Study of Two-Dimensional Kirigami in Different Materials

Joseph Noble

Bachelor of Science Thesis TRITA-ITM-EX 2018:696 KTH Industrial Engineering and Management

Machine Design SE-100 44 STOCKHOLM

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Examensarbete TRITA-ITM-EX 2018:696

Studie av tvådimensionell Kirigami i olika material

Joseph Noble

Godkänt

2018-10-01

Examinator

Ulf Sellgren

Handledare

Ellen Bergseth Uppdragsgivare

Ortrud Medical AB Kontaktperson

Caroline Dahl

Sammanfattning De mekaniska egenskaperna hos ett tvådimensionellt material kan ändras med hjälp av Kirigami, som är en japansk klippkonst i papper. Material där man med geometriförändringar ändrar materialegenskaperna kallas metamaterial. I det här examensarbetet dokumenteras inverkan av ett Kirigami-mönster i olika material, bland annat plast och papper. Resultaten kommer att användas för att utvärdera om något passar att användas till ett stasband framtaget av Ortrud Medical AB. Remsan har en mönstrad ”fjäderyta”, som påverkar styvheten, och en kraftzoon. I det här arbetet studeras enbart det mönstrade området. För att utvärdera materialen och välja det mest lämpade, användes Pughs utvärderingsmatris. Materialen utvärderas bland annat med avseende på robusthet, dragmotstånd och patientkomfort. Ett av materialen valdes ut för ytterligare provning på grund av dess intressanta deformationsbeteende. I det här arbetet tillämpas både experimentella och analytiska metoder. Resultaten användes sedan för att verifiera en FE-modell av systemet. Modellen och experimenten gav liknade resultat vid små deformationer, dock begränsades verifieringen av materialdatabasen. En delstudie visade att det är möjlighet att ställa in mönsterdimensionerna, så att töjningsegenskaperna hos metamaterialet kan justeras.

Nyckelord: FEM, materialval, metamaterial, styvhetsanpassning, venpunktion

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Master of Science Thesis TRITA-ITM-EX 2018:696

Study of two-dimensional Kirigami in different materials

Joseph Noble

Approved

2018-10-01 Examiner

Ulf Sellgren Supervisor

Ellen Bergseth Commissioner

Ortrud Medical AB Contact person

Caroline Dahl

Abstract The mechanical properties of a 2D material can be altered with Kirigami, a Japanese paper cutting art. Such altered materials are called metamaterials – where a certain geometry is imposed on a material to change its material properties.

This thesis documents the effects of a specific Kirigami pattern cut into a range of different 2D materials, such as plastic films or paper – the results of which will be used to evaluate the suitability of each material candidate to a product, the ‘IV strip’, designed and produced by Ortrud Medical AB.

The strip contains a patterned ‘spring’ area, which has reduced stiffness due to the patterned defects imposed on it, and a force indication zone. The force indication zone will not be considered.

The material selection study used a Pugh’s Evaluation matrix method to choose the best candidate. A few materials were chosen due their suitability in criteria such as robustness of results, tearing force and patient comfort. One material was selected for further experimentation due to its interesting stress/strain characteristics.

A further study was then carried out to assess the possibility of tuning the pattern dimensions to alter the tensile properties of the metamaterial. This study includes both computational and experimental methods to verify the feasibility of a simulation model. The study found that it is possible to draw relationships between cut length and stiffness of the pattern. Whilst the computational and experimental results were similar for very small deformations, the FEM simulation struggles at higher deformations because of the lack of available material properties for the program input.

Keywords: FEM, Material Selection, Metamaterial, Stiffness Tuning, Venepuncture,

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FOREWORD

This thesis was commissioned by Ortrud Medical AB. The founder and personal contact, Caroline Dahl, I am very grateful to for her compelling discussion, motivation and assistance throughout the course of this thesis. I feel lucky to have worked on a revolutionary and exciting new product. I would also like to thank Ellen Bergseth, my academic coordinator at KTH, who has provided extensive technical knowledge and support in co-ordinating and organising the progression of this work.

Joseph Noble

Stockholm, June 2018

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NOMENCLATURE

Here are the Notations and Abbreviations that are used in this thesis.

Notations

Symbol Description

A Area (m2)

d Deflection (m) E Young´s modulus (Pa)

F Force (N)

Lc Cut length (m)

P Pressure (Pa)

r Radius (m)

t Strip thickness (m)

w Strip width (m)

x Horizontal cut spacing (m)

y Vertical cut spacing (m)

σθ Axial stress (Pa)

Abbreviations CAD Computer Aided Design FEM Finite Element Modelling

IV Intravenous

PVC Peripheral Venous Catheter

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TABLE OF CONTENTS

SAMMANFATTNING ................................................................................................................... 1

ABSTRACT .................................................................................................................................... 3

FOREWORD .................................................................................................................................. 5

NOMENCLATURE........................................................................................................................ 6

TABLE OF CONTENTS ............................................................................................................... 7

1 INTRODUCTION ...................................................................................................................... 9

1.1 Background ......................................................................................................................... 9

1.2 Purpose ................................................................................................................................ 9

1.3 Delimitations ...................................................................................................................... 10

2 FRAME OF REFERENCE ..................................................................................................... 11

2.1 Medical Background ......................................................................................................... 11 2.1.1 – Medical Requirements ........................................................................................................................... 11 2.1.2 – Current Solutions and Materials ........................................................................................................... 12

2.2 Kirigami Metamaterials ..................................................................................................... 12 2.2.1 – Altering Stiffness .................................................................................................................................... 12 2.2.2 – Poisson’s Ratio ...................................................................................................................................... 13 2.2.3 – Pattern Deformation Regimes ............................................................................................................... 13

2.3 Materials ............................................................................................................................. 16

2.4 Product Manufacturing Methods..................................................................................... 17 2.4.1 - Laser Cutting machine ........................................................................................................................... 17 2.4.2 – Knife cutter/plotter ................................................................................................................................ 17 2.4.3 – Industrial Stencil Press .......................................................................................................................... 17

2.5 Finite Element Modelling (FEM) Methods ...................................................................... 17

3 MATERIAL FEASIBILITY STUDY ...................................................................................... 19

3.1 Evaluation Criteria ............................................................................................................ 19

3.2 Tearing Force Testing ...................................................................................................... 19 3.2.1 – Purpose of Test ...................................................................................................................................... 19 3.2.2 – Test Equipment ...................................................................................................................................... 20 3.2.3 – Test Procedure ....................................................................................................................................... 20 3.2.4 – Test Result ............................................................................................................................................. 21 3.2.5 – Test Conclusions .................................................................................................................................... 21

3.3 Tensile Testing .................................................................................................................. 21 3.3.1 – Purpose of Test ...................................................................................................................................... 21 3.3.2 – Test Equipment ...................................................................................................................................... 22 3.3.3 – Test Procedure ....................................................................................................................................... 22 3.3.4 – Test Result ............................................................................................................................................. 23 3.3.5 – Test Conclusions .................................................................................................................................... 23

3.4 Qualitative Criteria Evaluation ......................................................................................... 24

3.5 Material Evaluation – Weighted Pugh’s Matrix .............................................................. 24

4 GEOMETRY TUNING STUDY .............................................................................................. 27

4.1 FEM Simulation ................................................................................................................. 27

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4.1.1 – CAD test file preparation and initial testing.......................................................................................... 27 4.1.2 – Specifying Engineering Data ................................................................................................................. 28 4.1.3 – Model Simplification .............................................................................................................................. 28 4.1.4 – Boundary Conditions ............................................................................................................................. 28 4.1.5 – Mesh Convergence Study ....................................................................................................................... 28 4.1.6 – FEM Results .......................................................................................................................................... 28

4.2 Stiffness Tuning Experimentation .................................................................................. 29 4.2.2 – Test Equipment ...................................................................................................................................... 30 4.2.3 – Test Procedure ....................................................................................................................................... 30 4.2.4 – Test Result ............................................................................................................................................. 30 4.2.5 – Test Conclusions .................................................................................................................................... 31

4.3 Comparison of FEM and Materials Testing Results ..................................................... 31

5 DISCUSSION AND CONCLUSIONS .................................................................................... 33

5.1 Discussion ......................................................................................................................... 33

5.2 Conclusions ....................................................................................................................... 34

5.3 Further work ...................................................................................................................... 34

6 REFERENCES ........................................................................................................................ 35

APPENDIX I: MATERIAL DATA ............................................................................................. 37

APPENDIX II: TENSILE TESTS .............................................................................................. 38

APPENDIX III: MESH CONVERGENCE STUDY .................................................................. 41

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1 INTRODUCTION

This chapter describes the background, purpose and delimitations applied in the presented project.

1.1 Background Ortrud Medical is a medical company which has designed an intelligent single use paper tourniquet, shown in Figure 1. Named the ‘IV Strip’, it uses Kirigami, and ancient Japanese paper cutting method [1], to reduce the tensile modulus of a 2D material and indicate the applied force visually so that optimal pressure is applied to a patient’s arm for intravenous access. The company recognised a requirement for a device that can provide repeatable pressure application within the required range to increase the likelihood of successful attempts at PVC insertion [2].

Veins must be soft and palpable for optimal blood access. To achieve this, pressure within a certain range must be applied to the limb. Traditional methods for applying pressure include a simple buckled strap or tied elastic tourniquet, or a blood pressure cuff (sphygmomanometer), all of which have their limitations, as discussed in section 2.1.2.

Figure 1 - A schematic drawing of the IV strip. The patterned area only takes up a small area of the strip, whilst the indicator (not shown here) is between the pattern. The fastener is a hole for the strip end to secure through (the strip

end is secured with an adhesive backing).

1.2 Purpose Due to the relative age of the product, there has not yet been extensive testing and documentation of product parameters such as material choice, strip dimensions and strip patterns. The work carried out in this thesis aims to classify and document the suitability of a range of materials and then further investigate the effects of changing geometry sizing within the pattern.

Materials will be classified and ranked on a range of different criteria, after which they will be given a weighted numerical score using Pugh’s Evaluation Matrix. This will allow for easy identification of the best material candidates.

Secondly, a computational model will be developed to investigate the effects of changing the pattern dimensions in the strip. Physical experimentation will follow, the results of which will verify the computational model.

The research questions are as follows:

• What criteria must the chosen material meet to be effective for this application? • What materials are available and how suited are these materials? • How do pattern geometry dimensions affect deformation?

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• How effective can an FEM model prove in modelling the resistive forces of a sample under strain? What drawbacks/limitations does the FEM analysis have?

1.3 Delimitations Necessary delimitations arise from the existing form and specifications of the product:

• The width of the strip will not be investigated or altered. • Only the patterned area will be considered, not the entirety of the strip. • Material candidates are restricted to those made available for this thesis. • Resulting pressure will not be measured but approximated from the thin walled hoop

stress assumptions. Forces are measured using tensile tests.

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2 FRAME OF REFERENCE

This chapter presents the theoretical reference frame that is necessary for the performed research. It is a summary of the existing knowledge on the subject.

2.1 Medical Background 2.1.1 – Medical Requirements

Gaining intravenous access is one of the most common procedures performed in a hospital environment. This can, however, be especially challenging with some patient groups, such as the elderly, obese, infant and dark skinned [2]. It is obviously desirable to optimise patient comfort and limit the number of required attempts to achieve venous cannulation. Although possible without application of a tourniquet, venous prominence is improved and hence a successful attempt is more likely. Tourniquet pressure is of vital importance, to allow arterial inflow to the limb, but prevent venous outflow and hence cause venodilation [2]. There is no definitive consensus of the perfect tourniquet pressure, however most agree that a pressure just below systolic is optimal [2], which is in the range of 60 to 100 mmHg. The unit mmHg is a measure of pressure, equal to the pressure to raise a column of mercury by 1 mm, or 133.3 Pa.

A tourniquet must be of sufficient width to prevent injury to the patient. This is because a thinner tourniquet requires higher force to apply the same overall pressure, which could cause nerve damage [3].

The strip applies a pressure by application of a hoop stress around the limb. The simplified equation for thin walled cylinder hoop stresses (σθ) is [4]:

σθ=Prt

(1)

where P is pressure, r is radius, and t is strip thickness. This can be equated to the stress in the band, given by force divided by cross-sectional area:

σθ =F

tw

(2)

where F is force and w is strip width. Equations (1) and (2) can be equated to find the force required for a certain pressure, shown in Equation (3). To get an estimate of force, a pressure of 80 mmHg (10666 Pa) is used, as this is between the 60-100 mmHg suggestion. The average strip width is 2 cm and the average American male’s arm radius is 46 cm [5] which provides a force of approximately 10 N.

F = Prw (3)

This simple analysis constrains the design – the patterned area must be able to accommodate a force of around 10 N. This will depend on the material properties and the pattern used. Also, the user must be able to apply the required force. Each hand will be required to apply approximately 10 N as this is the tension required for product application. This equates to the same approximate force as lifting a 1 kg weight, which is no problem for anyone that is fit and healthy.

For use in a medical environment, many criteria must be met, for example:

• Stiffness - the pressure exerted by the patterned area of the strip must be in the range 60-100 mmHg.

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• Tearing force – the patterned area of the strip must tear sufficiently above the required pressure range, e.g. at 150 mmHg.

• Robustness - the force indicator must provide repeatable results. • Water Resistance – the product must not degrade in contact with fluids, e.g. sweat or

blood. • Ease of use – the required force to apply strip should be within capabilities of all fit

and healthy end users. • Patient Comfort – the band should be comfortable to wear, e.g. no sharp edges,

preferably breathable.

Other material properties such as environmental considerations, cost and machinability must also be considered, but these are not applicable to the medical requirements.

2.1.2 – Current Solutions and Materials

Currently, there are two common methods of pressure application – a strap tourniquet and a sphygmomanometer, or blood pressure cuff. Both are shown in Figure 2. The strap tourniquet can be made from canvas or rubber and can be tied or secured by buckle or Velcro. This method of pressure application is quick but does not allow for accurate pressure application and hence relies on the experience of the medical staff. The sphygmomanometer is an alternative that is often used when a result cannot be achieved by simple tourniquet. It is more accurate but is more time consuming and cumbersome to apply, the cuff must be the correct size to read accurate pressure, it must be held upright to read the dial accurately, the equipment is more expensive and often contains mercury – a hazardous substance. [6]

Figure 2 - Images of current methods of applying pressure to a patient's arm. Left) a buckled strap type tourniquet [7, image]. Right) A blood pressure cuff, or sphygmomanometer [8, image].

2.2 Kirigami Metamaterials The novel innovation in Ortrud Medical’s tourniquet design is the use of a Kirigami ‘pattern’ to reduce the resistive force of a 2D material. Kirigami is a Japanese paper art which involves cutting and folding. It can be used to alter the properties of a sheet of 2D material and turn it into a metamaterial – a material engineered to produce properties which do not occur naturally [9]. Kirigami metamaterials can be created in many different forms. Properties such as stiffness and Poisson’s ratio can be changed by altering cut lengths or patterns.

2.2.1 – Altering Stiffness

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Cutting a repeating pattern into a 2D sheet will decrease the in-plane stiffness of the sheet. Different patterns and pattern dimensions can be used to tune the stiffness [10]. Patterned defects can also be used to change the material properties of a 2D sheet in 3 dimensions – such as increasing buckling stiffness, as shown in Figure 3 [11].

Figure 3 - Image showing a flat foldable sheet which has much higher rigidity than the corresponding flat sheet (inset). This illustrates how Kirigami can be used to alter the stiffness in three dimensions [11].

2.2.2 – Poisson’s Ratio

Poisson’s ratio is the ratio of transverse contraction to longitudinal extension in the elastic regime when a force is applied to a material sample [12]. Specific ratios can be engineered into Kirigami metamaterials, by choice of slit pattern [13]. Poisson’s ratio is an important aspect of the tourniquet design because a specific pressure is required, and if the pattern contracts laterally during longitudinal strain then the total area that the hoop stress is applied over would be reduced and hence the overall pressure. Therefore, a Poisson’s ratio of zero would be ideal. Auxetic structures and materials have a negative Poisson’s ratio [14]. Such structures could be built into the pattern to negate thinning due to stretching.

2.2.3 – Pattern Deformation Regimes

For application to the tourniquet product, the main considerations are the stiffness and tearing force of the metamaterial. Many patterns have been experimented with, however I will focus on a simple parallel offset slit pattern, shown in the rendered test specimen in Figure 4, as this will simplify analysis by reducing complications in deformation regimes and stress concentrations which allows for a fairer comparison of materials. The pattern will alter the stiffness properties and increase the maximum strain of the 2D material.

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Figure 4 - Rendered image of an FEM test sample, where the staggered offset pattern can be seen.

Figure 5 – Graph with accompanying images to illustrate each of the three distinct deformation regimes [15].

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The introduction of cuts to the 2D material causes an unnatural change to stress/strain relationships. Unnatural deformation modes are realised when out of plane deformation occurs, caused by mechanical instability, as shown in Figure 5. The initial regime exhibits in-plane bending in each paper ‘beam’. In the second regime, the rotation and out of plane bending allow for more strain. In the third regime, the deformation is localised at the slit edges, which are stress concentrators, until tearing occurs [15].

Figure 6 – A) Schematic of the defining geometries of the simple slit pattern. B) Image of the deformed pattern, showing how each strut can be approximated as 2 beams [16].

The initial in-plane deformation regime can be approximated by modelling each strut as 2 beams of length L, as shown in figure 6B. Each ‘strut’ is the length of cut which overlaps with the cut below. The beams can be approximated as two free-end cantilevers (beam 1 and beam 2 from figure 6B), and upon application of simple beam bending theory, the deflection in each strut can be approximated as follows [16]:

where F is force, L is length of beam, E is Young’s modulus, w is the width of the beam and t is the thickness in the direction of deflection.

This can be rearranged for force and the stiffness can be multiplied by the ratio of the number of struts (Nstrut) to number of rows in the sample (Nrow) to find the total force. Substituting L (length of beam) for cut parameters Lc and x (note that w, beam width, is equal to y, vertical cut spacing), the total force can be expressed as follows [16]:

Noting that:

𝐹𝐹𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 =𝑁𝑁𝑠𝑠𝑡𝑡𝑠𝑠𝑠𝑠𝑡𝑡𝑁𝑁𝑠𝑠𝑡𝑡𝑟𝑟

8𝑑𝑑𝑑𝑑𝑑𝑑𝑡𝑡3

(𝐿𝐿𝑐𝑐 − 𝑥𝑥)3

𝐿𝐿 = 𝐿𝐿𝑐𝑐−𝑥𝑥4

(5)

(6)

𝑑𝑑𝑠𝑠𝑡𝑡𝑠𝑠𝑠𝑠𝑡𝑡 =

8𝐹𝐹𝐿𝐿3

𝑑𝑑𝐸𝐸𝑡𝑡3

(4)

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Equation (6) shows that for small deformations, the Young’s modulus of the material and the vertical cut spacing (y) are proportional to the force required to extend it at a certain deflection. Also, the cut length minus horizontal spacing, Lc – x, is inversely proportional to the power of 3 to this force.

This analysis applies to the beam pre- buckling. Post-buckling deformation is much more advanced and hence experimental or computer simulated analysis is more appropriate for analysis in these regimes [16].

Figure 7 - Experimental and FEM-calculated (inset) stress-strain curves for changing unit cell parameters. The curves show the trends of a) increasing x, b) increasing y and c) increasing Lc [17].

Figure 7 shows the effects of different pattern parameters for tensile tests at larger deflections, which are summarised in Table 1. The most intuitive result is that of increasing cut length, as the continuous theoretical path length is increased with a longer cut length, so the maximum strain will be larger. The stress is decreased in this case as the longer ‘beams’ offer less resistance.

Table 1 - Summary of the effects of changing dimensions that can be seen in Figure 7. ‘Stiffness’ is regarded as the stress/strain gradient in the second deformation regime.

Geometry change Effects Increase x Increased max stress, increased max

elongation, similar stiffness Increase y Same max stress, decreased max strain and

similar stiffness Increase cut length Reduced max stress, increased max strain,

similar stiffness

2.3 Materials This study will analyse the feasibility of a range of material choices dependant on the specification criteria. A range of 14 materials have been sourced.

Many of the materials investigated in this study are composite materials, in the form of layers of different materials sandwiched together under pressure and heat. For example, in Material 8 the combined properties of paper and plastic materials result in a material which has high stiffness, tearing strength and water resistance.

The materials supplied are largely packaging materials. Given their application, their material properties are not fully documented. This will mean that pre- test analysis and detailed discussion pertaining to inherent material properties will not be possible, however performance metrics will be generated through testing which will allow ranking of the materials by use of

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Pugh’s evaluation matrix. Such performance metrics will include analysis of stress/strain curves, tensile yield and other application related tests detailed in section 2.1.1.

2.4 Product Manufacturing Methods The product is manufactured by cutting from a sheet of material. Some advantages and disadvantages are summarised below.

2.4.1 - Laser Cutting machine

The experimental samples and prototypes will be manufactured using an Epilog Fusion M2 laser cutter. As the material samples are all films or papers, it is advisable to cut quickly on high power rather than slowly on low power which could cause edge imperfections and singes.

Tests will need to be carried out to obtain the correct settings for each material. The laser settings, power, speed and frequency will need to be tweaked to obtain high quality test samples.

Laser cutters offer quick prototyping, and the laser will not deteriorate through use. Their nature of operation is to remove a small amount of material which can be significant enough that it cannot be neglected.

2.4.2 – Knife cutter/plotter

Whilst vector knife plotter cutters exist, they are not widely used as laser cutters are favourable for prototyping. Cutting with a scalpel by hand can be good for quick prototypes but results are not repeatable due to the loss of precision in human error. Knives also become dull over time reducing repeatability in results and requiring replacement periodically.

2.4.3 – Industrial Stencil Press

These machines are preferred for the mass production of this product due to their speed and repeatability. However, there are long lead times and prototyping is not possible as products are fabricated in large quantities using a stencil.

2.5 Finite Element Modelling (FEM) Methods Finite Element Modelling (FEM) is powerful tool for product prototyping and testing. Accurate results can be found for complex loading schemes and geometries using FEM. Mechanical structures (continuums) are broken down into finite elements for analysis. Discretising (meshing) the structure creates elements and nodes. The governing differential equations of these discretised forms are solved, and an approximate solution is formed, the results of which approach the true continuum solution with smaller and smaller element sizes. The meshing size is refined until results show no significant change. FEM software will then output stresses, strains and displacements at each node, given sufficiently constrained boundary conditions [16].

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3 MATERIAL FEASIBILITY STUDY

A selection of materials deemed viable for this application have been supplied by Ortrud Medical’s current material supplier. The purpose of this study is to systematically select the most suitable material depending of a range of performance criteria which the product must satisfy. Pugh’s evaluation matrix will be used to rank and select the most suitable material.

3.1 Evaluation Criteria As discussed in Section 2.1, the product must adhere to a range of criteria to fulfil its purpose, outlined in Table 2 below.

Table 2 - Criteria which the product/material must fulfil.

Criterion Requirement/ Description

Tearing Force The IV strip must tear sufficiently above the required pressure range. The upper limit of the required pressure range is 100 mmHg (13300 Pa) which relates to an approximate force (from the hoop stress approximation) of 12 N. Taking a safety factor of almost 2, the test specimens must exceed a tearing force of 20 N.

Stiffness Stiffness of the strips is determined through tensile testing. This is heavily dependent on the deformation regime, as shown in Figure 5.

Robustness Repeatability of results show that pressure application is reliable. The deviation in tensile test results for each material will indicate how well they fulfil this criterion.

Water Resistance

The product must be able to continue to function in the presence of fluids such as saliva, sweat and blood which are present in a medical environment.

Environmental Considerations

The product must be as environmentally friendly as possible, from production to disposal. Therefore, the material choice and especially the elements which make up the material are of interest.

Patient Comfort

The material must provide sufficient patient comfort. For example, slippery film surfaces, sharp edges or potentially skin-irritating materials are not desired.

Tactility and Ease of Use

The product should be very easy to use, given the stressful medical surroundings. Therefore, material tactile properties are of interest.

Cost Material cost is a strong driving factor as it is a variable cost in the product manufacture. Unfortunately, no costing is available, so this will not be accounted for.

Machinability In production, the product is cut using an industrial stencil press. In testing, a laser cutter is used for prototyping, so the actual machinability cannot be speculated from the laser cutting results.

3.2 Tearing Force Testing 3.2.1 – Purpose of Test

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This test will screen out unwanted materials that do not meet the tearing force criterion. It will also provide an idea of the deformation modes in each material and provide an indication of the ultimate tensile stress. Speed of loading may alter the tearing force compared to the tensile tests conducted later. Material candidates may also be disqualified depending on any other criteria. Figure 8 shows the test equipment used to determine the tearing force of each specimen.

Figure 8 - Image of the test equipment with a loaded specimen.

3.2.2 – Test Equipment

The test equipment is comprised of the following instruments and tools:

• Custom made screw-down material clamp • Clamped rig • Newton meter • Test samples of each material • Cord

3.2.3 – Test Procedure

Four test specimens are cut from each material using the laser cutter. The dimensions are specified in Table 3 and are derived from previous product specification provided from Ortrud Medical. The test specimens were cut using a laser cutter, the specific settings of which are not relevant.

Table 3 – Dimension values for the test pieces used in the tearing force experiment.

Dimension Value (mm) x 2 y 2.5 Lc 4

Total pattern width 37.1 Total pattern length 35

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As shown in Figure 8, the test specimens were loaded into the custom clamps at either end, with one clamp being hooked onto the newton meter, set to read peak force. The other clamp was pulled by a cord through the central hole to ensure even force distribution – one sided force application could promote tearing. Pulling force was increased until tearing, and the peak force noted from the newton meter after tearing.

3.2.4 – Test Result

Figure 9 - Graph of the tearing forces of each material, ranked in increasing order. The bars are colour coded. Red is a paper material, purple are fibrous materials, blue are plastic films and green is a composite material. Error

bars show the standard error for each material, calculated from a set of four tests.

3.2.5 – Test Conclusions

Figure 9 shows how tearing force of the material samples varies greatly, from less than 10 to more than 40 N. Material types are highlighted. The paper material is very weak whilst the composite material is one of the strongest. Due to the requirements of the product, the very weak samples (less than 20 N) will be screened out of further materials testing. Material 5 was also screened out because it fractured violently in a brittle fracture with limited necking, leaving sharp edges, which is potentially harmful, especially given the product application. Material 3 has very variable measurements, as can be seen from the standard error bars on the graph. This leaves material numbers 4, 9, 1, 6, 3 and 8 for further testing.

3.3 Tensile Testing 3.3.1 – Purpose of Test

This test provides an insight into the critical points in the deformation modes of specimens made from each material. The remaining screened materials will be tested here. This test is not a true tensile test as elongation is a dependent variable and force is an independent variable, so the

0

5

10

15

20

25

30

35

40

45

50

7 14 2 12 10 13 11 4 9 1 6 3 8 5

Ave

rage

Tea

ring

For

ce (N

)

Material Sample Number

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resistive force cannot be decreased. In a true tensile test, strain is the independent variable and resistive force is measured via a force load cell. Figure 10 shows the equipment used to collect tensile profile data for each specimen.

3.3.2 – Test Equipment

The test equipment is similar to that used in the tearing force testing, and is comprised of the following instruments and tools:

• Custom made screw-down material clamp • Clamped rig • Metal bar and hook to secure sample to rig • Test samples of each material • Basket to hold masses • Bearing to act as pulley • 100 g, 500 g, 1000 g masses • Rope • Ruler and indicator tab

Figure 10 - Image showing the tensile testing setup. Weights are loaded into the bucket and the extension noted from the metal tab resting against the ruler. Two ball bearings are used to change the force direction as they have very

little friction.

3.3.3 – Test Procedure

Firstly, the test specimens are prepared as they were in section 3.2.3, although the total specimen length is increased to 100 mm. This will not affect strain measurements but allows for more accurate measurements as the deformations are larger and therefore the percentage error in the strain measurement is reduced.

As shown in Figure 10, the test specimens are loaded into the custom clamps at either end, with one clamp being hooked onto bar which is clamped into the rig. The other clamp was pulled by a rope through the central hole to ensure even force distribution. The rope is passed over a bearing

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which acts as a pulley. A basket is attached, and masses are added in 100 g intervals, waiting 2 minutes between each extension reading and mass addition to allow for creep. It should be noted that the bucket and cord weigh 47.9 g. This weight is required to ensure the specimens are taut before adding load. Consequently, all strain measurements are relative to 0% strain defined at a force of 0.47 N. This is not ideal but, given that the results are all taken equally this will not hinder the comparison of the material’s performance in this criterion.

3.3.4 – Test Result

Figure 11 - Tensile testing data for each of the remaining material candidates.

Figure 11 shows the large variation in stress/strain profiles. Note how the tearing force has changed from test 3.2 for some materials – this is due to dynamic properties of the materials which will not be investigated further. Individual stress-strain curves with repeated tests are shown in Appendix II. The median values are taken from the individual material test repeats, as a mean average for each force would not be representative as minor sample differences mean that readings from each sample are not directly comparable.

3.3.5 – Test Conclusions

Material 3 had very variable results which provide very little robustness. It is assumed that this is due to the random large-scale fibrous microstructure, shown in Figure 12. The profile of materials 3, 9 and 12 show extensive necking and little signs of change in deformation modes. These materials entered the second deformation mode very early and continued to deform plastically for a long time, which shows high ductility. Materials 1, 4 and 6 all have ‘s’ shaped profiles, each inflection point being a transition into the next mode of deformation. Due to its rigidity, material 8 (control) remained in the first mode of deformation for a very long time before snapping into the second/ third modes and tearing soon after.

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Figure 12 - A close-up photograph of Material 3, showing the random large-scale fibrous microstructure which is likely to be the cause of the variable tensile results.

3.4 Qualitative Criteria Evaluation There are four remaining criteria which can be evaluated qualitatively:

1. Water Resistance 2. Environmental considerations 3. Patient comfort 4. Tactility and ease of use

These criteria strongly rely on material surface condition, notes of which are summarised in Table 4 for each material. The materials will be ranked in section 3.5.

Table 4 - qualitative material notes, detailing material surface condition.

Material #

Qualitative Notes

1 One side gloss, one side matt, both plasticky feeling, not absorbent, good water resistance.

4 One side gloss, one side paper, likely to be affected by water. 6 One side gloss, one side matt, both plasticky feeling, not absorbent, good water

resistance. 8 One side gloss, one side paper. Breathable, but likely to be affected by water. 9 One side gloss, one side matt, both plasticky feeling, not absorbent, good water

resistance. 12 Glossy film, assume high water resistance.

3.5 Material Evaluation – Weighted Pugh’s Matrix A weighted Pugh’s matrix is used to evaluate the performance of each material and choose which is most suitable for the product. Firstly, the importance of each criterion is weighted and then the material candidates are ranked based on their performance in each criterion [19].

Table 5 - Scores of relative importance for each of the material evaluation criteria.

Criterion Description for higher score Relative importance (/10) Tearing Force Higher force 8 Deformation More dramatic critical deformation

transitions 8

Robustness Less variable measurements 8

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Water Resistance More resistant 7 Environmental Less environmental impact 5 Patient Comfort More suitable for patient comfort 5 Tactility/ ease of

use Easier to use 5

Table 5 shows the relative importance of each criteria. Tearing force and water resistance are highly weighted because repeatable pressure application is critical. Environmental considerations, patient comfort and tactility/ease of use also hold lower weightings because, whilst they are important considerations, they are not critical for medical functionality of the product.

Table 6 - Pugh's Evaluation Matrix, which concludes that materials 1, 6, 9 are all viable material choices with the highest score of 15.

Criteria

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Resistance 7 + - - + + +

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and Tactility/Ease

of use

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Weighted + 0 23 8 21 23 23 15 Weighted - 0 8 28 20 8 8 21

Weighted Total 0 15 -20 1 15 15 -6

Table 6 shows that materials 1, 6 and 9 are all better material candidates than the control (material 8, a material in use), given the weightings and the criteria used.

The evaluation matrix is compiled by first deciding whether a material performs better or worse than the datum in a specific criterion. This decision is evaluated by considering material surface properties - outlined in Table 5, and materials testing results – summarised in Figure 11.

To decide on the best material to continue testing with, the relative merits of materials 1, 6 and 9 must be evaluated. Material number 6 has less thickness and weight than materials 1 and 9. This would give a better environmental score but is counteracted by the lower weight making the product feel less substantial. Material 6 has the most non-linear stress-strain curve and has the highest tearing force (of the three), so in balance this material is the most suitable.

To conclude, the chosen material candidate (Material 6) exhibits superior mechanical properties, meeting the criteria for deformation range, robustness and tearing force well. The tactile and waterproof surface finish means that the material is also well suited for use in a medical environment as it is easy to handle and would not degrade in the presence of fluids.

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4 GEOMETRY TUNING STUDY

Given that the product is to be used in medical operations, it is vital that it fulfils the purpose accurately and effectively. Assuming an exact force is required every time, it would be useful to know the relationship between metamaterial pattern stiffness and the pattern geometry dimensions. In this study, the effect of Lc (cut length) will be investigated as it is one of the more influential pattern parameters as seen in Figure 7.

4.1 FEM Simulation ANSYS 18.2 commercial FEM software is used to explore correlations between changing the cut length dimension and pattern stiffness. The results will be cross checked against published sources and experimental data.

4.1.1 – CAD test file preparation and initial testing

SolidEdge™ was used to prepare the samples, with the dimensions specified in Table 7. An initial FEM analysis was carried out using the built in Simulation tool. Although unable to probe deformation or stresses, the tool provided an interesting visual representation of the stresses in the sample, shown in Figure 13. This clearly shows that the slit edges are stress concentrators and that the areas connecting the slit edges are under higher stresses.

For further testing, the CAD samples were imported to ANSYS™ using the geometry import tool. The slots for the pattern samples were distributed over a 0.05 mm (50 micron) thick plate using the rectangular pattern tool. This was repeated for each Lc (cut length). Figure 4 shows a sample for a cut length of 3 mm.

Figure 13 - Strain magnitude plot from SolidEdge™.

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Table 7 - Geometry dimensions for the simulation test specimens. These dimensions were chosen to capture the width of the product whilst the length was reduced to reduce computational expense.

4.1.2 – Specifying Engineering Data

No physical material properties data was available for the material samples. However, many of the material samples contain oriented PET, of which Mylar™ is a common trademarked material which consists of oriented PET fibres. The data for this material was found from the supplier’s website, and can be found in Appendix I.

Although this data does not provide any plasticity and elasticity data (which is likely to be non-linear) it can be assumed that for small strains (in plane deformation) the data is adequate.

4.1.3 – Model Simplification

It is possible simplify the model whilst including all data of the tessellated pattern, which would speed up computing times and allow for a smaller meshing size which is more accurate. However, this was not carried out, in order to capture the effect of the decreased total intact cross-sectional area as cut length is altered, given that the total strip width will stay constant.

4.1.4 – Boundary Conditions

Boundary conditions are required to fully constrain the constitutive equations in the FEM model. For this model, a fixed support (no freedom in any direction or rotation) is applied at the top end of the sample, whilst a displacement of 2 mm (in plane deformation limit) is prescribed at the lower end of the sample. Thus, the FEM model is fully constrained, and the resistive force can be probed at either end of the specimen during stretching to determine the tension in the strip.

4.1.5 – Mesh Convergence Study

The purpose of a mesh convergence study is to reduce element mesh sizing until no further reduction alters the result of a critical parameter [20]. A study was carried out on a 3 mm cut length sample, varying the mesh sizing from 3 mm down to 0.5 mm in 0.5 mm increments. The critical parameter was chosen as the normal reaction force at the displaced end, at a displacement of 2 mm. This parameter was chosen as it is the result that we will be using for analysis. Appendix III contains a graph of the converging solution, which was assumed to be satisfactorily converged at a mesh size of 0.5 mm.

4.1.6 – FEM Results

The resistive force was probed at the boundary condition of the lower end of the strip at 0.2 mm displacement intervals. Figure 14 shows the FEM results for percentage elongation against resistive force, the results of which show a linear correlation for each cut length. Figure 15 is a trendline of resistive force at 5% (2 mm) elongation for each of the cut lengths, which produces an inverse correlation.

Property Value Pattern Width 37.1mm

Patterned Length 40mm Total Specimen Length 60mm

Horizontal Distance between cuts 2mm Vertical distance between cuts 2.5mm

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Figure 14 – FEM result graphs for each cut length in small scale deformation, showing the resistive force at different percent elongation.

Figure 15 - Trend of resistive force at 2 mm (5%) elongation for each cut length.

4.2 Stiffness Tuning Experimentation Material 6 is chosen for further investigation in this experiment due to the interesting stress/strain profile. Figure 7 shows the effects of changing some geometry dimensions. It is shown that the dimensions x and y, the horizonal and vertical cut spacings respectively, do not affect the stress/strain profiles dramatically, therefore the dimension Lc can be changed to tune the strip tension and tearing force to the desired value.

4.2.1 – Purpose of Test

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The purpose of this test is to investigate the effect of changing pattern dimensions on the tensile testing results and ‘tune’ the pattern to achieve the desired stress/strain relationships. This test is not a true tensile test as elongation is a dependent variable and force is an independent variable, so the resistive force cannot be decreased.

4.2.2 – Test Equipment

The test equipment is identical to the test outlined in section 3.3.

4.2.3 – Test Procedure

The test procedure is similar to the test carried out in section 3.3, however patterns with differing cut lengths will be investigated (3, 4, 5, 6 mm) with all test specimens being prepared from Material 6.

4.2.4 – Test Result

Figure 16 - Experimental data averages for each cut length. Forces at the transition point between phases 2 and 3 are shown.

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Figure 17 - Trendlines for the force at inflection point and the force at breaking point for each cut length. Trendline equations are shown on the graphs.

4.2.5 – Test Conclusions

Figure 16 shows that the profile shape is clearly preserved for every cut length, but it is stretched – the maximum force decreases and the maximum strain increases as the cut length is increased. The forces at the transition points between deformation phases 2 and 3 are plotted on the inflection point trendline in Figure 17. These points are plotted as they show the maximum elastic strain. Using the 3rd order polynomial line fit (equation shown on graph) the cut length required to provide 10 N of resistive force at this inflection point is 4.40 mm. (given that the horizonal and vertical cut spacings are 2 mm and 2.5 mm respectively).

The trendline in the breaking point trend graph in Figure 17 can also be interpolated to find the breaking force for a cut length of 4.40 mm. Using the 3rd order polynomial line fit equation, the breaking force is determined as 18.28 N, which is acceptable.

4.3 Comparison of FEM and Materials Testing Results Although small-strain experimental data is not available due to the limitations of scale in the apparatus, some similarities can be read by comparing the FEM results and the experimental results, as shown in Figure 18.

The general trend of stiffness against cut length seems to be of an inverse nature for both the FEM and experimental data. Note that the FEM results are only similar to the experimental results when the deformation is very low (0.2 mm). The force magnitudes are also around 50% larger in the FEM tests. Further material properties will need to be supplied or investigated to improve this result. One possible solution would be to input pristine material sample tensile test results into ANSYS™, which can then calculate the elastic properties of the material.

The FEM results in Figure 14 are almost completely linear, which they should be according to the simple beam bending theory presented in section 2.2.3. It is unclear whether the experimental results in Figure 16 are linear at small deformations, again because of the limitations of scale in this equipment.

Unfortunately, at this stage the model requires some more information and refinement to be applied to Simulation Driven Design.

y = -0,1635x3 + 3,924x2 - 31,228x + 85,347 0

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Figure 18 - Graph showing the comparison of force at small deflection against cut length for FEM and experimental data sources. The theoretical results are included in Appendix III, however these results are not included here as they do not show agreement with the FEM or experimental results because they are quite rudimentary calculations considering the short beam lengths.

y = 13,137e-0,442x

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5 DISCUSSION AND CONCLUSIONS

The conclusions are based from the analysis with the intention to answer the formulation of questions that is presented in Chapter 1.

5.1 Discussion The aim of this thesis was to document and analyse the suitability of a range of materials by using both qualitative and quantitative methods, selecting the most suitable material for the product of interest. The possibility of tuning the selected material to meet the tensile requirements was then investigated by both computational and experimentational methods and the results were compared to determine the feasibility of the computational model.

The evaluation criteria were chosen through research into the medical requirements of the product, and parameterised where possible to be directly relatable to the results of specimen tensile tests.

The materials were investigated based on their suitability to this product, which involved careful consideration of the product criteria and evaluation based on Pugh’s evaluation matrix. This method of comparison enabled comparison of the performance of the material candidates in a range of criteria in relation to the control material, in this case a material in use. By not assigning individual scores and instead stating whether the material is simply better or worse than the control material, the performance of a material in a specific criterion may not receive all due credit. This work is not therefore fully comprehensive or precise but does allow for an efficient and adequate comparison of possible materials, especially as many quantitative criteria need only to meet a certain value. The mechanical properties criteria such as stiffness and tearing force rely on data from experiments 3.2 and 3.3. The test equipment was built at KTH, a commercial material testing machine would have been more accurate. This rig had its limitations, especially in experiment 3.3. There was a small amount of friction at the scale which caused it to stick occasionally and the bucket weight skewed the datum point as the specimens were under slight tension before the first load was added. Also, the extension was read from the scale by eye, which introduced human error, and the effects of acceleration of the applied load were neglected as the effect of stress wave propagation is deemed insignificant [16]. These experimental weaknesses do not make the results obsolete, and errors are minor and systematic, so data are still good for comparison of materials. Repeat measurements at each data point reduce the likelihood of random errors.

Experiments were carried out to determine the effect of changing the cut length, one of the most influential parameters to pattern stiffness. The purpose of such investigation was to enable tuning of the product to stiffness and breaking force preferences. A mathematical model was derived, enabling cut length to be chosen by interpolation to provide the preferred breaking stress or deformation criteria. This could be used to provide a specific set of deformation criteria if required in other revisions of the product. For example, given a patient’s arm circumference, the cuts can be fabricated to provide the perfect amount of resistance to apply the required pressure on the arm for optimal IV access conditions. The effect of changing vertical and horizontal spacings between cuts was not investigated due to time constraints, however further experimentation with these parameters could produce a more complete and complex model, albeit unnecessary for this study as tuning can be achieved by changing only one parameter. The model could be improved by collecting more data to make the predictions more accurate, however it serves at a proof of concept. The correlations drawn from the results agree with and

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build upon the correlations found in Figure 7 [3] and Table 1. Reference [3] states that ‘increasing the cut length weakens the material, lowers its critical buckling load, and increases its extensibility’, which matches the correlations shown in Figure 16. The tensile tests from this study [3] were carried out on a material testing machine and each curve was averaged over seven samples. Due to the difference in materials and methodology used, the two studies are not directly comparable, but the trends match.

The results from the FEM study of the effects of changing cut length were compared to the experimental results, and it was found that, whilst the magnitude of the results differed slightly from the experimental results, the FEM model predicted trends in tensile profiles well. As seen in Figure 18, the magnitude of the FEM reactive forces were, on average, 50% larger than the experimental magnitudes for each extension – this is likely due to inaccuracies in the material data used. There were also limitations in the scale increment of the experimental testing that prevented a more in-depth comparison of the two methods at small deformations. The FEM model is limited by the requirement of full material properties to provide accurate results, especially as different deformation regimes such as plastic deformation are being considered. This meant that evaluation with FEM at larger strains was not possible as the small-strain assumptions are not valid at large deformation. It also does not describe fibrous morphology observed in typical paper samples [16], whereas such morphologies and directional material properties are found in many of the materials investigated in this study. More advanced material data is required to increase model effectiveness and enable the use of simulation driven design.

5.2 Conclusions In the material selection study, evaluation criteria were defined and evaluated to optimise product functionality. This is an important study given the medical nature of the product and proved interesting given the shortage of previous materials documentation owing to time constraints.

The pattern dimension tuning study has provided a mathematical model relating cut length to breaking force and deformation properties – which had not been previously investigated or regarded. The introduction of this computational means of mechanical tunability offers new possibilities for the product.

FEM methods have validated some experimental trends in tensile data and provided insight into deformation dynamics such as stress distributions, however their application to the modelling of this product requires a more in-depth study, namely into deformation properties of the materials in use. This information would allow FEM methods to be used to their full advantage, enabling faster and more cost-effective comparison of material candidates and product prototype generation.

5.3 Further work Conclusions drawn from this thesis could be elaborated on in further investigations and product development. Further work could include:

• Product prototyping and testing on patients rather than just lab tests. • Refinement and further development of FEM model to test different geometry

dimensions in this pattern and other patterns, and investigation of advanced mechanical data to improve accuracy.

• Investigation of a wider set of materials. • Model the effects of horizontal and vertical cut length spacing on pattern stiffness.

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6 REFERENCES

[1] (no author) (2017). “New metamaterial based on Japanese art of Kirigami.” Retrieved 24/08/18 from https://materia.nl/article/new-metamaterial-kirigami/

[2] David Mbamalu, Ashis Banerjee. (1999). “Methods of obtaining peripheral venous access in difficult situations.” Postgrad Med J. Retrieved 04/05/18 from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1741330/

[3] Charlotta Olivecrona et al. (2013). “Tourniquet cuff pressure and nerve injury in knee arthroplasty in a bloodless field.” Acta Orthopaedica. Retrieved 04/05/18 from https://dx.doi.org/10.3109%2F17453674.2013.782525

[4] Steven R. Schmid, Bernard J. Hamrock, Bo. O. Jacobson. (2014). “Fundamentals of Machine Elements, Third Edition: SI Version.” CRC Press. Chapter 10: Stresses and Deformations in Cylinders.

[5] Cattermole, G. N., Graham, C. A., & Rainer, T. H. (2017). “Mid-arm circumference can be used to estimate weight of adult and adolescent patients.” Emergency Medicine Journal. Retrieved 5 4, 2018, from http://emj.bmj.com/content/emermed/early/2016/12/19/emermed-2015-205623.full.pdf

[6] Karen J. Tietze. (2012). “Clinical Skills for Pharmacists (Third Edition).” Mosby. Chapter 4 – Physical Assessment Skills.

(references 7 and 8 refer to image sources cited under ‘Images and Figures’)

[9] (no author) (no date). “Metamaterials.” Institute of Physics. Retrieved 24/08/18 from http://www.iop.org/resources/topic/archive/metamaterials/

[10] Doh-Gyu Hwang & Michael D. Bartlett. (2018). “Tunable Mechanical Metamaterials through Hybrid Kirigami Structures.” Nature Scientific Reports. Retrieved 04/05/18 from https://www.nature.com/articles/s41598-018-21479-7

[11] Rafsanjani, Ahmad and Bertoldi, Katia. (2017). “Buckling-Induced Kirigami.” Phys. Rev. Lett. Retrieved 04/05/18 from https://link.aps.org/doi/10.1103/PhysRevLett.118.084301

[12] Rod Lakes. (no date) “Meaning of Poission’s Ratio.” Retrieved 24/08/18 from http://silver.neep.wisc.edu/~lakes/PoissonIntro.html

[13] Yichao Tang, Jie Yin. (2017). “Design of cut unit geometry in hierarchical kirigami-based auxetic metamaterials for high stretchability and compressibility.” Extreme Mechanics Letters. Retrieved 04/05/18 from https://doi.org/10.1016/j.eml.2016.07.005

[14] R. Neville, F. Scarpa, A. Pirrera. (2016). “Shape morphing Kirigami mechanical metamaterials.” Retrieved 24/08/18 from https://www.nature.com/articles/srep31067.pdf

[15] Midori Isobe & Ko Okumura. (2016). “Initial rigid response and softening transition of highly stretchable kirigami sheet materials.” Scientific Reports. Retrieved 04/05/18 from https://www.nature.com/articles/srep24758

[16] Terry C. Shyu. (2016). “Engineering Responsive, Tunable, and Multifunctional Composites.” University of Michigan. Retrieved 04/05/18 from http://hdl.handle.net/2027.42/120756

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[16] Y. Tang, G. Lin, S. Yang, Y. K. Yi, R. D. Kamien, J. Yin. (2017). “Programmable Kiri-Kirigami Metamaterials.” Advanced Materials. Retrieved 04/05/18 from https://doi.org/10.1002/adma.201604262

[17] Terry C. Shyu et al. (2015). “A kirigami approach to engineering elasticity in nanocomposites through patterned defects.” Nature Materials Journal, 10.1038/NMAT4327. Retrieved 04/05/18 from https://www.nature.com/articles/nmat4327

[18] David Silverstein, Philip Samuel, Neil Decarlo. (2009). “The Innovator's Toolkit: 50+ Techniques for Predictable and Sustainable Organic Growth.” Breakthrough Management Group International. Technique 36, Pugh Matrix. [19] (no author) (no date). “The Importance of Mesh Convergence.” National Agency for Finite Elements and Standards. Retrieved 24/08/18 from https://www.nafems.org/join/resources/knowledgebase/001/

Images and Figures - these links are to provide recognition to the image sources, which are used for illustrative purposes only and do not constitute any scientific interest.

[7, image] https://www.doccheckshop.eu/en/Practice/Injection-Infusion/Tourniquet/Praemeta-Tourniquet-Replacement-Strap-for-the-Grey-One.html

[8, image] https://www.amazon.com/LotFancy-Pressure-Sphygmomanometer-Stethoscope-Approved/dp/B0126MS5VA

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APPENDIX I: MATERIAL DATA

The data for Mylar™ material, used in the FEM analysis, is tabulated below. This data was found on a manufacturer’s website: http://www.matweb.com/search/datasheettext.aspx?matguid=4868d027ab83480db97d1d3e4c84426e

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APPENDIX II: TENSILE TESTS

Here the repeated test results are shown from each material. Figure 11 contains the average result from tensile tests for each material/cut length.

Note – a fourth test was carried out on material number 3 as the results were so variable. Also, axes go higher than on other graphs – 40 instead of 25.

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APPENDIX III: MESH CONVERGENCE STUDY

Here the mesh convergence study data is summarised and briefly discussed.

Figure 19 – Reaction force at 5% elongation – this should converge to a constant value as the mesh size is

decreased. The reaction force values at mesh sizes of 2.5, 2, 1.5 and 1 mm are all very similar suggesting that the solution has converged. A mesh size of 0.5 mm was used in the simulations to ensure mesh convergence, given that

computational power or time did not differ greatly at this mesh size, and convergence is certain.

Figure 20 – Inclusion of the theoretical result in comparison with the FEM and experimental results, which is found to be invalid, as discussed in the caption of Figure 18.

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