0
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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Fig. 1

Honeycomb with regular hexagonal cells and the corresponding unit cell

Grahic Jump Location
Fig. 2

Square cellular geometry and the corresponding unit cell

Grahic Jump Location
Fig. 3

Honeycomb with inverted cellular geometry and the corresponding unit cell

Grahic Jump Location
Fig. 4

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

Grahic Jump Location
Fig. 5

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

Grahic Jump Location
Fig. 6

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

Grahic Jump Location
Fig. 7

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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In