Research Papers

Thermomechanically Tunable Elastic Metamaterials With Compliant Porous Structures

[+] Author and Article Information
Hyeonu Heo

Department of Mechanical and
Energy Engineering,
University of North Texas,
Denton, TX 76207
e-mail: Hyeonu.Heo@unt.edu

Kwangwon Kim

School of Aerospace and
Mechanical Engineering,
Korea Aerospace University,
Goyang-si 10540, South Korea
e-mail: kwangwon84@gmail.com

Addis Tessema

Department of Mechanical Engineering,
University of South Carolina,
Columbia, SC 29208
e-mail: ATESSEMA@email.sc.edu

Addis Kidane

Department of Mechanical Engineering,
University of South Carolina,
Columbia, SC 29208
e-mail: kidanea@cec.sc.edu

Jaehyung Ju

UM-SJTU Joint Institute,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: jaehyung.ju@sjtu.edu.cn

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received May 13, 2017; final manuscript received September 16, 2017; published online October 27, 2017. Assoc. Editor: Toshio Nakamura.

J. Eng. Mater. Technol 140(2), 021004 (Oct 27, 2017) (15 pages) Paper No: MATS-17-1138; doi: 10.1115/1.4038029 History: Received May 13, 2017; Revised September 16, 2017

Adding programmable function to elastic metamaterials makes them versatile and intelligent. The objective of this study is to design and demonstrate thermomechanically tunable metamaterials with a compliant porous structure (CPS) and to analyze their thermomechanical behaviors. CPS, the unit cell of the metamaterial, is composed of rectangular holes, slits, and bimaterial hinges. By decomposing kinematic rotation of a linked arm and elastic deformation of a bimaterial hinge, a thermomechanical constitutive model of CPS is constructed, and the constitutive model is extended to a three-dimensional (3D) polyhedron structure for securing isotropic thermal properties. Temperature-dependent properties of base materials are implemented to the analytical model. The analytical model is verified with finite element (FE) based numerical simulations. A controllable range of temperature and strain is identified that is associated with a thermal deformation of the bimaterial hinge and contact on the slit surfaces of CPS. We also investigate the effect of geometry of CPS on the thermal expansion and effective stiffness of the metamaterial. The metamaterial with CPS has multiple transformation modes in response to temperature while keeping the same mechanical properties at room temperature, such as effective moduli and Poisson’s ratios. This work will pave the road toward the design of programmable metamaterials with both mechanically and thermally tunable capability, providing unique thermomechanical properties with a programmable function.

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Fig. 1

Geometry of CPS and deformation mechanisms: (a) geometry of CPS, (b) cubic lattice made of CPS, (c) rotational mechanism of the inclined link part, (d) the bimaterial flexure hinge, (e) free-body diagram of the inclined link, and (f) free-body-diagram of the flexure hinge

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Fig. 2

Dynamic mechanical analysis (DMA) test results of Procast and PLA samples: (a) temperature-dependent modulus and (b) tanδ

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Fig. 3

(a) Experimental setup thermal expansion measurement of samples and (b) CTE of Procast and PLA as a function of temperature

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Fig. 4

Constitutive relations and Poisson’s ratios of 2D CPS from the analytical modeling and FE simulations: stress–strain behaviors for a uniaxial loading in the x-direction (a) and the y-direction (b), Poisson’s ratios for a uniaxial loading in the x-direction (c) and the y-direction (d). CPS shows a bi-stiffness after internal contact of slit-surfaces for a compressive loading (a), resulting in an increase in stiffness and strength after contact, together with a sudden change of Poisson’s ratio (c).

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Fig. 5

Thermal behavior of CPS with bi-layer hinges: Combination of bi-layer hinges (a), thermal strains (b), and thermal expansion coefficients (c) of the 2D CPS

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Fig. 6

An experimental setup for measuring thermal expansion of CPS: (a) a sample of CPS with the bimaterial hinges at room temperature and (b) the CPS submerged in water at 50 °C

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Fig. 7

A cubic lattice structure built from 2D CPS with double-layered hinges: (a) unit cell (isometric view), (b) front view of the unit cell, (c) stacked model (isometric view), and (d) stacked model (front view) and the center regions of CPS that are tie-connected

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Fig. 8

Thermal behaviors of a cubic lattice made of 2D CPS: thermal strain (a) and CTE (b)

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Fig. 9

Relationship between the effective CTE (α*) of the cubic lattice with CPS and the difference in CTE, Δα (=αa-αb) of their component materials with the thickness (t)

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Fig. 10

Samples fabricated by combining a single-material based 3D printing with a puzzle-piece based assembly: (a) piecewise samples by 3D printing; PLA and Procast were independently manufactured with different fabrication techniques, e.g., fused deposition modeling (FDM) for PLA and Polyjet for Procast, followed by key based joining for the bimaterial hinge. Note that PLA piece is in yellow and Procast one is in blue in the online version; (b) Male and female locking joints are used for assembly of compliant porous structures; (c) a square assembly composed of four compliant porous structures; and (d) a cubic assembly made up of six squares (24 compliant porous structures).

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Fig. 11

The experiment with a 3D cubic lattice structure made up of CPS; (a) initial state, (b) submerged state at t∼3s, and (c) submerged state at t∼6 s; NTE effect in the circled area

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Fig. 12

Deflection of a bimaterial strip while uniformly heated

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Fig. 13

The deflection and angle at the free end of the double-layered hinge

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Fig. 14

Flowchart to calculate the effective properties of CPS with the bimaterial hinges



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