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Research Papers

Response of Honeycombs Subjected to In-Plane Shear

[+] Author and Article Information
Youming Chen

Centre for Advanced Composite Materials,
Department of Mechanical Engineering,
University of Auckland,
Auckland 1010, New Zealand
e-mail: cyou659@aucklanduni.ac.nz

Raj Das

Centre for Advanced Composite Materials,
Department of Mechanical Engineering,
University of Auckland,
Auckland 1010, New Zealand
e-mail: r.das@auckland.ac.nz

Mark Battley

Centre for Advanced Composite Materials,
Department of Mechanical Engineering,
University of Auckland,
Auckland 1010, New Zealand
e-mail: m.battley@auckland.ac.nz

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received January 20, 2016; final manuscript received March 5, 2016; published online March 28, 2016. Assoc. Editor: Daining Fang.

J. Appl. Mech 83(6), 061004 (Mar 28, 2016) (10 pages) Paper No: JAM-16-1034; doi: 10.1115/1.4032964 History: Received January 20, 2016; Revised March 05, 2016

Study on the response of honeycombs subjected to in-plane shear helps establish the constitutive relations for honeycombs and shed light on the mechanics of cellular materials. The present study explores the nonlinear elastic response of honeycombs under in-plane shear by analyzing the large deflection of cell walls in a unit cell. Governing equations are established which relate the macroscopic response of honeycombs to the deflection of cell walls. Solving these equations, the behavior of regular honeycombs under in-plane shear along horizontal (X) and vertical (Y) directions was investigated. It is found that the response of regular honeycombs under in-plane shear depends on the nondimensional shear stress which is a parameter combining the thickness-to-length ratio of cell walls, the Young's modulus of base materials, and macroscopic shear stress. Lateral shrinking is a distinctive characteristic for honeycombs under in-plane shear, which should be taken into account when establishing constitutive relations and performing simple shear experiments. Expressions for predicting the shear strength of honeycombs are formulated in this paper. It is noted that the normalized shear strength of regular honeycombs depends on two ratios: the thickness-to-length ratio of cell walls and the ratio of Young's modulus to yield strength of base materials, and the former has a dominant effect. By comparing honeycombs with cell walls of uniform thickness against honeycombs with vertical cell walls of double thickness, it is found that doubling the thickness of vertical cell walls of honeycombs increases their shear strength along horizontal (X) direction nearly twice, but does not improve the shear strength that much along the vertical (Y) direction.

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Figures

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Fig. 1

Cantilevered beam subjected to a force at free end

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Fig. 2

Schematic of a honeycomb structure

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Fig. 3

(a) Undeformed and deformed configurations of a unit cell under shear along X direction and (b) boundary conditions of the half-unit cell

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Fig. 4

Deformation of cell walls (a) AB, (b) CB, and (c) DB under shear along X direction

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Fig. 5

Undeformed and deformed configurations of a unit cell under shear along Y direction

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Fig. 6

Deformation of cell walls in the half-unit cell under shear along y direction

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Fig. 7

(a) Geometry of the finite element model and (b) configuration of a deformed honeycomb under in-plane shear along X direction

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Fig. 8

Comparison of the stress–strain curves of honeycombs along X direction from FEM analysis and from the developed equations (8a)(13)

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Fig. 9

Comparison of the stress–strain curves of honeycombs along Y direction from FEM analysis and from the developed equations (22a)(29)

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Fig. 10

Universal stress–strain curves of regular honeycombs under shear along horizontal (X) and vertical (Y) directions

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Fig. 11

Variation of lateral shrinkage with shear strain

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Fig. 12

Variation of the normalized shear strength of the polymer and aluminum honeycombs with the thickness-to-length ratio

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Fig. 13

Variation of normalized shear strength of honeycombs with the ratio of Young's modulus to yield strength of base materials

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Fig. 14

Variation of shear strength ratio of honeycombs with thickness-to-length ratio

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