Edited by John A. Rogers, Northwestern University, Evanston, IL, and approved June 26, 2018 (received for review April 19, 2018)
The bottom-up assembly of deterministic structures by lattice cell structures for surpassing properties of individual components or their sums by orders of magnitude is of critical importance in materials by design. Here, we present a theoretical strategy in the search and design of heterogeneously architected 2D structures (HASs) by assembling arbitrarily shaped basic lattice structures and demonstrate that an extremely broad range of mechanical properties can be achieved. This strategy allows designing HASs through interface properties of close relevance to assembly patterns and bonding connections between basic lattice structures. Studies using extensive numerical experiments validate the robust, reliable, and lucrative strategy of searching and designing HASs and offer quantitative guidance in the discovery of emerging 2D superstructures.
Architected 2D structures are of growing interest due to their unique mechanical and physical properties for applications in stretchable electronics, controllable phononic/photonic modulators, and switchable optical/electrical devices; however, the underpinning theory of understanding their elastic properties and enabling principles in search of emerging structures with well-defined arrangements and/or bonding connections of assembled elements has yet to be established. Here, we present two theoretical frameworks in mechanics—strain energy-based theory and displacement continuity-based theory—to predict the elastic properties of 2D structures and demonstrate their application in a search for novel architected 2D structures that are composed of heterogeneously arranged, arbitrarily shaped lattice cell structures with regulatory adjacent bonding connections of cells, referred to as heterogeneously architected 2D structures (HASs). By patterning lattice cell structures and tailoring their connections, the elastic properties of HASs can span a very broad range from nearly zero to beyond those of individual lattice cells by orders of magnitude. Interface indices that represent both the pattern arrangements of basic lattice cells and local bonding disconnections in HASs are also proposed and incorporated to intelligently design HASs with on-demand Young’s modulus and geometric features. This study offers a theoretical foundation toward future architected structures by design with unprecedented properties and functions.
Author contributions: B.X. designed research; W.Y. and B.X. performed research; W.Y., Q.L., Z.G., Z.Y., and B.X. analyzed data; and W.Y., Q.L., Z.G., Z.Y., and B.X. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1806769115/-/DCSupplemental.
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