Spinodoid metamaterials
A new class of metamaterials
After a decade of periodic truss-, plate-, and shell-based architectures having dominated the design of metamaterials, we introduced the new class of spinodoid metamaterials. Inspired by natural self-assembly processes, spinodoid metamaterials are a close approximation of microstructures observed during spinodal phase separation in, e.g., nanoporous metal foams, microemulsions, and polymer blends.
Topology generation by in silico mimicking the interfacial topolgy during spinodal decomposition (Kumar et al., 2020)
Additively manufactured spinodoid topology
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.
Spinodoid metamaterials with seamless anisotropy (from left to right): isotropic, lamellar, columnar, and cubic topologies. (Kumar et al., 2020)
Inverse design enabled 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.
Currently, we are collaborating with experimentalists towards combining the ML-guided invere design with two-photon lithography to design and fabricate 3D porous scaffolds with prescribed elastic properties. (Coming soon!)
ML-driven inverse design for mimicking trabecular bone (Kumar et al., 2020)
ML-driven two-scale topology optimization for compliance minimization (Zheng et al., 2021)
Toplogy optimization for lightweight spinodoid structures
We presented a two-scale topology optimization framework for the design of macroscopic bodies with an optimized elastic response, which is achieved by means of a spatially-variant spinodoid architecture on the microscale. As a departure from classical FE2-type approaches, we replaced the costly microscale homogenization by a ML-based surrogate model (using deep neural networks). We designed porous structures for minimal compliance with structural features spanning several orders of magnitude in lengthscale.
Publications
S. Kumar, S. Tan, L. Zheng, D. M. Kochmann, Inverse-designed spinodoid metamaterials, npj Computational Materials, 6 (2020), 73. [code-topology] [code-ml] [data] (requires GIBBON: https://www.gibboncode.org/)
L. Zheng, S. Kumar, D. M. Kochmann, Data-driven topology optimization of spinodoid metamaterials with seamlessly tunable anisotropy, Computer Methods in Applied Mechanics and Engineering, 383 (2021), 113894.
TU Delft, Mekelweg 2, Delft 2628 CD, Netherlands
