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Research Papers

# Design of Honeycombs for Modulus and Yield Strain in Shear

[+] Author and Article Information
Jaehyung Ju, John Ziegert, George Fadel

Clemson Engineering Design Application and Research Group (CEDAR), Department of Mechanical Engineering, Clemson University, Clemson, SC 29634-0921

Joshua D. Summers1

Clemson Engineering Design Application and Research Group (CEDAR), Department of Mechanical Engineering, Clemson University, Clemson, SC 29634-0921jsummer@clemson.edu

1

Corresponding author.

J. Eng. Mater. Technol 134(1), 011002 (Dec 06, 2011) (15 pages) doi:10.1115/1.4004488 History: Received September 09, 2009; Revised April 25, 2011; Accepted June 15, 2011; Published December 06, 2011; Online December 06, 2011

## Abstract

The low in-plane modulus of honeycombs may be used for compliant structures with a high elastic limit while maintaining a required modulus. Numerical and finite element (FE) studies for a functional design of honeycombs having a high shear strength, (τpl *)12 and a high shear yield strain, (γpl *)12 are conducted with two material selections—mild-steel (MS) and polycarbonate (PC) and five honeycomb configurations, when they are designed to be a target shear modulus, G12 * of 6.5 MPa. A numerical study of cellular materials theory is used to explore the elastic limit of honeycombs. FE analysis is also employed to validate the numerical study. Cell wall thicknesses are found for each material to reach the target G12 * for available cell heights with five honeycomb configurations. Both MS and PC honeycombs can be tailored to have the G12 * of 6.5 MPa with 0.1–0.5 mm and 0.3–2.2 mm cell wall thicknesses, respectively, depending on the number of vertical stacks, N. The PC auxetic honeycomb with θ= −20 deg shows high shear flexibility, when honeycombs are designed to be the $G12*$ of 6.5 MPa; a 0.72 MPa (τpl *)12 and a 13% (γpl *)12 . The authors demonstrate a functional design with cellular materials with a large design space through the control of both material and geometry to generate a shear flexible property.

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## Figures

Figure 1

Unit cell geometry for (a) conventional and (b) auxetic honeycombs

Figure 2

2D view of honeycomb and with built PC and MS samples

Figure 3

Five honeycomb configurations used in this study when h = l

Figure 4

Cell heights as a function of number of unit cells for each honeycomb configuration (when α = 1 and H = 12.7 mm)

Figure 5

Effective moduli of honeycombs with 60 deg cell angle (h = 3.33 mm, base material: MS)

Figure 6

Effective moduli of honeycombs with 30 deg cell angle (base material: MS)

Figure 7

Effective moduli of honeycombs with 15 deg cell angle (base material: MS)

Figure 8

Effective moduli of honeycombs with −10 deg cell angle (base material: MS)

Figure 9

Effective moduli of honeycombs with −20 deg cell angle (base material: MS)

Figure 10

Effective moduli of honeycombs with 60 deg cell angle (h = 3.4 mm, base material: PC)

Figure 11

Effective moduli of honeycombs with 30 deg cell angle (base material: PC)

Figure 12

Effective moduli of honeycombs with 15 deg cell angle (base material: PC)

Figure 13

Effective moduli of honeycombs with −10 deg cell angle (base material: PC)

Figure 14

Effective moduli of honeycombs with −20 deg cell angle (base material: PC)

Figure 15

Effective shear yield strain, (γpl *)12 as a function of density when honeycombs are designed to have a G12 * of 6.5 MPa

Figure 16

Cell wall thicknesses in Fig 1

Figure 17

Normalized (γpl *)12 as a function of cell angle, θ for a designed G12 * of 6.5 MPa

Figure 18

Effects of 1/cosθ and t2 /(hl) on (γpl *)12 (normalized values)

Figure 19

Material models for FE analysis

Figure 20

Shear stress-strain curves of MS honeycombs

Figure 21

Shear stress-strain curves of PC honeycombs

Figure 22

(γpl *)12 as a function of density

Figure 23

(τpl *)12 of honeycombs as a function of density for a G12 * of 6.5 MPa

Figure 24

( τpl *)12  − (γpl *)12 diagram for high shear strength and shear strain design

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