title: Optimal fractal-like hierarchical honeycombs.
abstract: Hexagonal honeycomb structures are known for their high strength and low weight. We construct a new class of fractal-appearing cellular metamaterials by replacing each three-edge vertex of a base hexagonal network with a smaller hexagon and iterating this process. The mechanical properties of the structure after different orders of the iteration are optimized. We find that the optimal structure (with highest in-plane stiffness for a given weight ratio) is self-similar but requires higher order hierarchy as the density vanishes. These results offer insights into how incorporating hierarchy in the material structure can create low-density metamaterials with desired properties and function.
authors.affiliation: Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115, USA.
authors.forename: Ramin
authors.initials: R
authors.lastname: Oftadeh
authors.affiliation: Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115, USA.
authors.forename: Babak
authors.initials: B
authors.lastname: Haghpanah
authors.affiliation: Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, United Kingdom.
authors.forename: Dominic
authors.initials: D
authors.lastname: Vella
authors.affiliation: Laboratoire Reproduction et Développement des Plantes and Laboratoire Joliot-Curie, INRA, CNRS, ENS, Université de Lyon, 46 Allée d'Italie, F-69364 Lyon Cedex 07, France.
authors.forename: Arezki
authors.initials: A
authors.lastname: Boudaoud
authors.affiliation: Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115, USA.
authors.forename: Ashkan
authors.initials: A
authors.lastname: Vaziri