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Research Papers

Hyperelastic Constitutive Modeling of Hexagonal Honeycombs Subjected to In-Plane Shear Loading

[+] Author and Article Information
Jaehyung Ju, Joshua D. Summers

Department of Mechanical Engineering, Clemson University, Clemson, SC 29643-0921

J. Eng. Mater. Technol 133(1), 011005 (Dec 01, 2010) (8 pages) doi:10.1115/1.4002640 History: Received February 11, 2010; Revised June 25, 2010; Published December 01, 2010; Online December 01, 2010

The in-plane flexible shear property of hexagonal honeycombs may be useful for the compliant structural applications. In this paper, hyperelastic strain energy functions are developed for a finite in-plane shear deformation of hexagonal honeycombs over a constituent material’s elastic range. Effective shear stress-strain curves of hexagonal structures and local cell wall deformation are investigated using the finite element based homogenization method. The hyperelastic models, which are only related to the effective properties of a honeycomb, may not be good enough to capture the nonlinear behavior at a high macroscopic shear strain level. The primary microscopic cell wall deformation mode under macroscopic in-plane shear loading was identified to be the bending of the vertical cell wall h, which is perpendicular to the macroscopic loading direction. The re-entrant hexagonal structures having a negative Poisson’s ratio shows a high macroscopic shear flexible property associated with the high h when the honeycombs are designed to have the same macroscopic shear modulus.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of representation of an infinite cellular solid with a periodic microstructure and its corresponding unit cell

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Figure 2

Schematics of the in-plane displacement boundary conditions for simple shear

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Figure 3

Stress-strain curves of 3D printed polycarbonates

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Figure 4

Effective shear stress-strain curve of the regular hexagonal honeycomb with deformed shapes (θ=30 deg, h=l)

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Figure 5

Effective shear stress-strain curve of the auxetic hexagonal honeycomb with deformed shapes (θ=−30 deg, h=2l)

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Figure 6

Shear stress-strain curves of hyperelastic models (θ=30 deg, h=l)

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Figure 7

Effective shear stress-strain behaviors within a constituent material’s elastic range and the corresponding deformed geometries at the material’s yield point

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Figure 8

(a) Vertical cell wall components of unit cells and (b) normalized k values from Eq. 24

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