**4. Discussion**

We investigated the influence of degradation products on the elastic stiffness properties of biodegradable metallic scaffolds. For this, a hypothetical compound of degradation products was modeled as a thin-walled layer with a homogeneous cross section. The compound of degradation products consists for the most parts of hydroxides, phosphates and carbonates [29–32]. Since there is no sufficient database, yet, for the mechanical properties of the degradation products, hypothetical Young's moduli were defined using multiples of the Young's modulus of the base material, which was obtained from literature data [3,12,13,16–24]. By this, the influence of the degradation products on the elastic stiffness properties as a function of the layer thickness and Young's modulus could be investigated. This was done using analytical models and finite-element simulations for single struts, to show the direct influence of the layer of degradation products on the axial and bending stiffness, as well as for whole scaffold geometries, to show the superposed influence on the axial smeared Young's modulus of a specific scaffold geometry. Two modeling approaches were contrasted for the FE simulations, first a meshing strategy using a 3D volume mesh and second using beam elements. Both approaches show concurring results. For this reason, the beam model was used for a parametric study on whole lattice scaffold geometries, due to the enormous difference regarding the calculation time. To validate the FE model, scaffolds were produced via LPBF and compression tests on two scaffolds were done.

From the single strut investigations can be concluded that depending on the substrates Young's modulus and the ratio of strut radius to thickness of the substrate layer, significant increases of the composite axial and bending stiffness is expected. The effect intensifies, the smaller the base strut radius in the initial state is. This applies as well as for relatively low Young's moduli of the substrate layer as for very high Young's moduli. In comparable studies [2,14,15,25,26], mentioned in the introduction part, strut diameters of 300–400 μm were used for orthopaedic scaffolds. Even for low layer thicknesses (i.e., 10 μm) and low Young's moduli, for single struts with diameters in this range, depending on the thickness of the substrate layer and the composite module, an increase of more than 10% for the Young's modulus under axial compression and more than 40% in bending stiffness can be

expected, which is not to be confused with the Young's modulus in the bending load case. To validate the base FE model, physical test results were compared to an equivalent FE simulation, using beam elements for meshing. As presented in the results section, the beam modeling shows similar results, compared to a much more numerically expensive meshing strategy with solid elements. The compression tests on LPBF produced scaffolds show reproducible results and furthermore equivalent smeared Young's moduli in the FE model and physical tests. For this reason, a FE parametric study on the tested geometry was done by varying the substrate layer thickness and the Young's moduli of the compound of the degradation products in the substrate layer, to study the influence of the substrate layer on the smeared Young's modulus of complex scaffold geometries. Our results show that an enormous increase in stiffness can be expected even for complex geometries, which was also observed by Li et al. [2] for diamond lattice structures made from WE43. For the previously mentioned example of strut diameters of 300–400 μm, the investigations on the scaffolds show that a much stronger effect can be observed due to the superposition of the axial and bending stiffness increase. As presented in the results section, the increase of the smeared axial Young's modulus under compression can be quantified to approximately 10–40% for a layer thickness of 10 μm and varying Young's moduli. The effect intensifies to values of approximately 20–80%, if i.e., a layer thickness of 20 μm is assumed. From this can be followed that compared to the separated reflection of the influence of the substrate layer on axial and bending stiffness of single struts, the effect of a stiffness increase is clearly more pronounced in the case of scaffold geometries. This is mainly attributable to the combined loading in compression and bending of the struts, which both ultimately have a direct effect on the smeared Young's modulus of the scaffold. Nevertheless, the investigations on single struts give clear indications about the formation of the effect. Furthermore, the analytical expressions show the direct influence of the thickness and Young's modulus of the degradation products.

## **5. Conclusions**

In conclusion, our analytical and numerical modeling approach basically confirmed earlier assumptions by Li et al. [2] that the increase in stiffness of corrosion product layer-coated AM WE43 is indeed due to formation of a composite beam of base strut and substrate layer. As shown in this discussion, even for low thicknesses and Young's moduli of the degradation product layer, axial stiffness increases of more than 40% can be achieved. Even though the geometry of the scaffold is different at the investigations of Li et al., this study clearly shows the influence on the stiffness. Nevertheless, our results must be validated by further investigations on corroded single struts or equal, to validate the formation of an almost homogeneous layer of degradation products and to obtain more knowledge about the real composite Young's modulus, or rather the Young's modulus of the compound of degradation products.

**Author Contributions:** J.B. performed most of the analytical analyses, J.B. modeling, physical testing, and drafted the paper. J.B., M.V. and H.J. contributed to the design of the scaffold, while M.V. produced them H.J. initiated and supervised the study, including the analyses. J.H.S. and K.-U.S. contributed their extensive experience, gave advice regarding the content and the manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** Parts of this work were supported by the Federal Ministry of Education and Research (BMBF) and the Ministry of Culture and Science of the State of North Rhine-Westphalia (MKW) under the Excellence Strategy of the Federal Government and the Länder (OPSF597).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Acknowledgments:** The authors thank the BMBF for funding of the work.

**Conflicts of Interest:** The authors declare no conflict of interest.
