Mechanics of Minimal Surface-based Architected Materials

M.-T. Hsieh


For decades, high strength and high fracture toughness have been among the most sought-after mechanical properties by scientists and engineers in the field of light-weight materials. One way to achieve such mechanical properties is by using an architected cellular material (a two-phase material where one phase is void space and the other phase is the constituent solid, with the volume fraction of the latter defining the relative density ρ ̅) with optimized unit cell topology. Hence, one can design a lighter and lighter cellular material with the same constituent solid by reducing ρ ̅ while striving to achieve the highest possible strength and fracture toughness. In addition, size effect (often leading to a ‘smaller is stronger’ behavior) can further improve mechanical properties if the constituent solid is a metal or a ceramic with nanoscale dimensional features. The ultimate material is hence an architected material with an optimal topology at the nanoscale. However, such materials are often not scalable by conventional additive manufacturing technologies for practical engineering applications. We propose that the spinodal cellular topology derived from spinodal decomposition of a solid (or liquid) solution could provide a possible solution, as such a process followed by material conversion techniques has been demonstrated to produce architected material samples with overall size in the centimeter range and the smallest feature size of the architecture ranging from a few hundred nanometers to tens of microns. Unlike topologically optimized architected materials (which are almost always periodic), spinodal-derived architected materials are intrinsically stochastic. Given the large body of knowledge that supports the structural benefit of periodic architectures, a fundamental question arises on the mechanical efficiency of these stochastic topologies. In this thesis, we first numerically investigate the stiffness and strength of architected materials with spinodal topologies, considering both spinodal cellular solids (when one spinodally decomposed phase represents the solid constituent) and spinodal cellular shells (where the solid constituent occupies the thickened interface between two spinodally decomposing phases). We show that spinodal cellular solids are generally inferior to state-of-the-art topologies, whereas spinodal cellular shells are extremely stiff, strong, and imperfection-insensitive, features attributed to their minimal surface characteristics. Inspired by the excellent mechanical efficiency and scalability of spinodal shell topology, and the possibility to design spinodal shell architected materials with extremely large specific surface area (the smaller the unit cell size, the larger the surface area per unit volume), we numerically explore the potential benefits of these architected materials as porous long bone bio-implants, and compare them with more established periodic truss and minimal surface-based designs. By using mechanical and bio-mechanical performance indices, we suggest that minimal surface-based topologies are in general more suitable for bone implants than beam-based topologies. Furthermore, we show that spinodal shells have the potential to evoke more bone growth via periodic application of shear stresses to the surrounding tissues. When coupled with the intrinsic scalability of spinodal shell-based architected materials, which allows fabrication of biologically relevant implants with pore sizes at the micron-millimeter range (hence promoting large tissue/implant contact), these results suggest a strong potential as long bone implant materials. Although micro/nano-architected materials can be designed with exceptional specific strength, their fracture toughness (an essential engineering properties for structural materials) is typically very low. While compressive strength and stiffness are relatively easy properties to model and experimentally measure in architected materials, extraction of fracture toughness (whether from numerical or experimental approaches) is much mor challenging. In the final chapter of this thesis, we develop a versatile numerical approach to calculate the fracture toughness/R-curve of a cellular material. The approach is based on Finite Elements Analysis of the J-integral on a single-edge-notch-bend specimen, with a local maximum strain-based damage model. This approach is applied to 2D isotropic lattices. We show that the initial fracture toughness calculated from our approach agrees well with the results obtained from other methods. In addition, we show that careful design of unit cell topology can result in values of the steady-state fracture toughness that match or even exceed the initial fracture toughness of the constituent material itself. In the future, we plan to apply this approach to investigate the fracture toughness and R-curve of spinodal shells-based architected materials, with the overarching goal of identifying design strategies to optimize this essential property.