Multi-scale analysis and modeling of robocasted scaffolds mechanical properties
Résumé
Robocasting is considered one of the top candidates to fabricate highly structured porous ceramics for numerous applications including bone regeneration implants.
While the process-microstructure link is completely straightforward, precise relations between microstructure and mechanical properties, which are critical for most applications, remains to be elucidated.
Indeed, qualitative understanding of the physics underlying the response of robocasted scaffolds under mechanical loading has been established, but robust quantitative tools are still missing.
Here, we present a multi-scale theoretical and experimental analysis of the scaffolds mechanics, as well as associated numerical tools.
Even though we focus on hydroxyapatite inks, most of the study could be transposable to other inks.
The final aim is to quantitatively optimize their morphology with regards to fundamental properties such as stiffness or strength.
On the rod's scale (200-800 μm), three point bending tests were performed on single rods with different diameters.
On the scaffold's scale (5-20 mm), compression tests were performed on several samples.
Sanchez-Palencia homogenization and Weibull analysis of periodic representative volume elements were used to bridge those two scales.
In terms of stiffness, it is established that the Young modulus is an intrinsic property of the rods.
The measured modulus is quite scattered, from 2 GPa to 10 GPa, with a mean value of 5.5 GPa.
This rather classical observation validates the delicate experimental analysis on single rods.
It is also established that the link between rods and scaffolds stiffness can be achieved through numerical homogenization.
It is important to point out that once this bridge is validated, it can also be used in an inverse manner to derive rods stiffness from scaffolds data.
In terms of strength, we have observed a surprising yet highly interesting fact: Weibull moduli are not intrinsic, and depend on rods diameter.
Increasing the diameter, while changing the length to keep the same volume, increases the mean strength and decreases the dispersion.
It is most probably due to a process-induced change in defects distribution, and ongoing morphological analysis of rods sections will help us conclude on that.
Using these data to compute scaffold compressive strength distributions thanks to Weibull theory leads to encouraging yet not satisfactory enough predictions when compared to experimental data.
This is certainly due to the fact that the scaffolds do not actually break following the weakest link rule, and possibilities to extend our model will be discussed.
In conclusion, we present a multi-scale analysis of the mechanical properties of robocasted scaffolds, with powerful numerical tools for the quantitative optimization of the scaffolds microstructure, which will allow us to build tougher and stronger materials, e.g., for the repair of load-bearing bone defects.