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Research Papers

Numerical Evaluation of the Size-Dependent Elastic Properties of Cellular Polymers

[+] Author and Article Information
Gurudutt Chandrashekar

Department of Mechanical Engineering,
University of Wyoming,
1000 East University Avenue,
Laramie, WY 82071
e-mail: gchandra@uwyo.edu

Chung-Souk Han

Department of Mechanical Engineering,
University of Wyoming,
1000 East University Avenue,
Laramie, WY 82071
e-mail: chan1@uwyo.edu

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received December 5, 2016; final manuscript received June 2, 2017; published online August 9, 2017. Assoc. Editor: Vikas Tomar.

J. Eng. Mater. Technol 140(1), 011004 (Aug 09, 2017) (8 pages) Paper No: MATS-16-1354; doi: 10.1115/1.4037272 History: Received December 05, 2016; Revised June 02, 2017

Several experimental studies have revealed that the size-dependent deformation in polymers at nano- to micro-meter length scales is significantly associated with elastic deformation. Such size-dependent deformation in polymers is expected to affect the in-plane macroscopic elastic properties of cellular polymers with micrometer-sized cells. A finite element (FE) formulation of a higher-order elasticity theory is applied to evaluate the in-plane macroscopic elastic properties of different polymer cellular geometries by varying the cell size from the macroscopic to micron length scale. For a given relative density of the cellular solid, a reduction in the cell size from the macroscopic to micron length scale resulted in geometry-specific variations in the in-plane macroscopic elastic moduli and Poisson's ratios. Furthermore, an increase in the relative density for a given cell size revealed variations in the size dependence of the elastic properties. The size dependence of elastic properties is interpreted based on the influence of rotation gradients with varying cell size of the cellular solid. Also, the evaluated size-dependent elastic properties are compared with the available analytical solutions from the literature.

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Figures

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Fig. 1

Honeycomb with regular hexagonal cells and the corresponding unit cell

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Fig. 2

Square cellular geometry and the corresponding unit cell

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Fig. 3

Honeycomb with inverted cellular geometry and the corresponding unit cell

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Fig. 4

Degrees-of-freedom for the four-node plane strain element

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Fig. 5

Unit cells for (a) honeycomb with regular hexagonal cells, (b) square cellular geometry, and (c) honeycomb with inverted cellular geometry

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Fig. 6

Normalized elastic modulus Ex/Ex0 versus cell wall thickness t at different relative densities ρ for the honeycomb with regular hexagonal cells

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Fig. 7

Poisson's ratio νxy  versus cell wall thickness t at different relative densities ρ for the honeycomb with regular hexagonal cells

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Fig. 8

Rotation gradients χ13 for (a) t = 3.125 μm, and (b) t = 500 μm, at ρ = 0.12 for an applied displacement resulting in a strain of 0.005 in the x direction

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Fig. 9

Normalized elastic moduli (a) Ex/Ex0 and (b) Ey/Ey0 versus cell wall thickness t at different relative densities ρ for the square cellular geometry

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Fig. 10

Poisson's ratios (a) νxy and (b) νyx versus cell wall thickness t at different relative densities ρ for the square cellular geometry

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Fig. 11

Normalized elastic moduli (a) Ex/Ex0 and (b) Ey/Ey0 versus cell wall thickness t at different relative densities ρ for the honeycomb with inverted cellular geometry

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Fig. 12

Poisson's ratios (a) νxy and (b) νyx versus cell wall thickness t at different relative densities ρ for the honeycomb with inverted cellular geometry

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