Spinodoid metamaterials

Spinodoid metamaterials offer several advantages over conventional metamaterials.

• Spinodoid metamaterials consist of smooth, non-intersecting, and bi-continuous surfaces that avoid points of stress concentration (unlike truss- and plate-based metamaterials) while also showing excellent scaling of stiffness and strength with respect to density (leveraging the benefits of doubly-curved surfaces that engage slender structures primarily in stretching rather than bending). 

• The non-periodicity and lack of symmetry in spinodoid topologies make them more resilient to fabrication-based symmetry-breaking defects – by contrast to periodic metamaterials whose sensitivity to defects deteriorates their mechanical properties. 

• Spinodoid topologies cover an extreme and seamless range of anisotropic (direction-dependent) mechanical properties, as demonstrated, e.g., by their tailorable anisotropic elastic moduli – creating materials that are stiff in some directions and soft in others.

Inverse-designed mechanics by machine learning

We showed that the spinodoid design space can be integrated with an efficient and robust machine learning (ML) technique for the inverse design of (meta-)materials, in particular, uniform and functionally-graded cellular mechanical metamaterials with tailored direction-dependent (anisotropic) stiffness and density. 

We explored the application of this inverse design framework toward synthetic bones and scaffolds. Specifically, the inverse design ML model accurately predicts topologies that match the target relative density and anisotropic elastic stiffness as well as bear geometric resemblance to the natural trabecular bone topologies and achieves this, remarkably, without prior information about bone during the learning stage. 

We further validated the ML-design framework using two-photon lithography and nanomechanical testing to design and fabricate 3D porous scaffolds with the prescribed elastic properties. These theory-informed experiments are in close agreement with ML-predicted shape and stiffness anisotropy, which opens a pathway for uncovering previously unattainable design space of hierarchical materials in a quantifiable and deterministic way, useful in multiple applications, i.e., bio-scaffolds, heat exchangers, and deployable structures.

Curvatures-by-design for bio-scaffolds and implants

In bio-scaffolds and implants, topological properties are just as crucial as mechanical properties for ensuring biocompatibility. For instance, the microstructural curvature of metamaterial-based scaffolds significantly influences spatiotemporal growth, differentiation, and migration of biological cells and tissues. But how can we design tunable curvature topologies that adapt to patient-specific and anatomical site-specific requirements?

We explored surface curvature as a design parameter in spinodoid metamaterials to create topologies with tailored curvature profiles. By integrating microstructural curvature into the energetics of spinodal decomposition and leveraging machine learning-based inverse design frameworks, we can generate diverse topologies with tubular, membranous, or particulate features. Our work demonstrated the successful inverse design of topologies that mimic the curvature profile of trabecular bone, specifically for applications in bio-scaffolds and implants.

Additionally, we bridged curvature and mechanics, showing how topological curvature can be engineered to promote mechanically advantageous stretching-dominated deformation, as opposed to bending-dominated deformation.