Elastostatics of star-polygon tile-based architectured planar lattices

Celal Soyarslan*, Andrew Gleadall, Jiongyi Yan, Hakan Argeso, Emrah Sozumert

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)
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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 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.

Original languageEnglish
Article number111580
Number of pages17
JournalMaterials and Design
Publication statusPublished - Feb 2023


  • 2D mechanical metamaterials
  • Architectured lattices
  • Auxeticity
  • Homogenization
  • Star-polygon tiling
  • UT-Gold-D


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