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Research Papers

Compliant Cellular Materials With Elliptical Holes for Extremely High Positive and Negative Poisson's Ratios

[+] Author and Article Information
Jaehong Lee

School of Aerospace and
Mechanical Engineering,
Korea Aerospace University,
Goyang, Gyeonggi 412-791, South Korea
e-mail: cjb8944@gmail.com

Kwangwon Kim

School of Aerospace and
Mechanical Engineering,
Korea Aerospace University,
Goyang, Gyeonggi 412-791, South Korea
e-mail: kwangwon84@gmail.com

Jaehyung Ju

Mem. ASME
Department of Mechanical and
Energy Engineering,
University of North Texas,
Denton, TX 76203-5017
e-mail: jaehyung.ju@unt.edu

Doo-Man Kim

Mem. ASME
School of Aerospace and
Mechanical Engineering,
Korea Aerospace University,
Goyang, Gyeonggi 412-791, South Korea
e-mail: dmkim@kau.ac.kr

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received March 27, 2014; final manuscript received August 12, 2014; published online September 5, 2014. Assoc. Editor: Hareesh Tippur.

J. Eng. Mater. Technol 137(1), 011001 (Sep 05, 2014) (17 pages) Paper No: MATS-14-1072; doi: 10.1115/1.4028317 History: Received March 27, 2014; Revised August 12, 2014

Cellular materials' two important properties—structure and mechanism—can be selectively used for materials design; in particular, they are used to determine the modulus and yield strain. The objective of this study is to gain a better understanding of these two properties and to explore the synthesis of compliant cellular materials (CCMs) with compliant porous structures (CPSs) generated from modified hexagonal honeycombs. An in-plane constitutive CCM model with CPSs of elliptical holes is constructed using the strain energy method, which uses the deformation of hinges around holes and the rotation of links. A finite element (FE) based simulation is conducted to validate the analytical model. The moduli and yield strains of the CCMs with an aluminum alloy are about 4.42 GPa and 0.57% in one direction and about 2.14 MPa and 20.9% in the other direction. CCMs have extremely high positive and negative Poisson's ratios (NPRs) (νxy* ∼ ±40) due to the large rotation of the link member in the transverse direction caused by an input displacement in the longitudinal direction. A parametric study of CCMs with varying flexure hinge geometries using different porous shapes shows that the hinge shape can control the yield strength and strain but does not affect Poisson's ratio which is mainly influenced by rotation of the link members. The synthesized CPSs can also be used to design a new CCM with a Poisson's ratio of zero using a puzzle-piece CPS assembly. This paper demonstrates that compliant mesostructures can be used for next generation materials design in tailoring mechanical properties such as moduli, strength, strain, and Poisson's ratios.

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References

Figures

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Fig. 1

Concept of CCM with CPS

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Fig. 2

Deformation mechanism of CPS-I

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Fig. 3

Deformation mechanism of CPS-II

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Fig. 4

Geometric parameters of CPSs; (a) CPS-I was designed based on the regular hexagonal honeycomb link mechanism, (b) CPS-II was designed based on the re-entrant hexagonal honeycomb link mechanism, (c) cross-sectional profile of the half flexure hinge of an elliptical hole, and (d) free body diagram at the flexure hinge

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Fig. 5

Spring model of flexure hinges and a link (a) and (b), and its free body diagram (c)

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Fig. 6

Boundary conditions on CPSs for FE simulations

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Fig. 7

Stress (von Mises) distribution of CCM-I and CPS-I for a uni-axial loading in the x-direction

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Fig. 8

Stress (von Mises) distribution of CCM-II and CPS-II for the uni-axial loading in the x-direction

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Fig. 9

Effective stress–strain curves (a) and Poisson's ratio, νxy* (b) of CCMs for uni-axial loading in the x-direction

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Fig. 10

Stress (von Mises) distribution of CCM-I and CPS-I for a uni-axial loading in the y-direction

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Fig. 11

Stress (von Mises) distribution of CCM-II and CPS-II for a uni-axial loading in the y-direction

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Fig. 12

Effective stress–strain curves (a) and Poisson's ratios, νyx* (b) of CCMs for uni-axial loading in the y-direction

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Fig. 13

Flexure hinges with varying elliptical hole geometries

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Fig. 14

Effective stress–strain curves (a) and Poisson's ratios, νxy* (b) of CCM-Is for uni-axial loading in the x-direction

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Fig. 15

Effective stress–strain curves (a) and Poisson's ratios, νxy* (b) of CCM-IIs for uni-axial loading in the x-direction

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Fig. 16

Effective stress–strain curves (a) and Poisson's ratios, νyx* (b) of CCM-I for uni-axial loading in the y-direction

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Fig. 17

Effective stress–strain curves (a) and Poisson's ratios, νyx* (b) of CCM-II for uni-axial loading in the y-direction

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Fig. 18

Synthesis of CPS-III with a zero-Poisson's ratio

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Fig. 19

Poisson's ratio and effective stress–strain curve of CCM-III

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Fig. 20

Flowchart to calculate the effective properties of CCMs

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