heterogeneously architected structures; lattice structures; deterministic assembly; elastic properties; interface

Weizhu Yang, Qingchang Liu, Zongzhan Gao, Zhufeng Yue, and Baoxing Xu
Play with your matchsticks for assembling extremely soft or hard 2D structures.
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 welldefined*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 ondemand*Young’s modulus and geometric features. This study offers*a theoretical foundation toward future architected structures*by design with unprecedented properties and functions.