Plate-nanolattices at the theoretical limit of stiffness and strength

Cameron Crook,Cristine Santos De Oliveira,Juliana Martins De Souza E Silva,Jonathan B Berger,Jens Bauer,Lorenzo Valdevit,Anna Guell Izard

doi:10.1038/s41467-020-15434-2

Abstract

Though beam-based lattices have dominated mechanical metamaterials for the past two decades, low structural efficiency limits their performance to fractions of the Hashin-Shtrikman and Suquet upper bounds, i.e. the theoretical stiffness and strength limits of any isotropic cellular topology, respectively. While plate-based designs are predicted to reach the upper bounds, experimental verification has remained elusive due to significant manufacturing challenges. Here, we present a new class of nanolattices, constructed from closed-cell plate-architectures. Carbon plate-nanolattices are fabricated via two-photon lithography and pyrolysis and shown to reach the Hashin-Shtrikman and Suquet upper bounds, via in situ mechanical compression, nano-computed tomography and micro-Raman spectroscopy. Demonstrating specific strengths surpassing those of bulk diamond and average performance improvements up to 639% over the best beam-nanolattices, this study provides detailed experimental evidence of plate architectures as a superior mechanical metamaterial topology.

Highlights

Though beam-based lattices have dominated mechanical metamaterials for the past two decades, low structural efficiency limits their performance to fractions of the HashinShtrikman and Suquet upper bounds, i.e. the theoretical stiffness and strength limits of any isotropic cellular topology, respectively
The three-dimensional intersections of plates prevent the formation of kinematic mechanisms, ensuring the plate-lattice topology is always stretching-dominated, which may not be true in a corresponding beam topology
Our study clearly shows a tremendous performance improvement to be gained from plate-based topologies compared to state-of-theart beam-based designs and provides crucial fabrication insights to enable additive manufacturing of high-performance plate-lattice materials

Summary

Introduction

Though beam-based lattices have dominated mechanical metamaterials for the past two decades, low structural efficiency limits their performance to fractions of the HashinShtrikman and Suquet upper bounds, i.e. the theoretical stiffness and strength limits of any isotropic cellular topology, respectively. Closed-cell architectures, consisting of plates arranged corresponding to the closest packed planes of crystal structures, have computationally been predicted to reach the HS and Suquet upper bounds[18,21,22]; their manufacturing complexity has far prevented any experimental validation The simplest such topology is the cubic+octet (CO) plate-lattice, known as the simple cubic + face centered cubic configuration (SC-FCC), characterized by a cubic-plate unit cell embedded in an octetplate unit cell. While the above challenges are a general obstacle to the application of plate-lattices, they especially complicate synthesis approaches at the nanoscale where size effects are exploitable

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Conclusion