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Research Papers

Multistable Cylindrical Mechanical Metastructures: Theoretical and Experimental Studies

[+] Author and Article Information
Jian Hua

State Key Laboratory of Mechanics and Control of Mechanical Structures,
Nanjing University of Aeronautics and Astronautics,
Nanjing 210016, China
e-mail: jianhua714@126.com

Hongshuai Lei

Beijing Key Laboratory of Lightweight Multi-Functional Composite Materials and Structures,
Beijing Institute of Technology,
Beijing 100081, China;
State Key Laboratory of Explosion Science and Technology,
Beijing Institute of Technology,
Beijing 100081, China
e-mail: leihongshuai@pku.edu.cn

Zhong Zhang

Beijing Key Laboratory of Lightweight Multi-Functional Composite Materials and Structures,
Beijing Institute of Technology,
Beijing 100081, China
e-mail: fyblv5@163.com

Cunfa Gao

State Key Laboratory of Mechanics and Control of Mechanical Structures,
Nanjing University of Aeronautics and Astronautics,
Nanjing 210016, China
e-mail: cfgao@nuaa.edu.cn

Daining Fang

Beijing Key Laboratory of Lightweight Multi-Functional Composite Materials and Structures,
Beijing Institute of Technology,
Beijing 100081, China;
State Key Laboratory of Explosion Science and Technology,
Beijing Institute of Technology,
Beijing 100081, China
e-mail: fangdn@pku.edu.cn

1Corresponding authors.

Contributed by the Applied Mechanics Division of ASME for publication in the Journal of Applied Mechanics. Manuscript received January 5, 2019; final manuscript received March 17, 2019; published online April 15, 2019. Assoc. Editor: Pedro Reis.

J. Appl. Mech 86(7), 071007 (Apr 15, 2019) (10 pages) Paper No: JAM-19-1008; doi: 10.1115/1.4043283 History: Received January 05, 2019; Accepted March 18, 2019

An innovative bistable energy-absorbing cylindrical shell structure composed of multiple unit cells is presented in this paper. The structural parameters of the single-layer cylindrical shell structure that produces bistable characteristics are expounded both analytically and numerically. The influence of the number of circumferential cells and the size parameters of the cell ligament on the structure’s macroscopic mechanical response was analyzed. A series of cylindrical shell structures with various size parameters were fabricated using a stereolithography apparatus (SLA). Uniaxial loading and unloading experiments were conducted to achieve force–displacement relationships. Deformation of the structural multistable phase transition response was discussed based on experimental and finite element simulation results. The results show that the proposed innovative single-layer cylindrical shell structure will stabilize at two different positions under certain parameters. The multilayer cylindrical shell exhibits different force–displacement response curves under loading and unloading, and these curves enclose a closed area. In addition, this structure can be cyclically loaded and unloaded, thanks to its good stability and reproducibility, making it attractive in applications requiring repetitive energy absorption.

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Figures

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Fig. 1

(a) A bistable planar curved beam and (b) two types of schematic force–displacement curves for this beam

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Fig. 2

Geometric configuration and parameters of a novel multistable cylindrical shell with multiple unit cells: (a) cylindrical shell, (b) and (c) unit cell

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Fig. 3

The boundary conditions of the spatial curved beam in a unit cell of the multistable cylindrical shell

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Fig. 4

Multilayer multistable cylindrical shells and tensile test samples fabricated with an SLA 3D printer

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Fig. 5

Experimental setup of the multistable cylindrical shell under uniaxial compression

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Fig. 6

Stress–strain curves of parent material obtained by tensile tests

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Fig. 7

Finite element model and boundary conditions of the multistable cylindrical shell

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Fig. 8

Comparison of the analytical and numerical compressive response of single-layer cylindrical shells (L = 60 mm, t = 1 mm, and b = 3 mm): (a) A = 4, (b) A = 6, (c) A = 8, and (d) A = 10

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Fig. 9

Comparison of the theoretical and simulated phase transition values when t = 1 mm: (a) Q = 6, b = 3 mm, and L = 60 mm for various A values; (b) A = 6, Q = 6, and L = 60 mm for various b values; (c) A = 6, Q = 6, and b = 3 mm for various L values; (d) Q = 6, b = 3 mm, and L = 120 mm for various maximum normalized force values, various A values, and a planar curved beam

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Fig. 10

Criterion for a unit cell to exhibit bistable behavior as a function of two selected geometric parameters

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Fig. 11

Numerically and experimentally obtained axial force–displacement relationships of cylinders with different layers: (a) two-layer, (b) four-layer, and (c) six-layer

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Fig. 12

Comparison of the experimental and simulated deformation behavior of a six-layer cylindrical structure

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