Bending of kerf chiral fractal lattice metamaterials

Wenjiao Zhang; Robin M Neville; Dayi Zhang; Jie Yuan; Roderic Lakes; Fabrizio  Scarpa

doi:10.1016/j.compstruct.2023.117068

Bending of kerf chiral fractal lattice metamaterials

Wenjiao Zhang, Robin M Neville, Dayi Zhang, Jie Yuan, Roderic Lakes, Fabrizio Scarpa^*

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

16 Citations (Scopus)

Abstract

We describe the out-of-plane bending of kerf chiral fractal lattices metamaterials by using a combination of theoretical models, full-scale finite elements and experimental tests representing the flexural behaviour of metamaterial beams under three-point bending. Good agreement is observed between the three sets of results. Parametric analyses show a linear log-log relation between bending modulus and aspect ratios of the unit cells, which are indicative of the fractal nature of the metamaterial. The ratio between the bending and in-plane tensile moduli of these chiral fractal metamaterials ranges between ~ 5 and ~ 34 and is linearly proportional to the square of the ratio between length and width of the ribs of the chiral unit cells at different fractal orders. These properties suggest that the class of chiral fractal lattice metamaterials offer metacompliance properties between the flexural and in-plane stretching behaviours, which can be tailored by the adoption of the fractal scales.

Original language	English
Article number	117068
Journal	Composite Structures
Volume	318
Early online date	30 Apr 2023
DOIs	https://doi.org/10.1016/j.compstruct.2023.117068
Publication status	Published - 15 Aug 2023

Bibliographical note

Funding Information:
WZ and DZ would like to thank Chinese Scholarship Council (CSC) for the funding of their research work through the University of Bristol. RN also acknowledges the support from UK Engineering and Physical Sciences Research Council (EPSRC EP/N509619/1) for his Postdoctoral Fellowship. JY would like to acknowledge the support of the Small Research Grant from Royal Society of Edinburgh (RSE/1754). FS would like to thank the European Commission for the computational and testing logistics provided through the H2020-1.3.1.675441 MSC ITN VIPER and ERC-AdG-H2020 101020715 NEUROMETA projects. The raw/processed data required to reproduce these findings cannot be shared at this time due to technical or time limitations.

Funding Information:
WZ and DZ would like to thank Chinese Scholarship Council (CSC) for the funding of their research work through the University of Bristol. RN also acknowledges the support from UK Engineering and Physical Sciences Research Council (EPSRC EP/N509619/1) for his Postdoctoral Fellowship. JY would like to acknowledge the support of the Small Research Grant from Royal Society of Edinburgh (RSE/1754). FS would like to thank the European Commission for the computational and testing logistics provided through the H2020-1.3.1.675441 MSC ITN VIPER and ERC-AdG-H2020 101020715 NEUROMETA projects.

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© 2023 The Author(s)

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title = "Bending of kerf chiral fractal lattice metamaterials",

abstract = "We describe the out-of-plane bending of kerf chiral fractal lattices metamaterials by using a combination of theoretical models, full-scale finite elements and experimental tests representing the flexural behaviour of metamaterial beams under three-point bending. Good agreement is observed between the three sets of results. Parametric analyses show a linear log-log relation between bending modulus and aspect ratios of the unit cells, which are indicative of the fractal nature of the metamaterial. The ratio between the bending and in-plane tensile moduli of these chiral fractal metamaterials ranges between ~ 5 and ~ 34 and is linearly proportional to the square of the ratio between length and width of the ribs of the chiral unit cells at different fractal orders. These properties suggest that the class of chiral fractal lattice metamaterials offer metacompliance properties between the flexural and in-plane stretching behaviours, which can be tailored by the adoption of the fractal scales.",

author = "Wenjiao Zhang and Neville, {Robin M} and Dayi Zhang and Jie Yuan and Roderic Lakes and Fabrizio Scarpa",

note = "Funding Information: WZ and DZ would like to thank Chinese Scholarship Council (CSC) for the funding of their research work through the University of Bristol. RN also acknowledges the support from UK Engineering and Physical Sciences Research Council (EPSRC EP/N509619/1) for his Postdoctoral Fellowship. JY would like to acknowledge the support of the Small Research Grant from Royal Society of Edinburgh (RSE/1754). FS would like to thank the European Commission for the computational and testing logistics provided through the H2020-1.3.1.675441 MSC ITN VIPER and ERC-AdG-H2020 101020715 NEUROMETA projects. The raw/processed data required to reproduce these findings cannot be shared at this time due to technical or time limitations. Funding Information: WZ and DZ would like to thank Chinese Scholarship Council (CSC) for the funding of their research work through the University of Bristol. RN also acknowledges the support from UK Engineering and Physical Sciences Research Council (EPSRC EP/N509619/1) for his Postdoctoral Fellowship. JY would like to acknowledge the support of the Small Research Grant from Royal Society of Edinburgh (RSE/1754). FS would like to thank the European Commission for the computational and testing logistics provided through the H2020-1.3.1.675441 MSC ITN VIPER and ERC-AdG-H2020 101020715 NEUROMETA projects. Publisher Copyright: {\textcopyright} 2023 The Author(s)",

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AU - Zhang, Wenjiao

AU - Neville, Robin M

AU - Zhang, Dayi

AU - Yuan, Jie

AU - Lakes, Roderic

AU - Scarpa, Fabrizio

N1 - Funding Information: WZ and DZ would like to thank Chinese Scholarship Council (CSC) for the funding of their research work through the University of Bristol. RN also acknowledges the support from UK Engineering and Physical Sciences Research Council (EPSRC EP/N509619/1) for his Postdoctoral Fellowship. JY would like to acknowledge the support of the Small Research Grant from Royal Society of Edinburgh (RSE/1754). FS would like to thank the European Commission for the computational and testing logistics provided through the H2020-1.3.1.675441 MSC ITN VIPER and ERC-AdG-H2020 101020715 NEUROMETA projects. The raw/processed data required to reproduce these findings cannot be shared at this time due to technical or time limitations. Funding Information: WZ and DZ would like to thank Chinese Scholarship Council (CSC) for the funding of their research work through the University of Bristol. RN also acknowledges the support from UK Engineering and Physical Sciences Research Council (EPSRC EP/N509619/1) for his Postdoctoral Fellowship. JY would like to acknowledge the support of the Small Research Grant from Royal Society of Edinburgh (RSE/1754). FS would like to thank the European Commission for the computational and testing logistics provided through the H2020-1.3.1.675441 MSC ITN VIPER and ERC-AdG-H2020 101020715 NEUROMETA projects. Publisher Copyright: © 2023 The Author(s)

PY - 2023/8/15

Y1 - 2023/8/15

N2 - We describe the out-of-plane bending of kerf chiral fractal lattices metamaterials by using a combination of theoretical models, full-scale finite elements and experimental tests representing the flexural behaviour of metamaterial beams under three-point bending. Good agreement is observed between the three sets of results. Parametric analyses show a linear log-log relation between bending modulus and aspect ratios of the unit cells, which are indicative of the fractal nature of the metamaterial. The ratio between the bending and in-plane tensile moduli of these chiral fractal metamaterials ranges between ~ 5 and ~ 34 and is linearly proportional to the square of the ratio between length and width of the ribs of the chiral unit cells at different fractal orders. These properties suggest that the class of chiral fractal lattice metamaterials offer metacompliance properties between the flexural and in-plane stretching behaviours, which can be tailored by the adoption of the fractal scales.

AB - We describe the out-of-plane bending of kerf chiral fractal lattices metamaterials by using a combination of theoretical models, full-scale finite elements and experimental tests representing the flexural behaviour of metamaterial beams under three-point bending. Good agreement is observed between the three sets of results. Parametric analyses show a linear log-log relation between bending modulus and aspect ratios of the unit cells, which are indicative of the fractal nature of the metamaterial. The ratio between the bending and in-plane tensile moduli of these chiral fractal metamaterials ranges between ~ 5 and ~ 34 and is linearly proportional to the square of the ratio between length and width of the ribs of the chiral unit cells at different fractal orders. These properties suggest that the class of chiral fractal lattice metamaterials offer metacompliance properties between the flexural and in-plane stretching behaviours, which can be tailored by the adoption of the fractal scales.

U2 - 10.1016/j.compstruct.2023.117068

DO - 10.1016/j.compstruct.2023.117068

M3 - Article (Academic Journal)

SN - 0263-8223

VL - 318

JO - Composite Structures

JF - Composite Structures

M1 - 117068

ER -

Bending of kerf chiral fractal lattice metamaterials

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