An homogenized damage model for bio-inspired ceramic structures made by freezecasting

Freezecasting is considered one of the top candidates to fabricate highly structured porous ceramics for numerous applications including bone regeneration implants as well as structural materials. It consists in the unidirectional solidification of ceramic suspensions, thus forming complex microstructures made of ice crystals and ceramic layers, which are then freezedried to remove the ice, and sintered to strengthen the ceramic. It has been shown that the microstructure of the final scaffold can be precisely controlled by varying process parameters such as cooling rate, suspensions density, viscosity, etc. However, precise guidelines are still missing to materials scientists concerning optimal architectures with regards to each specific application. Here, we present our approach to quantitatively master the mechanics of freezecasting scaffolds, from elastic behavior, to onset of cracking and final rupture. Basically, we follow the recent work of Ladeveze & Lubineau for laminated composites. First, from extensive computations on cracked micro-cells, a computational bridge is built between the micro (here, the scaffolds walls and bridges, i.e. 10-100 microns) and macro (the specimen, 10 mm) scales. This bridge allows (i) to characterize the effect of damage on macroscopic stiffness, and (ii) to link macroscopic damage variables and more microscopic ones such as crack densities. Then, instead of using the equivalence between micro and macro energy release rates as in Ladeveze's work, we use the Weibull's theory of rupture probability to derive the damage variables and the mechanical load. At the end, the discrete and homogenized models, together with the computational bridge that link them, provide an extremely valuable insight into the mechanics of ceramic scaffolds made by freezecasting: in a single framework, we derive scaling laws for both stiffness and strength, which are key properties for numerous biomedical and structural applications. Moreover, augmented with a localization controller, the homogenized model will also be used to derive scaling laws for toughness, another property of first interest. These scaling laws will represent precious guidelines for materials scientists to optimize the freezecasting process, and build even stronger materials.