Inverse-designed spinodoid metamaterials

Siddhant Kumar,Li Zheng,Stephanie Tan,Dennis M Kochmann

doi:10.1038/s41524-020-0341-6

Abstract

After a decade of periodic truss-, plate-, and shell-based architectures having dominated the design of metamaterials, we introduce the non-periodic class of spinodoid topologies. Inspired by natural self-assembly processes, spinodoid metamaterials are a close approximation of microstructures observed during spinodal phase separation. Their theoretical parametrization is so intriguingly simple that one can bypass costly phase-field simulations and obtain a rich and seamlessly tunable property space. Counter-intuitively, breaking with the periodicity of classical metamaterials is the enabling factor to the large property space and the ability to introduce seamless functional grading. We introduce an efficient and robust machine learning technique for the inverse design of (meta-)materials which, when applied to spinodoid topologies, enables us to generate uniform and functionally graded cellular mechanical metamaterials with tailored direction-dependent (anisotropic) stiffness and density. We specifically present biomimetic artificial bone architectures that not only reproduce the properties of trabecular bone accurately but also even geometrically resemble natural bone.

Highlights

Tailoring the architecture of cellular materials — including random foams as well as deterministic truss, plate, and shell-based lattices — has produced a wide variety of metamaterials whose macroscale physical and mechanical properties can be controlled by a careful design at the microstructural level
Metamaterials based on smooth topologies — such as triply periodic minimal surfaces (TPMS) — address this shortcoming[19] by avoiding points of stress concentration while showing excellent scaling of stiffness and strength with respect to density[20,21,22]
Spinodal topologies — extensively studied in the 1960s–1990s — have found a revival in metamaterials[26,27,28,29]. They are naturally created by self-assembly processes such as spinodal decomposition during phase separation[30,31] in, e.g., nanoporous metal foams[32,33,34], microemulsions[35,36], and polymer blends[37,38]

Summary

Introduction

Tailoring the architecture of cellular materials — including random foams as well as deterministic truss-, plate-, and shell-based lattices — has produced a wide variety of metamaterials ( referred to as architected materials) whose macroscale physical and mechanical properties can be controlled by a careful design at the microstructural level. We focus on the anisotropic elasticity of spinodoid architectures (and demonstrate their potential for, e.g., spatially varying patient-specific bone replacements), our inverse design approach — inspired by similar problems in the nanophotonic and plasmonic community60–65 — is sufficiently general to apply, in principle, to any physical material properties and to any finite set of design parameters.

Results

Conclusion