Theoretical search for heterogeneously architected 2D structures

Abstract

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.

Density scaling in the mechanics of a disordered mechanical meta-material

“…Random elastic networks are widely studied [36][37][38] , but there are still large gaps between theoretical investigations and practical purposes such as real solid materials. Mechanical meta-materials with increasing degree of disorder are just emerging [39][40][41][42][43] . Whether disorder is merely the price to pay for self-assembly or whether it provides some advantage is still an open issue.The structural behaviour of lattice based metamaterials, made up of beams with non-hinged nodes, is generally divided into two regimes: stretching-dominated and bending-dominated 44 .…”

Mechanical anisotropy of two-dimensional metamaterials: a computational study

“…Recent years have witnessed the explosive growth of research into metamaterials, rationally designed multiscale composite systems which exhibit material properties not found in most conventional materials, due to their potential for a broad range of applications. [1][2][3][4][5][6] The unique properties of these materials, e.g. negative Poisson's ratio, 5,7,8 superior mechanical performance [9][10][11] and structural reconguration, [12][13][14] are usually dominated by their structure, although the inuence of their composition cannot be neglected either.…”

“…Among candidates for constituents of metamaterials, two-dimensional materials with one-atom thickness have attracted signicant interest due to their unique physical and chemical properties. 1,2,7,[15][16][17][18][19][20][21][22][23][24][25][26] Lattice metamaterials made of two-dimensional materials such as graphene have attracted extensive research interest, indicating great potential in applications such as exible electronic devices, 5,[27][28][29][30] photonic and phononic devices, [31][32][33][34] and mechanically controllable thermal devices. 5,[35][36][37] However, the microstructure-property relationship and composition-property relationship of metamaterials made of two-dimensional materials remain an open question.…”

“…Previous research studies set up a solid foundation for future studies investigating the structure-property relationship for 2D lattice structures. 5,25,38,39 For 2D lattice structures with multiple cut patterns, several theoretical models have been proposed to predict the microstructure-property relationship, which could not be well explained through classical theory in composite materials. 5,25 Other studies focus on edge termination problems for 2D lattice structures made of 2D materials, which is a critical issue for mechanical performance and structural stability.…”

Thermal theory for heterogeneously architected structure: Fundamentals and application

“…Even so, heterogeneously architected structures have aroused less attention in thermotics than in mechanics (e.g., see Ref. [26] and references therein). This situation mainly results from the lack of enough fundamental thermal theories for handling heterogeneously architected structures.…”