Elastostatics of star-polygon tile-based architectured planar lattices

TL;DR

This paper explores star-polygon tile-based planar lattices, revealing their wide range of elastic properties, deformation mechanisms, and isotropy, supported by numerical, experimental, and additive manufacturing methods.

Contribution

It introduces a comprehensive framework for star-polygon lattices, demonstrating extensive tunability of mechanical properties and unifying various known lattice topologies under one family.

Findings

Over 250-fold range in elastic modulus achieved.

Good agreement between numerical predictions and experimental results.

Most sub-families exhibit in-plane elastic isotropy.

Abstract

A panoptic view of architectured planar lattices based on star-polygon tilings was developed. Four star-polygon-based lattice sub-families, formed of systematically arranged triangles, squares, or hexagons, were investigated numerically and experimentally. Finite-element-based homogenization allowed computation of Poisson's ratio, elastic modulus, shear modulus, and planar bulk modulus. A comprehensive understanding of the range of properties and micromechanical deformation mechanisms was developed. Adjusting the star-polygon angle achieved an over 250-fold range in elastic modulus, over a 10-fold range in density, and a range of $-0.919$ to $+0.988$ for Poisson's ratio. Additively manufactured lattices, achieved by novel printing strategies, showed good agreement in properties. Parametric additive manufacturing procedures for all lattices are available on \url{www.fullcontrol.xyz/#/models/1d3528}. Three of the four sub-families exhibited in-plane elastic isotropy. One showed high stiffness with auxeticity at low density and a primarily axial deformation mode as opposed to bending deformation for the other three lattices. The range of achievable properties, demonstrated with property maps, proves the extension of the conventional material-property space. Lattice metamaterials with Triangle-Triangle, Kagome, Hexagonal, Square, Truncated Archimedean, Triangular, and Truncated Hexagonal topologies have been studied in the literature individually. Here, it is shown that these structures belong to the presented overarching lattice family.