*2.3. Materials and Mechanical Properties*

This study focuses a non-commercial Zinc-Magnesium alloy (Zn1Mg—1 wt% Mg), atomized by Nanoval GmbH (Berlin, Germany). The elastic material properties used for the numerical and analytical studies are based on literature data [19,34–36]. Validation tests are done on additively manufactured Zn1Mg scaffolds. Furthermore, this study is based on a previous study using Mg-based (WE43) scaffolds [2]. Young's modulus and yield strength of Zn1Mg were reported by Yang et al. [19]. Young's modulus of Zn1Mg is documented to be *EZn*<sup>1</sup>*Mg* ≈ 19 GPa and yield strength *σy*,*Zn*1*Mg* ≈ 74 MPa. The mechanical properties for Zn1Mg have been extracted via tensile tests. Both the zinc content as well as the magnesium content will take part in the biochemical reaction process. Material properties for Zn(OH)2, Mg(OH)2, ZnCO3 and MgCO3 from degradation processes are not sufficiently documented in the literature, but can be approximated by extrapolating data i.e., from Ulutan et al. [34], who reported values for the Young's modulus of Mg(OH)2 of *EMg*(*OH*)<sup>2</sup> = 64 GPa, Ulian et al. [35] reporting throughout anisotropic behavior an *EMg*(*OH*)<sup>2</sup> ≈ 64–180 GPa, or Yao et al. [36] reporting the Young's modulus of MgCO3 to be *EMgCO*<sup>3</sup> ≈ 150–260 GPa. For Mg(PO)4 and the degradation products of Zn, insufficient data were found. Due to the poor data concerning material properties and proportions of the composite material, hypothetical Young's moduli were defined by multiples of the base materials Young's modulus, which is adequate for the analytical and numerical investigations concerning the general influence.

## *2.4. Analytical Model*

The metallic strut and the enclosing compound of degradation products can be modeled as a composite beam. Here, the metallic core is surrounded by a thin-walled mineral cross section, which is idealized to be perfectly round in the following, and is demonstrated in Figure 4. Afterwards, the axial and bending stiffness of a composite strut can be calculated by a summation of the individual layer stiffnesses. The resulting equivalent composite axial stiffness *EA* can be calculated as followed:

$$\overrightarrow{EA} = \sum E\_j A\_j = E\_s r\_s^2 \pi + E\_{\text{sub}} \left( 2r\_s t\_{\text{sub}} + t\_{\text{sub}}^2 \right) \pi \,\tag{3}$$

where *Es* is the base materials Young's modulus, *E*sub is the Young's modulus of the compound of degradation products in the substrate layer, *rs* is the inner radius of the substrate layer, or rather the base strut radius, and *t*sub is the thickness of the substrate layer. For the equivalent composite bending stiffness *E J* results:

$$\left| \overline{E} \right\rangle = \sum E\_j I\_j = E\_s \frac{\pi}{4} r\_s^4 + E\_{\text{sub}} \frac{\pi}{4} \left( \left( r\_s + t\_{\text{sub}} \right)^4 - r\_s^4 \right). \tag{4}$$

**Figure 4.** Cross section of the idealized corroded strut; in grey: base strut, in orange: compound of degradation/reaction products.
