smart shape memory alloy chiral honeycomb

5/25/2018 Smart shape memory alloy chiral honeycomb

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Materials Science and Engineering A 481482 (2008) 654657

Smart shape memory alloy chiral honeycomb

M.R. Hassan a,, F. Scarpa b, M. Ruzzene c, N.A. Mohammed d

aDepartment of Mechanical Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, United KingdombDepartment of Aerospace Engineering, The University of Bristol, Bristol BS8 1TR, United Kingdomc School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332, United States

dDepartment of Mechanical and Material, Universiti Kebangsaan, Malaysia

Received 19 May 2006; received in revised form 18 October 2006; accepted 29 October 2006

Abstract

An auxetic (or negative Poissons ratio) material expands in all directions when pulled in only one, behaving in an opposite way compared withclassicalmaterials. A structurenot super-imposable withits mirror image is defined aschiral. A chiral structural honeycomb(noncentresymmetric)

features auxeticity, i.e., a negative Poissons ratio behaviour in the plane. Although chirality is common in nature and organic chemistry, it is an

unusual characteristic in structuralmaterialsand components. We have manufactured trussassemblies based on cells of chiral honeycomb topology

using shape memory alloy (SMA) ribbons as core material. The main objective of this work is to obtain a new functional structure combining the

chiral honeycomb topology and shape memory alloys as a new concept of smart cellular solid. The chiral SMA honeycomb can be used in new

types of deployable antenna reflectors, allowing the compression of the structure in a small volume of space for subsequent deployment. The new

honeycomb concept could also be used in packaging applications to store strain energy during an impact loading and as a core for a sandwich

structure for damping or for crashworthiness.

2007 Elsevier B.V. All rights reserved.

Keywords: Auxetic; Chiral; Poissons ratio; Pseudoelasticity; Deployable

1. Introduction

Since their first release in 1987 [1], auxetic (or negative

Poissons ratio materials) have found potential applications in

several engineering designs, such as damage tolerant laminates

[2],microwave absorbers[3]and medical prosthesis[4].Chiral

topologies have been presented as a source of auxetic behaviour

in 2D lattice models of hexagonal molecules at high density

[5].The first study of a structural chiral honeycomb has been

reported by Prall and Lakes[6].A unit cell of chiral honeycomb

is shown inFig. 1.The chiral hexagonal cell is composed of

circular elements or nodes of equal radiusrjoined by straight

ligaments or ribs of equal length L. The ligaments are con-

strained to be tangential to the nodes, with an angle between

adjacent ligamentsequalto 60. Thehoneycombsimultaneously

possessesboth hexagonal symmetry anda two-dimensionalchi-

ral symmetry. Structures exhibiting hexagonal symmetry are

mechanically isotropic in-plane[6].The main objective of this

work is to obtain a new functional structure combining a chi-

Corresponding author. Tel.: +44 114 22225678; fax: +44 114 22227890.

E-mail address: [email protected](M.R. Hassan).

ral honeycomb topology and the use of shape memory alloys(SMAs) as a core material for deployable antenna reflectors,

or in packaging applications to store strain energy during an

impact loading. Moreover, if the effective Poissons ratio of

the smart SMA cellular structure is made negative by using

specific cell shapes, the domed or synclastic curvature can be

achieved naturally[7].The payload and size are major con-

straints in satellite design. By using a SMA auxetic cellular

solid, the structure can be compressed in a small volume of

space and can be deployed into space. This solution would pro-

vide an alternative to inflatable deployable solutions, such as

modular mesh deployable, balloon type portable and aperture

unfurlable antennas. The shape restoring capabilities are alsoa feature that could be successfully employed energy absorb-

ing applications. Currently, honeycomb structures are used in

packaging, railway, aerospace industry and in crashworthiness

applications because of their energy absorption capabilities at

different strain rate loadings[8].However, a crushed and densi-

fied honeycomb does not retain anymore its structural function.

It is conceivable to design a cellular core with shape memory

capabilities that, once heavily loaded, tends to return or oppose

the external force and maintain to a certain extent its structural

integrity.

0921-5093/$ see front matter 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.msea.2006.10.219
mailto:[email protected]://localhost/var/www/apps/conversion/tmp/scratch_8/dx.doi.org/10.1016/j.msea.2006.10.219http://localhost/var/www/apps/conversion/tmp/scratch_8/dx.doi.org/10.1016/j.msea.2006.10.219mailto:[email protected]


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M.R. Hassan et al. / Materials Science and Engineering A 481482 (2008) 654657 655

Fig. 1. Hexagonal chiral unit cell layout (from[6]).

2. Chiral honeycomb manufacturing

Theshapememory alloysribbon used to manufacture thechi-

ral honeycombs was produced by @Medical Technologies n.v.

The ribbon was 0.27 mm thick and 4.67mm wide, produced by

thin rolling process.Theprototype of thechiralstructural honey-

comb was manufactured using mild steel hollow cylinders, with

1 mm of internal thickness. Screws have been used to guarantee

the fastening of the ligaments to the single node. Initially, the

ribbon was cut to the desired length for the ligament, then a mild

steel pipe was cut to match the size of the width of ribbon. The

size of cylinder or node and the length of the ligament follow

the cell aspect ratioR/r(seeFig. 1)for the honeycomb. In this

work, all prototypes had a value ofR/requal to 5. All internal

nodes have 6 tangent ligaments, while the nodes at the edge will

only have three or four ligaments. Thecomplete structure of this

SMA chiral honeycomb can be seen inFig. 2,while the loading

directions are represented in the unit cell ofFig. 1.

3. Numerical models

The in-plane compression simulations were carried out using

a unit cell of the chiral honeycomb structure with periodic

boundary conditions. A model of the unit cell was developed inthe commercial finite element (FE) package ANSYS[9]using

the TB, SMA option to model the shape memory alloys ele-

ment using 2D PLANE183 elements. This specific element was

chosen because of its nonlinear material and geometrical capa-

bilities, while using a consistent tangent stiffness approach for

large strain applications. The micromechanical model imple-

mented is the pseudo-elastic/superelastic hysteretic one with no

permanent strain[10].

The FE model has been made parametric by using the nondi-

mensionalgeometry parametersas in [6]. The unitcellofa chiral

honeycomb structure is shown in Fig. 3 hasanR/rratio of5, sim-

ilar to the geometry of the Prall and Lakes work. The Poissons

Fig. 2. Mild steel cylinders honeycomb.

ratios of the chiral structure has been obtained by applying a

compressive force in bothXandYdirections to the structure

and subsequently measuring the displacement values and cal-

culate the averaged equivalent strains over the unit cell This

analysis was carried out in justifying whether the unit cell (with

theshapememory alloyas theligament) conforms to thetheoret

ical valueof1 for thePoissons ratio [6]. It must bepointed out

that in the theoretical model proposed by Prall and Lakes, only

bending deformation provides the rotation of the ligaments and

therefore the in-plane negative Poissons ratio effect. At small

strains, however, for 2D honeycomb assemblies a contribution

from the axial stiffness of the ribs has also been recorded fromfinite element analysis[11].

Two different materials were defined for the unit cell: the

shape memory alloy for the ligaments, while the second was a

fictitious metal with Youngs modulus equal to 10 times the one

of stainlesssteel. Thefictitiousmaterial was chosento model the

Fig. 3. Hexagonal chiral unit cell finite elementsolid model.


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Fig. 4. Deformed FE model hexagonal chiral unit cell along theY-direction.

nodes; to avoid the deformations of the nodes under loadings,

and simulate pure rigid body motion. In this way, the numerical

model could be related to theassumption made for theanalytical

approach taken by Prall and Lakes[6](Fig. 4).

4. Mechanical tests

The chiral honeycomb as shown inFig. 2was tested under

tensile compressive loading in full austenite regime. The tensile

machine used was INSTRON 5567 with 5 kN load cell. In order

to allow the honeycomb freely wind at the node, the sample

was placed in a special metal slot. In this test, the feed rate that

has been used was 5mm/min. An Image Data Processing tech-

nique similar to the one adopted to measure the Poissons ratio

of auxetic foams[12]has been used to measure the longitudi-

Fig. 5. Poissons Ratio for the chiral sample.

nal and lateral displacements of the honeycomb sample, with a

frame capture rate of 1 min1. A suitable calibration procedure

to consider optical distortion effects hasbeen applied [13]. Fig.5

shows the measured Poissons ratios for the chiral honeycomb.

After the initial take-up of the samples (due also to the edge

effects given by the slots), the Poissons ratios along both planes

(xyandyx) are constant and equal for tensile loading up to 15%,

with and average Poissons ratio value of0.75.

The experimental values of the Poissons ratios are affected

by near-neighboring effects due to thesmall numberof unit cells

composing the honeycomb. Cellular assemblies with reduced

number of cells provide lower values of in-plane Poissons

ratios, as verified numerically and experimentally also in cen-

tresymmetric shape memory alloy honeycomb configurations

[14].For small compressive strains (up to 5%), the effect given

by the clamps of the ligaments and axial stiffness provide a

decrease of the Poissons ratio value, as for centresymmet-

ric honeycomb structures[15].The FE results are related to

a unit cell representing periodic boundary conditions, there-

fore related to an infinite two dimensional honeycomb. Thenumerical results feature higher magnitude compared to the

experimental one, and present a general trend towards the

theoretical value of 1[6], with some effects due to small

degree of anisotropy given by the ligament clamps. Both the

experimental and numerical results show a tendency to provide

constant values of Poissons ratio for higher compressive strains

(above 10%).

5. Deployable truss prototype

Another prototype made of 3 4 chiral cells has been devel-

oped to demonstrate the capability of the chiral hexagonalconfiguration to support the concept of deployable truss anten-

nas. The nodes of the chiral truss were made using hollow PVC

cylinders, and the ligaments used were the Nitinol ribbons. The

Fig. 6. Thermal expansion ratio for chiral sample.


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M.R. Hassan et al. / Materials Science and Engineering A 481482 (2008) 654657 657

Fig. 7. Deformation mechanism of the deployable antenna prototype.

cell aspect ratioR/ris 5. The actuation was simply provided

by electric heater. The result of experimental thermal expansion

ratio for the chiral honeycomb is shown in Fig. 6. The character-

istic of thermal expansion ratio for the honeycomb is toward to

1. The actuation imposed on the chiral truss can be viewed fol-lowing the arrows indicated inFig. 7.It was possible to achieve

an overall 50% compression of the whole structure, giving fur-

ther indication that this structural topology is able to provide a

large volume deformation from full packing, and hence giving

an advantage in space saving.

6. Conclusions

In this work we have described the modeling, manufacturing

and testing of a shape memory alloy honeycomb with a chiral

configuration. The FE models developed represent a unit cell

with periodic boundary conditions, i.e., a honeycomb structurewith infinite extension in the plane. The honeycomb manufac-

tured, however, has a limited number of cells. The Poissons

ratio measured would be therefore affected by near-neighboring

effects, and the effective values of the Poissons ratio decreased.

This is consistent with analogousmodels andmeasurementscar-

ried out on centre symmetric SMA honeycomb structures[14].

These characteristics have been used to develop a working pro-

totype of a deployable antenna from full packing configuration

to deployment. The aspect ratio used for the prototype was 5,

leading to a 50% increase in the original volume. Larger vol-

ume increase can be achieved with different cell aspect ratios,

while the expansion effect dictated by the Poissons ratio of

the structure would remain virtually unchanged.

Acknowledgements

This work has been supported by the grant (W911NF04-1-

0141) from the Army Research Office, with Dr. Gary Anderson

as program manager and technical monitor for the ARO project

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smart shape memory alloy chiral honeycomb

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