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  • Neville, R. M., Pirrera, A., & Scarpa, F. (2014). Open shape morphinghoneycombs through kirigami. In ASME 2014 Conference on SmartMaterials, Adaptive Structures and Intelligent Systems, SMASIS 2014 (Vol.1). [SMASIS2014-7489] Web Portal ASME (American Society ofMechanical Engineers).

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  • OPEN SHAPE MORPHING HONEYCOMBS THROUGH KIRIGAMI

    Robin M. NevilleUniversity of Bristol

    Bristol, England

    Alberto PirreraUniversity of Bristol

    Bristol, England

    Fabrizio ScarpaUniversity of Bristol

    Bristol, England

    ABSTRACTThis work presents an open and deployable honeycomb

    configuration created using kirigami-inspired cutting andfolding techniques. The open honeycomb differs fromtraditional closed honeycomb by its reduced density and itsincreased flexibility. The exploitation of these characteristicsfor multifunctional applications is the focus of this work.Potential fields in which the open honeycomb could findapplication include sandwich panel manufacturing, morphing,and deployable structures.

    NOMENCLATUREh h-wall width

    l l-wall width

    b wall length

    t sheet material thickness

    internal cell wall angle

    hinge opening angle

    H unit cell width

    L unit cell length

    T unit cell thickness

    Amat area of sheet material in unit cell

    mat density of sheet material

    tmat thickness of sheet material

    INTRODUCTIONKirigami is the ancient Japanese art of folding and cutting

    paper. Nojima and Saito developed a method of creatinghoneycombs using this process [1]. Slitting, corrugation, andfolding operations are used to form a 2D sheet material into a3D cellular structure. Mating faces can be bonded together tocreate a closed honeycomb or left unbonded to create an openhoneycomb. The geometry of the honeycomb can be varied byaltering the pattern of slits, giving a design flexibility

    otherwise not available with other techniques. By varying thespacing of slits on the sheet it is possible to produce ahoneycomb with a varying thickness profile [2,3]. It is alsopossible to produce different cell shapes by changing the shapeof the moulds used and adapting the slitting patternaccordingly [4] Including circles in the slitting pattern givesholes in the cell walls. Such holes have previously been usedfor ventilation [5] but could also be used for (wire) access oractuation. Such features would be difficult to machine out oftraditional honeycomb without causing damage [6]. Wedescribe how the mechanical and actuation properties of theopen honeycomb change with the Kirigami pattern and thefold angle. Finite Element Analysis (FEA) has been used toinvestigate the effect of fold angle and fold stiffness on themechanical properties of the open honeycomb. A mechanicaltesting programme is planned to validate the FEA models.Subsequent work will focus on the multifunctionality of thestructure. Of particular interest is the use of smart hinges madewith Shape Memory Polymer (SMP), and the inclusion ofventilation or access holes with tuneable wires to create classesof deployable smart honeycombs using the Kirigami process.

    KIRIGAMI MANUFACTURINGThe kirigami process for creating honeycombs [1],

    converts a 2D sheet of material into a 3D cellular structureusing four processing steps, as shown in Figure 1. An openhoneycomb is produced by simply omitting step 4 and leavingthe honeycomb unbonded. The kirigami process is flexible interms of input materials and processing techniques; all that isrequired is that the sheet material can be cut, folded, andbonded to itself. This affords the user some choice in terms ofmaterials selection. In this case, Victrex PEEK film was usedfor its good formability and mechanical properties[7].

    The slits were made using a Blackman & White ply cutter.The corrugations were created by thermoforming the PEEKfilm between semi-hexagonal moulds using a hot press at200C. The slits in the sheet line up with the edges of themoulds as shown in Figure 2; this alignment is importantbecause it allows the corrugated sheet to be folded back onitself to produce a hexagonal geometry.

    1 Copyright 2014 by ASME

    Proceedings of the ASME 2014 Conference on Smart Materials, Adaptive Structures and Intelligent Systems SMASIS2014

    September 8-10, 2014, Newport, Rhode Island, USA

    SMASIS2014-7489

  • After thermoforming, the corrugated sheet is folded backon itself repeatedly such that the slits (which are now semi-hexagonal) open up into hexagonal holes, resulting in the openhoneycomb geometry shown in Figure 3. This is done at roomtemperature, by hand, and simply creates plastic deformationin the material where folded.

    Figure 1: The four steps of the Kirigami manufacturingprocess for honeycombs.

    Figure 2: Slitted sheet material conforming to hexagonalmould geometry.

    Figure 3: The open honeycomb geometry

    Holes or other such features can be included in the slittingpattern, which will later form part of the honeycomb, as shownin Figure 4.

    Figure 4: Left: cutting pattern with holes and channels. Right:The honeycomb produced by this cutting pattern

    If the slitting pattern is modified, a variant on the openhoneycomb can be created with some parallelogram-shapedwalls, as shown in Figure 5. To distinguish between the openconfigurations they shall henceforth be called open rec andopen par, where rec and par are short for rectangularand parallelogram, respectively, and refer to the shape of thewalls.

    2 Copyright 2014 by ASME

  • Figure 5: The relationship between cutting patterns andhoneycomb geometries. The black shapes on the lowest cuttingpattern represent material removed. The brown material on thecutting pattern becomes the brown cell on the right. Thedotted box shows the bounding volume of the cell. The celledges which touch the bounding box are shown in blue. Greyreplica cells are shown to illustrate the tesselation of thestructure.

    VOLUMETRIC ANALYSISThe two distinguishing features of the open honeycomb

    are its increased (and directional) flexibility and its reduceddensity. In this section the unit cell and the variable density ofthe open honeycomb are examined.

    Figure 6 shows the unit cell of the closed honeycomb.

    Figure 6: The unit cell of theclosed configuration.

    Dimensions h, l, b, and are determined by the moulds andcutting pattern. Dimensions H, L, T and sheet material area Aare calculated as follows:

    H closed=2h+2 l sin (1)

    Lclosed=l cos (2)

    T closed=b (3)

    A closedmat =2bh+2bl (4)

    Figure 7 shows the unit cell of the open rec honeycomb,with a side view along the 1-direction.

    Figure 7: The unit cell of the open rec configuration. The viewon the right is a view along the 1-direction.

    This structure is essentially the same structure, rotatedabout the 1-axis by angle from the vertical. The dimensionsand area A are calculated as follows.

    H rec=2h+2 l sin (5)

    Lrec=l coscos +b sin (6)

    3 Copyright 2014 by ASME

  • T rec=l cossin +b cos (7)

    A recmat=2bh+2bl (8)

    Figure 8 shows the unit cell of the open par honeycomb,with a side view along the 1-direction.

    Figure 8: The unit cell of the open par configuration. The viewon the right is a view along the 1-direction.

    The dimensions and area A are calculated as follows.

    H par=2h+2 l sin (9)

    Lpar=lcoscos

    +b sin (10)

    T par=bcos (11)

    A parmat=2bh+2bl (12)

    To isolate the effect of angle on the density of thehoneycombs, dimensions l, h, b, and must be fixed. Theabsolute density is of little interest; instead the density of theopen configurations will be compared relative to the density ofthe closed configuration. The density of each configuration isgiven by:

    =mV

    = Amatmat tmat

    HLT(13)

    It can be seen that H and Amat are the same for allconfigurations. If the same sheet material is used to make allconfigurations then mat and tmat are also constant. As a resultthese variables cancel out when the relative density iscalculated as follows.

    openclosed =

    Lclosed T closedLopenT open

    (14)

    By substituting in equations (2-3,6-7,10-11) andrearranging, the following two expressions are obtained.

    recclosed =

    1

    ( l2 cos2+b2

    2bl cos)sin 2+1

    =1

    C sin 2+1 (15)

    where C=( l2cos2+b2

    2blcos )

    And

    parclosed =

    1

    ( b2

    2bl cos)sin2+1

    =1

    D sin 2+1 (16)

    where D=( b2

    2bl cos)

    When = 45, sin2 = 1 and the relative density of theopen configurations is at a minimum with a value of 1/(C+1)or 1/(D+1) depending on the configuration, as shown in Figure9.

    Figure 9: The variation of relative density with angle .

    The magnitudes of these minima are de