Elastostatics of star-polygon tile-based architectured planar lattices
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 to 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.
Cite
@article{arxiv.2209.09899,
title = {Elastostatics of star-polygon tile-based architectured planar lattices},
author = {Celal Soyarslan and Andrew Gleadall and Jiongyi Yan and Hakan Argeso and Emrah Sozumert},
journal= {arXiv preprint arXiv:2209.09899},
year = {2023}
}