scaffolds under axial compression in comparison to the FE result. The tests show reproducible behavior regarding the stiffness. The smeared Young's modulus of the scaffolds can be calculated in the linear region of the load-displacement curves by *E* = *Fh*/(*Au*), where *F* is the measured force in the machines load cell, *h* is the total height of the scaffold, *A* is the projected smeared cross section of the scaffold and *u* is the displacement associated with the measured force. From the tests, a Youngs's modulus of approximately *Etest* ≈ 1125 MPa can be determined, measured in the area between 600–800 N. From the FE model a Young's modulus of *EFE* = 1258 MPa can be extracted. Furthermore, the FE model shows that for loads smaller 800 N, nowhere the strutstresses have exceeded the yield point. The slight differences could be attributed to local deviations in the strut diameter of the AM scaffolds, as shown in Section 2.2 respectively

Figure 3. Furthermore, the modeling using beam elements neglects the accumulation of material in the nodes of the real scaffold. Furthermore, the used Young's modulus is based on literature data and it is well known that Young's moduli of AM materials tend to show slight differences (see also Section 1). Nevertheless, the tests show that the FE model based on beam elements provides sufficiently accurate results in terms of the resulting smeared axial stiffness and can be used for the parametric study.

**Figure 12.** Validation of FE model: Resulting load-displacement curve of two tested LPBF produced scaffolds and equivalent FE model.
