inflatable silicone cells, zoi-karagkiozi 2012

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INFLATABLE SILICONE CELLS

Simulaon and analysis of dierent aggregates

using parcle spring systems

Karagkiozi Zoi

This dissertaon is submied in paral fullment of the requirements for the degree of Master of

Science in Adapve Architecture and Computaon from University College London

Bartle School of Graduate Studies | University College of London | September 2012



I, Karagkiozi Zoi, conrm that the work presented in this thesis is my own. Where informaon

has been derived from other sources, I conrm that this has been indicated in the thesis.

Karagkiozi Zoi

UCL | AAC | 2012 | KARAGKIOZI ZOI | INFLATABLE SILICONE CELLS

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Abstract

In respect of the recent emergence of So Robocs as an innovave generaon

of robocs cras, so actuated pneumac networks with no rigid links or rotaon joints

challenge new potenal applicaons on responsive design. This study aempts to address

the challenge to fully predict and control the shape of their deformaon within a complex

aggregate paern. The proposed design strategy allows innate characteriscs and behaviors ofthe material system to be engaged into the computaonal design which is constantly updated

through feedback from the fabricaon process of the physical model. The computaonal

design tool is a generave algorithm that involves a process of negoaon between form

and integrated constraints based on a parcle spring system. An inial experiment is carried

out to determine its tness to the design problem of a single unit and then further tests

are conducted to test and report its eciency in more complex systems when aggregang

mulple components. The nal outcome indicates a design tool that is capable to control the

bend formaon of the physical model and provide results in small assemblies with high rate

of accuracy which gradually decreases as the prole geometry becomes more intricate by

aggregang larger assemblies.

Word count : 10370


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Acknowledgements

I would like to express my deepest gratude to my tutors:

Sean Hanna, for all his valuable supervision, support and inspiraonal discussions

Ruairi Glynn, for his inial advice and encouragement to work on the eld of So Robocs

Maria Eleni Scavara, for her support and paence

Also, I would like to thank my AAC colleagues:

Ben Haworth, for the construcve discussions on our common interest, So Robocs

Gkougkoustamos Stefanos, for his inspiraon and encouragement at all mes


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Contents

Abstract.........................................................................................................................................3

Acknowledgment..........................................................................................................................4

List of Illustraons.........................................................................................................................6

1.0 Introducon.........................................................................................................................8

1.1 Material Design....................................................................................................8

1.2 Responsive Materials-So Robocs.....................................................................9

1.3 The Architectural Problem and Thesis Aims........................................................9

1.4 Structure of the Thesis......................................................................................10

2.0 Background Research.......................................................................................................11

2.1 Free-form Metal Inaon and the Persistent Model.........................................11

2.2 Exploring Pneumac Networks within the design Context..............................12

3.0 Methodology.....................................................................................................................15

3.1 Fabricaon.........................................................................................................15

3.1.1 Observaon on Material System...........................................................15

3.1.2 Selecon of the structure geometry......................................................17

3.1.3 Experimentaon–Physical Tesng.........................................................17

3.2 Computaonal Design.......................................................................................24

3.2.1 Algorithm...............................................................................................24

3.2.2 Integrang Constraints..........................................................................25

4.0 Tesng and Results..........................................................................................................26

4.1 Tesng on Single Unit.........................................................................................28

4.2 Tesng on Double Component.........................................................................30

4.3 Tesng on Aggregate System of four components..............................................32

4.4 Tesng on Aggregate System of six components................................................34

5.0 Discussion.........................................................................................................................37

5.1 Overview of ndings..........................................................................................37

5.2 Crical Assessment............................................................................................38 5.3 Future Developments........................................................................................39

6.0 Conclusion.........................................................................................................................40

7.0 References..........................................................................................................................41

Appendix I..................................................................................................................................43

Appendix II..................................................................................................................................50


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List of Illustraons

Figure 1. Le: Detail of the connecon between discreet components to construct an aggregate. Right:

Schemac indicang how the persistent model (consisng of both representaon and arfact) is nest-

ed within the environment of operaon and coupled through lines of acon and feedback.( Source: <

hp://cita.karch.dk/Menu/Projects/Behaving+Architectures/Persistent+Model+%231+%282010%29>

..............................................................................................................................................11

Figure 2.Visualizaon using processing in 3D to explore spring Physics further. Points in a mesh are

displaced according both to the frequency and volume of the sound. The form of which is diminished

or augmented according to the strength of user’s voice. The mesh points behave in accordance to trig-

gered “guide” points by assessing the relave height of their neighbors.............................................13

Figure 3. The wrapping moon of a so robot during air pressure.....................................................14

Figure 4. So robot in a shape of star sh...........................................................................................14

Figure 5. Bend formaon towards the strong silicone layer...................................................................16

Figure 6. First prototypes of two acrylic moulds with dierent input channel......................................18

Figure 7. Acrylic mould with single big air channel for both silicone layers. The so silicone is the thicker

layer and contains the channel and the hard silicone is the thinner......................................................18Figure 8. Aggregate System : Four stages of the experiments..............................................................18

Figure 9. Aggregate paern of six components a, b, c, d, e and f with mixed bend formaon.............19

Figure 10. Proporon of the horizontal projecon of the curve to its height......................................19

Figure 11. Graph of deviaon for the rao of the horizontal projecon of curve to its height in 6 dier-

ent phases............................................................................................................................................19

Figure 12. Graph of deviaon of node posion in Z (mm) in accordance to dierent amount of insert-

ing air (cm3).........................................................................................................................................20

Figure 13. Secon view of the single physical component in equilibrium state (le) and under inaon

(right)...................................................................................................................................................20

Figure 14. Plan view of the single physical component in equilibrium state (le) and under inaon

(right)...................................................................................................................................................20

Figure 15. Views of the double inatable component bending towards the lower silicone layer..........21

Figure 16. Views of the double inatable component bending towards the upper silicone layer............21

Figure 17. Average deviaon of node posion in each cell (mm) under dierent amount of air (cm3) for

the stage 2 and stage 3.........................................................................................................................22

Figure 18. Maximum deviaon (mm) of the horizontal projecon of the curve and its height for each of

the six components (a, b, c, d,e, f) within the aggregate system on stage 4.........................................22

Figure 19. Plan view of the aggregate system in two dierent states..................................................23

Figure 20. Secon view of the aggregate system with reversed curvatures........................................23

Figure 21. Detailed focus of secon views of the aggregate system....................................................23

Figure 22. Paral view of ve allocated spring connecons within the hexagon.................................25

Figure 23. Column chart of maximum deviaon on each spring length (mm) for equilibrium and the state

under inaon......................................................................................................................................27

Figure 24. Column chart for each observaon that refers to dierent resulng spring lengths............27

Figure 25. Column chart for single component that shows the length to height rao of curvature measured

in mm for each observaon..................................................................................................................28

Figure 26. Column chart for single component that shows the average error between physical length

to height rao of curvature for each observaon..................................................................................28

Figure 27. Minimum Deviaon of node posion (mm) in Z :Observaon 1.........................................29

Figure 28. Maximum Deviaon of node posion (mm) in Z : Observaon 2.......................................29

Figure 29. Views of digital buckling formaon of single component towards its lower layer...............29

Figure 30. Column chart for length to height rao of the curvature developed in a and b component foreach observaon..................................................................................................................................30

Figure 31. Column chart of average error from physical length to height rao of curvature displayed both


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on a and b component for each observaon.........................................................................................30

Figure 32. Minimum Deviaon of nodes posion in Z: Observaon2..................................................31

Figure 33. Maximum Deviaon of nodes posion in Z: Observaon 4...............................................31

Figure 34. Views of digital buckling formaon of double component towards its weak layer.............31

Figure 35. Aggregate system of four adjacent components with reversed bending aributes...........32

Figure 36. Column chart of length to height rao of the curvature developed in four components for

each observaon..................................................................................................................................32Figure 37. Column chart of average deviaon from physical rao displayed on four components for

each observaon..................................................................................................................................33

Figure 38. Dierent views of digital simulaon of the inated aggregate system based on 4 compo-

nents.................................................................................................................................................33

Figure 39. Aggregaon with 6 components of reversed bending properes.......................................34

Figure 40. Column chart for average deviaon of digital length to height rao of curvature displayed

on six components for each observaon..............................................................................................34

Figure 41. Column chart of length to height rao of the curvature developed in six components for

each observaon .................................................................................................................................35

Figure 42. Trendline for the average error in digital deformaon of dierent aggregate paerns com-

pared to physical ones..........................................................................................................................35

Figure 43. Digital representaon of inatable aggregate system composed by 6 elements................36

Figure 44. Single Unit...............................................................................................................................43

Figure 45. Single Unit................................................................................................................................43

Figure 46. Double Unit..............................................................................................................................43



Figure 49. Double Unit.............................................................................................................................44

Figure 50. Aggregate System of six components......................................................................................45

Figure 51. Aggregate System of six components.......................................................................................45

Figure 52. Aggregate System of six components.......................................................................................45Figure 53. Aggregate System of six components......................................................................................46

Figure 54. Aggregate System of six components.......................................................................................46

Figure 55. Aggregate System of six components......................................................................................46

Figure 56. Digital Simulaon of single unit...............................................................................................47

Figure 57. Digital Simulaon of double unit.............................................................................................47

Figure 58. Digital Simulaon of Aggregate System of four components..................................................48

Figure 59. Digital Simulaon of Aggregate System of four components..................................................49


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1.0 Introducon

The general framework of this study refers to a design strategy that explores complex

aggregate material systems based on two parallel procedures: Fabricaon and Computaonal

Design. The result that emerges from this interface is the development of a reliable digital

design tool that simulates the material assembly behavior under certain environmental

inuences. The study concerns about issues relang to the role of representaon being

extended into materiality and the queson that emerges is how computaonal design can

be correlated to the represented and at what level of complexity can this model be reliable

to predict accurately the material system behavior under certain environmental inuences.

Based on the observaon of the complex relaon between the micro scale of material make

up and macro scale of material system derived through the physical tesng, a computaonal

design method is developed to explore the inaon of complex aggregate pneumac

networks into inuences of force vectors. The proposed method is based on a parcle–spring

system that establishes connecons within the material system. These connecons aim to

bond a semanc relaonship between the physical arfact and its representaon on digital

world.

1.1 Material Design

Unlike sculptors and other arsts, Architects rarely have the privilege to work directly

with the object of their inspiraon. In that architectural context, design is oen considered

to tackle issues of form framework while material based design corresponds directly to the

discourse between form and tectonic exchange that lies on a series of observaons, tests

and speculaons over material’s behavior (Schropfer, 2011). Thinking Design materially is

a procedure that acvates the role of representaon to both realize design objecve and

equally updates the objecve itself. A closer focus on properes of a material such as texture,

elascity and fragility automacally displays the opportunies and constraints of workingwith it (Schropfer, 2011). An in-depth understanding of material capacies can be derived

from physical tesng through bending, stretching and other various acons. A combinaon

of observaon and experimentaon on material capacies would suggest certain types of

assembly formaon such as tessellaon or seconing, in order to fulll the design intent.

Then this knowledge must be embedded into a digital design space to establish a semanc

interface with the real model.

Once the medium of representaon altered from a simple drawing to a digital model

which is constantly being informed by material system behavior, according to Phil Ayres,

the privilege to design materiality in a digital environment lies on a built framework that

accommodates changes and enables the consideraon of me to become explicit rather

than inferred (Ayres, 2012). In other words, the main idea is that an adapve digital model

emerges from being encoded with updated informaon derived from real me experiments

on a material system. For a digital model to achieve a persistence of materiality, it must go

beyond a precise geometrical descripon to deploy an in-depth discourse of formaon based

on behavior of maer (Ayres, 2012). In other words, the aim is not to make a model of a

material but a model that can compute material logics and explore the material capacies

within the digital interface. Encoding material properes into digital modeling refers to

relaonal topographies that connect the shape of maer under the inuence of forces

(Goulthorpe, 2008). The recent shi on the role of representaon in architectural praxis,

extends the noon of design from being just geometric enes like lines, solids and vertexwith a meaningless context to a smart geometry that actual co–operates with the designer

for implemenng material invesgaon digitally.


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1.2 Responsive Materials-So Robocs

One of the greatest features of working digitally on material computaon is the me

factor that is taken into consideraon as a fourth dimension. Design in the fourth dimension

enables architects to deploy dynamic building methodologies. The emergence of roboc

media in architectural context has highlighted the interest to material assemblies that

support dynamic forms that are subjected to transformaons through me. The result ofthis technological shi, is the emergence of a responsive architecture. Since, architecture is

dened by physical components that are materials, we can speak about responsive materiality

(Schropfer, 2011).

Speaking about robocs, our current understanding of them, their funcons and

behaviors have become ubiquitous with ideas of precision, eciency and harbor. Over the

last ten years, the eld of Robocs Research has seen a development away from this tradion.

With researchers developing so Robocs that provide new capacies in comparison to their

ancestry. Our denion can be expanded somewhat whereby Robots can be considered as

hard or so on the basis of the compliance of their underlying materials. Whereas hard robots

have mulple but discrete amount of exible joints connected by s links, each providing

a degree of freedom (df), So Robocs have distributed deformaon with theorecally an

innite number of df (Trivedi et al., 2008). With no rigid links or rotaon joints, the emergence

of an innovave generaon of robocs cras is evident and can be exploited further into a

mulple of potenal applicaons on responsive design.

1.3 The Architectural Problem and Thesis Aims

The research is focused on both the fabricaon and digital design of inatable silicone

aggregates with high rate of complexity while the aim is to create an algorithmic simulaonthat probes the relaonship between the virtual model and its physical arfact. The queson

that emerges is how the digital assembly can be correlated to the represented and at what level

of complexity can we rely on the proposed algorithmic method while aggregang paerns.

The computaonal design embedded with material properes, aims to provide adequate

results about the bend formaon of a double curved membrane composed of hexagonal

silicone cells. To achieve the physical dynamic simulaon, a generave algorithm has been

formulated based on principles of a parcle-spring system that plays the key role to develop

a controllable design tool which both simulates the inaon of silicone cellular structure and

further explores a range of dierent conguraons in respect to its performance capacity.

The algorithm proposed is an iterave process that simulates structural behaviorwith the aid of springs that exert aracve and repulsive forces among mass nodes that are

aached to (Gordon, 2003). Calibrang the material intent, the design environment is also

updated by constraints which enable material system to be self-organized and thus generate

geometry and topology of the tessellated double curved membrane consisted of mulple

hexagonal cells. The key role of the algorithm is the local distribuon of spring connecons in

each cell with dierent expansion rates because they are able to control and dene the bend

formaon with posive or negave curvature.

There are two design approaches to calibrate material system within digital design.

Persistent Modelling refers to the rst approach that completes a two way discourse between

the act of making and the act of designing. By looping over the feedback from both physical

tesng and computaonal design, new structural systems can be invesgated and composed


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within this interface (Ayres, 2012). The other approach proposes a more linear procedure by

taking advantage of the feedback derived from physical tesng and fabricaon of the arfact

and then engaging changes and exploraons within the digital design space accordingly. In

other words, physical tesng provides measurements which are computed digitally. In this

sense, the digital design space, rstly has a passive role of being constantly embedded with

material logics. Being exible over the relaonship between input and transformaon, digital

model becomes substute of the physical arfact and expands its role into the computaonalframework. The proposed design strategy in this study is outlined by the second methodology

which best ts to its purpose to highlight the acve role of the computaonal design within

the design process.

1.4 Structure of the Thesis

In the next secon, a background research is presented with chosen related projects

that deploy material design methods. In the following secon 3, the methodology will be

presented which covers two parts: the fabricaon of the aggregate material system and

the implemented algorithmic method. Secon 4 contains an in depth descripon of the

implemented code which then is subjected to various tests in order to dene the level of

complexity to which it can accurately predict the material assembly behavior. The results of

the experiments will be analyzed and accessed in full detail in secon 5. Moreover, the overall

approach will be evaluated and some future possible direcons for further development

will also be menoned. The conclusion in secon 6 will present an overall review of this

invesgaon.


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2.0 Background Research

“In one philosophy one thinks of form or design as primarily conceptual or cerebral, something

to be generated as a pure thought in isolaon from the messy world of maer and energy.

Once conceived, a design can be given a physical form by simply imposing it on material

substratum, which is taken to be homogeneous, obedient and recepve to the wishes of

the designer... The opposite stance may be represented by a philosophy of design in which

materials are not inert receptacles for a cerebral form imposed from the outside, but acve

parcipants in the genesis of from. This implies the existence of heterogeneous materials,

with variable properes and idiosyncrasies which designer must respect and make an integral

part of the deign which, it follows, cannot be rounized.”

(Manuel DeLanda, 2001)

2.1 Free-form Metal Inaon and the Persistent Model

The project Free–form Metal Inaon by Phil Ayres, proposes a design strategy

that sets representaon and arfact in a circular relaonship in order to decrease the

unpredictability throughout the various stages of the architectural praxis: design–fabricaon

and use/occupancy (Ayres, 2011). The project proposes representaon to be a place of

observaon and exploraon in an aempt to specify and temper the deviaon derived from

making of things and making of informaon. Two sheets of steel are welded at the seam toform a sealed cushion into which a uid medium is introduced ( gure 1). This material system

turned to behave as an inatable component while the internal pressure increases, pushing

the material over its elasc limit (Ayres, 2011). The results indicate the reciprocal frame

established between material behavior and the nature of imposed geometry. Comparing the

physical with the digital, the amount of deviaon is measured and invesgated unl the

system to come up with greater degrees of predictability. The dramac transformaon from

planar to plasc buckling components is a consequence of a complex matrix of interacons

within microstructure and macrostructure of material assembly (Ayres, 2011).

Figure 1. Le: Detail of the connecon between discreet components to construct an aggregate.

Right: Schemac indicang how the persistent model (consisng of both representaon and artefact) is nested

within the environment of operaon and coupled through lines of acon and feedback.


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The representaon combined with the process of fabricaon aempts to probe

and display the signicant and oen unpredictable deformaon of arfact. However, the

currently computer based simulaon is unable to predict accurately the buckling informaon

derived from the inaon process. Apparently, these inaccuracies at the component itself

are highlighted when aggregaon is being considered (Ayres, 2011). Observing the results

of some series of experimentaon over the arfact inaon, the rst step is to record

certain predictable lines in relaon to geometrical aributes of cushion prole. Then, these

points with predictable deformaon are examined within the digital design space unl a

relaon between their formaon and geometric aributes to be established. However, as

the geometry of material assembly becomes more complex shaping aggregate paerns,

in addion to predictable lines,there is unpredictable buckling occurring in the individual

components (Ayres, 2011). Then the concern is focused on trying to determine the locaons

of unpredictable formaon. This strategy proposed in Free-form Metal Inaon aempts to

deploy a design space where ancipaon is tackled with acve feedback (Ayres, 2011). In

other words, it is an alternave method to linear design to construcon procedure where the

discourse occurs between representaon and fabricaon through feedback. The outcome

of such a non-linear architectural procedure, is the producon of sensive and adapve

architectural forms objected to constraints and aributes of material systems.

2.2 Exploring Pneumac Networks within the design Context

So Robocs Research Project for Digital Ecologies Module in AAC

Supervisor: Ruairi Glynn

Authors: Karagkiozi Zoi, Ben Haworth

Methods for developing actuated Pneumac networks have developed recently and

maintained within the context of Chemistry, Engineering and material Science. Increasingly,more and more designers and architects are showing interest in this eld but the inaccuracies

on results to manage enrely predictability in the microstructure of material system limit its

applicaon in architectural context.

Robots can be considered as hard or so on the basis of the compliance of their

underlying materials. Unlike hard robots, so have distributed deformaon with theorecally

an innite number of df (degree of freedom). These degrees of freedom are out of proporon

with the amount of actuators required thus a more integrated system is established between

actuator and material construcon methods. In short, the disncon between “actuator”

and “actuated” becomes narrower to the point of being one. Further advantages of the so

robot can be compiled from Calis (Calis et al., 2011) among others:

1. Innite degrees of freedom and limited number of actuators

2. High Dexterity

3. Capability to work in Unstructured environments ( in which Environmental constraints

not known a priori)

4. Low resistance to stress forces

5. Compliant and able to conform to obstacles

6. Can carry so and fragile objects

7. Can perform diverse tasks with minimum control

However, challenges would lie to fully control the shape of deformaon in so robots.

Depending on requirements, resulng mobilies may dier and not be predicted easily. With


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no rigid links or rotaon joints, a new shi is evident to an innovave generaon of robocs

cra.

Typically examples of so robocs prototypes can be seen to be following two disnct

methods: Electro acve Polymer (EAP) and Pneumac arcial Muscle (PAM) actuators. “So

Robocs for Chemists” (Whitesides et al., 2011) outlines one such method of PAM using

Pneumac networks or “Pneu Nets”. The so Robots are constructed from two types of

silicone rubber that have varying tensile properes and their moulds are 3D Printed (ALM)with detailed layouts of walls that form internal capillary systems. On compleon of the

robots, actuaon is triggered with a source of pressurized air creang moving appendages

that bend, grab, walk and hold.

Currently, these methods tend to remain within the context of Material Science.

Technical demands have to a degree excluded other disciplines from taking an acve

involvement. Acve materials currently available in use in so robocs manipulators have

shortcomings that make their commercial use impraccal (Trivedi et al. 2008). Scale is another

issue. It is hard to imagine a simple “scaling up” process resulng in larger objects being

manipulated in the same way as scaled up hard robocs. The possibility of failure due to

fragility of materials used and the requirements to keep the structure air ght are oen being

prohibive. However, the advantages of working with so actuated Robots are inherently

spaal, in parcular the ability to explore “unstructured” environments. Moreover, so robots

by their very nature are compliant to stress force, hence in order to exist and funcon in real

world, the material itself must form a direct dialogue through contact with its surroundings.

The environment is having an eect on their form just as it is true vice versa. Both of these

ideas lend themselves to architectural research and praxis.

The project concerns to create a human interface with the view to develop interacons

between viewers and the robots themselves. So robot movements are quite dierent from

those of humans, thus humans operators are geng confused and disoriented. In this view,an interacon is built between two devices that respond to human breathing paerns. This

interface between the breathing process and inaon of so actuators plays the major key

role. In other words, a dialogue has been developed between two parcipants, so actuators

and human.

The input device that responds to the sound of breathing provides a stable soluon

to the problem. A user could breathe into a mask aached to a tube and a microphone at

the other end sends the sound data into Processing environment via Arduino. The signal

and resultant sound wave were documented using a sample rate of varying resoluon. Euler

spring Physics was used within some Processing Code in order to smooth out the sound

values over me ( gure 2). This created far more stable values that could be easily controlled

depending on required relaonships between input and output.

Figure 2.Points in a mesh are displaced

according both to the frequency and

volume of the sound. The form of which is

diminished or augmented according to the

strength of user’s voice. The mesh pointsbehave in accordance to triggered “guide”

points by assessing the relave height of

their neighbors.


13



Having tested so robots with syringes, a device was built that would combine the

syringe with a linear actuator. The signal from the input device can be transferred easily via

the Processing /Arduino interface. The syringe performs a mediang role in the interacon

procedure between user and so robot controlling the rate of inaon.

Moulds were designed in 3D (Rhino) and printed in Nylon. An inial aempt at

recreang the mulgait quadruped (Whitesides et al., 2011) provided some encouragingresults. Whilst not actually managing to walk, each channel performed as expected when was

treated independently. Aer the rst prototypes were tested, next step was to design roboc

actuators that had only one single channel input. Several moulds were produced with varying

lengths and tested. The most successful was a robot with 9cm and 16.4cm in size supplied

with air pressure from a 500 ml syringe. The level of actuaon exceeded expectaons with

so robot performing a wrapping moon whereby one end would wrap completely into itself

( gure 3). Another successful so robot was in a shape of star sh. Each limb of it can be

controlled independently. A similar curvature was noted as before with a key disncon. That

being the eect of a tapered design as opposed to a uniform “straight” network. The taper

has the eect of reducing the degree of the maximum rotaon of the actuator at each node

point. Therefore, the wider part bends more than the narrower part ( gure 4).

The aim of the project was to invesgate silicone rubber aributes and fabricate so

actuators in order to explore the bend behavior of so pneumac networks based on their

capillary internal channel. However, the computaonal design was not engaged with material

properes, thus it is not able either to simulate the physical deformaon or deploy exploratory

creavity over the design process. The problem can be addressed through an exploraon of

physical models that simulate the behavior with high level of accuracy based on analysis of

uid mechanisms, thermodynamics and chemical kinecs. A beer understanding of these

topics would drive to more accurate models, thus to beer design and control.

Figure 3. The wrapping moon of a so

robot during air pressure.

Figure 4. So robot in a shape of star

sh.


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3.0 Methodology

Taking the previous project on So Robocs into consideraon, the task of this study

is to develop a greater understanding of the material behavior within the fabricaon process

of more complex pneumac networks that compose a silicone membrane based on the

honeycomb structure. As it has been menoned before, there are two design approaches

to calibrate material system within digital design. One strategy is to bond the representaon

and the arfact in a circular relaonship in a way to temper the indeterminacy throughout

the dierent phases of the architectural praxis (Ayres, 2011). Feedback is constantly updated

through physical tesng and digital exploraon on material logics. Feedback bridges the gap

between the role of representaon and physical arfact by measuring the level of deviaon.

The result of this circular procedure is the fact that design space is constantly updated with

changes concerning geometries and forms being more sensive and adapve on the basis

of the compliance of their underlying material (Ayres, 2011). Such a circular design strategy

involves a me–consuming procedure where the design is constantly changing in a close

loop for numerous mes unl the deviaon rates between the goal and current state to

be narrowed up to the opmum according to designer’s intent. In this study, the proposedstrategy completes a part of this circular procedure. In other words, the approach proposes

a more linear procedure by taking advantage of the feedback derived from physical tesng

and fabricaon of the arfact and then engaging changes and exploraons within the digital

design space accordingly. In that sense, innate characteriscs, behavior and capacies of the

material assembly integrate computaonally to the digital design. The proposed methodology

ts best to the purpose of this study that focuses on the highlights of the computaonal

design and its extended role to act as a morphogenec driver within design process. This

secon explains the methodology of material design and it is divided into two main categories:

Fabricaon and computaonal design. Fabricaon enty covers the observaon, selecon

of the structure geometry and experimentaon of physical arfact and the computaonal

design secon rst presents and explains the algorithm itself and then invesgates and goesdeeper into its exploratory properes to unfold the material assembly gestalt.

3.1.0 Fabricaon

3.1.1 Observaon on Material System

Silicone rubber is an elastomer composed of silicone–polymer containing silicon

together with carbon, hydrogen and oxygen. Silicone rubbers are two parts polymers and is

generally non-reacve, stable and resistant to extreme environments and temperatures from

-55 oC to +300 oC while sll maintaining its useful properes. Compared to organic rubbers,

however, silicone rubber has a very low tensile strength. The material is also very sensive to

fague which refers to localized structural damage that occurs when a material is subjected

to cyclic loading. Silicone rubber is available in a range or hardness levels between 10 and

100, the higher number being the harder compound.

For the purpose of this study, two types of silicone are used for the experiments

and the outcome of physical components, a so (Eco Flex 00-30) and a hard silicone

rubber (Addion Cure 33). For both of these types of silicone rubber, the mixing

procedure is the same. Aer mixing the same volumes of two parts of these polymers,

the mixture becomes homogeneous. Before use, the mixed silicone should be correctlyde-gassed in a vacuum chamber to remove air trapped within the mix. These air

bubbles formed inside the mixture can cause serious impairments on the nish quality


15



of the resulng mould. When the material is degassed in a vacuum, it expands to

approximately ve mes its original volume and then collapse. At this point, the material has

been successfully vacuumed and it is ready for use.

Although, silicone rubber is currently a homogeneous mixture, when it is used for

building pneumac networks, the material system is segmented into voids which are the

air channels. In that sense, silicone assembly evolves to a dierenated cellular structure.Its anisotropic aributes are due to the non-uniform distribuon of air pressure inside the

mould. Various conguraons in paerns of input channel employ dierent inated areas,

thus dierent deformaon and overall shape while air pressure increases.

In respect of the physical tests completed for the purpose of the previous project

on So Robocs for Digital Ecologies Studio in AAC, pneumac networks based on silicone

rubber components show an interesng deformaon under air pressure. They perform a

wrapping moon whereby one end would wrap completely into itself. Such curved formaon

of pneumac structures is established due to the coupling of two dierent silicone rubbers,

one hard and the other so. The so rubber part is basically the thicker layer which contains

the inner capillary channel. The strong part is the thinner layer that displays lower rate of

elascity in comparison to the so rubber. The bend formaon is operang towards the hard

layer as its expansion rate is lower.

Thus, while air increases internally the mould, the so layer is under tension and the

hard layer is under compression ( gure 5). This study is taking advantage of such combinaonal

rubber layers to deploy both negave and posive curvature by changing the locaon of

these layers. The general inspiraon behind the aim of this study, refers to the fabricaon

of a double curved membrane whose curvature is generated by its dierenated inatable

cellular structure. Aached hexagonal cells, as individual components with reversed layout

of strong and so layer, are forming a honeycomb aggregate paern that allows changesby allocang such individual components dierently. For such material systems that are

complex and display non-linear behavior when exposed to dynamic environment inuences

and changes, a successful design strategy must conceive the micro scale of the material

make-up and macro scale of material system as a constant reciprocal framework (Menges,

2012). Most building materials such as metal and glass which are designed and produced

mainly for building components, are typically homogeneous which means uniform synthesis

that deploy similar aributes within its range. Unlike convenonal materials, intricate

structure and complex behavior based on inaon of rubber cellular structure becomes a

design challenge which this study tries to explore by employing computaon to navigate and

discover unknown paths within the design space.

Figure 5.Bend formaon towards the strong silicone layer.


16



3.1.2 Selecon of the structure geometry

Based on the previous observaons over the material aributes and combinaonal

behavior of two aached rubber layers under air pressure, the cellular structure of silicone

membrane requires a geometrical paern that would unfold such material behavior and also

permit great level of its deformaon. Cellular structures can be seen as forms that appear

in nature and produced by biological organisms. Such organisms have evolved numerous

variaons of form that is reciprocal to their structure and material. Aggregate paerns

develop complex hierarchies within their assemblies based on self-organizaon principles

(Weinstock, 2006). The self-organizaon of biological material system is a dynamic procedure

over me that enables the system to change the structure and its order and then to modify its

behavior respecvely (Weinstock, 2006). The evoluon of self–organized systems proceeds

from small components that are assembled together to form larger and more complex

structures. Cellular structures are polyhedral and may be regular or irregular forms with

dierent distribuon.

Honeycomb is an example of hexagonal cellular structure found in nature. It isorganized in parallel rows and tends to have more regular cells. Honeycomb structures

allow the minimizaon of the amount of used material to reach minimal weight and

minimal material cost. Its structural formaon provides minimal density and relavely high

compressive strength. Consequently, honeycomb structures are widely used to compose at

or curved surface where high strength to weight rao is valuable. For the purpose of this

study, according to previous observaons and design intenons, hexagonal paern has been

chosen to form the shape of each silicone cellular structure. Units of hexagonal inatable

rubber components with internal air channel are aached together and through repeon

would form the double curved surface. This lightweight material assembly is constructed

as inially planar surface that inates as the internal air pressure increases, pushing the

material to its elasc limit.

3.1.3 Experimentaon–Physical Tesng

The rst prototypes of silicone components get their shapes from two acrylic moulds

with dierent internal channels. The shape of both two moulds is a regular hexagon with

20mm each side. In the rst mould the single channel is developed in a capillary system

where a central tube runs within the range of the hexagon and is divided into more secondary

tubes perpendicular to the main and parallel to each other. In the second mould, the single

channel covers bigger area and is not divided into any secondary unit ( gure 6). Based

on the physical tesng of these prototypes, each of these two components deploys a rate

of deformaon which is proporonal to the amount of internal air pressure. The silicone

hexagon cell based on the mould with the single big channel operated maximum inaon on

upper layer with a slight and gentle curve on its overall range and presented maximum tensile

strength compared to the other one. On the other hand, capillary channel with mulple

secondary tubes performed higher overall buckling, with minimum inaon on upper layer

and minimum rate of tensile strength.

Comparing the results of two components, it can be seen that the shape of internal

channel indicates the direcon of air force towards the most sensive areas with lower rate of

sness within its range. Thus the input channel triggers dierent bend formaons. For example,

the single big channel pushes the air towards the upper layer which is thinner thus less rigid thanthe outer perimeter of hexagon. The result is that air pushes the upper layer to its elasc limit

forming a big inatable bubble and a slight and gentle curve on its overall range. The capillary


17



channel, on the other hand, contains thin layers of silicone among its channels that are

mainly subject to higher force loading. As the air increases internally, the direcon of its

force is towards these thin layers within the range of capillary system. Thus the silicone

is bending along its range forming a dramac curve and a slight inaon on its upper layer.

Based on these observaons and considering the fact that the single big channel de-

ploys higher tensile strength during the experiments, the nal shape of individual component isbased on this channel type for opmum structural performance. Moreover, the shape of the in-

dividual unit is an aggregate paern composed by three hexagons which are aached together

in a way to form 120 degrees angle ( gure 7 ). The size of each hexagon is slightly bigger than

the rst prototypes (40mm long each side) considering the fact that the rate of structural dam-

age is narrowed as scale increases. The gure 7 illustrates the mould structure and the shape

of overall input channel.

According to this conguraon, individual components are aached with each other

to form aggregates that compose a double–curved membrane. This membrane is not solid and

contains voids among its cells in order to allow greater rate of bend formaon ( gure 8, 9). The

components have been allocated with reversed distribuon of their local rubber layers thus

some of them are performing posive and some other negave curvature. The distribuon

of the two layers in the overall paern is oponal and can be dierenated within numerous

experimentaons. For the purpose of this study the selected paern displays six aached units

with blending curvature as it is illustrated in the gure 9.

The experiments were carried out in four stages: the rst test was the inaon of the

single component, then the double component, following the 4-component aggregate paern

and last the 6-component structure ( gure 8 ).

Figure 7. Acrylic mould with single big air channel

for both silicone layers.

Figure 8. Aggregate System: Four stages of the experiments.


18

Figure 6. First prototypes of two acrylic moulds

with dierent input channel



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Figure 12. Graph of deviaon of node posion in Z (mm) in accordance to dierent amount of inserng air (cm3 ).

Figure 14. Plan view of the single physical component in equilibrium state (le) and under inaon (right).

Figure 13. Secon view of the single physical component in equilibrium state (le) and under inaon (right).


20



Following to the next step of the fabricaon process, two separately units (a, b) with

the same allocaon of the hard layer, are aached together. In equilibrium, the total size

of the aggregate system is 208mm in width and 200mm in length. In this case, under air

pressure, the double cellular structure displays a well-shaped inatable dome. Despite the

aachment of two components, the buckling formaon has remarkably remained the same as

previously tested in single component. Both two these cells display the maximum buckling as

it would have done without being aached to each other. The gures 15, 16 display dierentviews form the inatable double component. The symmetry of both two buckling formaons

outlines the fact that there is no physical deviaon between the two cellular structure.

The following experiments were carried out for a four-component cellular structure

with two posive units (a, b) aached to other two (c, d) with negave curvature ( gure

9). In equilibrium, the total size of the aggregate system is 208mm in width and 380mm

in length. In this case, the buckling formaon is slightly inuenced by the aggregaon and

unlike previously, there is a gentle decrease on curvature of each cell. The graph of gure

17 illustrates the slight decrease on average deviaon of node posion in each cell under

dierent amount of air for the stage 2 (double component) and stage 3 (4-component

aggregate paern).

Figure 15. Views of the double inatable component bending towards the lower silicone layer.

Figure 16. Views of the double inatable component bending towards the upper silicone layer.


21



Figure 17. Average deviaon of node posion in each cell (mm) under dierent amount of air (cm3 ) for the stage

2 and stage 3.

The next and nal task of physical tesng was to aach six units together (a, b, c,

d, e, f) with reversed distribuon of silicone layers ( gure 9). In equilibrium, the total size

of the aggregate system is 208mm in width and 560mm in length. Unlike the predictable

deformaon of individual and double component, the behavior of this inated aggregate

cellular structure was not easily predictable, parcularly as the prole geometry becomes

more complex. The experiments record a double-curved surface that is subjected to an

uniform ripple formaon. The local buckling formaon reects the locaon of strong and

so layer, thus the overall buckling of this surface depends on the distribuon of aached

components within the honeycomb structure. In other words, an alternave combinaon

of individual components would result to a dramac deviaon in curvature. Through theinaon period, pressure readings informed higher distoron in the middle units which

perform negave curvature. On gure 18 , the graph shows the maximum deviaon for

the length to height rao of curvature for each of the six components within the aggregate

system. The middle units are subjected to higher loading pressure from their adjacent units,

thus the length to height rao of curvature is diminished approximately to the half value in

contrast to the other units. Moreover, under inaon, the aggregate structure displays a slight

rotaon upon itself. Clearly, this deformaon at each component level, are only compounded

when considering aggregates. Unlike the previous tests, this unexpected distoron raises the

interest whether the computaonal model will be considered sucient to overcome this

state of unpredictability.

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22

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Figure 18. Maximum deviaon (mm) of the horizontal projecon of the curve and its height for each of the six

components (a, b, c, d, e, f) within the aggregate system on stage 4.



Figure 19. Plan view of the aggregate system.

Figure 21. Detailed focus of secon view of the aggregate system.

Figure 20. Secon view of the aggregate system with reversed curvatures.


23

The following gure 19 shows in plan view the aggregate pneumac system. In

equilibrium this cellular structure has planar surface and under inaon the structure is

subjected to a dramac buckling according to the assigned bending aributes of each cell.

Moreover, gures 20 and 21 illustrate in secon view of the aggregate arfact the length to

height rao of curvature in each cell. Clearly, the middle components display a slight decrease

on their buckling formaon.



3.2.0 Computaonal Design

The previous procedure of physical tesng that covers the observaon, the selecon

of cellular structure and experiments on material system aims to gather the material

informaon needed to be embedded on the computaonal design. Employing computaon

to conceive the intricate relaon between material microstructure and its behavior, allows

complex material systems that present non-linear reacon under dynamic environmental

forces to be explored and navigated in relaon to their structural performance. The intent is

not to make a model of a material but a model for exploring material logics (Nicholas, 2012).

3.2.1. Algorithm

The algorithm was developed in the Processing programming language and its

main aribute is the key role of the dynamic behavior of a parcle–spring system. Parcles

represent points on the edges of each hexagonal paern.

Parcles are programmed as instances of a class of node elements which have twovectors: posion and velocity. The system was remained considerably simple as each parcle

has insignicant value of mass, and there is also no use of acceleraon or viscous damping

for the purpose of this simulaon. The system is inialized with the parcles at predened

topology. The predened posion of points is recorded in a csv le that is exported from

the autoCAD framework where the topology of the tessellated honeycomb paern was

developed. In other words, such geometric enes like points developed in design soware

with meaningless context are due to be manipulated and be engaged with material knowledge

in order to display specic behaviors. Back to the processing framework, the two vectors,

posion and velocity of each node are updated at every iteraon according to the previous

frame rate and the current posion is calculated and stored as a result of the sum of its

vectors. The next step of interacons among the parcles is based on the current posion.

A node is connected with another node by a spring, which is illustrated as a line that

is dened by its sness, actual length and rest length. The noon of spring line is used

to represent the elasc properes of the silicone rubber. When the spring is not at its rest

length, each spring generates a force to the nodes that is aached to. More specically, in

every iteraon, the system calculates the distance Dab

between two parcles a and b. If the

Dab

is less than the threshold D that represents the rest length, then the spring connecon

is in compression state which means that a repulsive force is exerted upon them in order to

restore its equilibrium. If the Dab

is more than the threshold D, then the spring is in tension and

an aracve force is exerted that push the two parcles closer to each other in its rest length.

In case that the distance Dab

is equal to the rest length D, then the spring is in equilibrium,

thus no forces exerted upon them. Once the temporary force vector is stored in each parcle,

this vector is added in the velocity vector of each parcle. Then, the system calculates the

temporary posion of each node by adding to the original posion the updated vector velocity.

This procedure is iterave unl the system converges to the equilibrium state which means

that all velocies are narrowed close to zero. According to the ideal length of each spring, the

system has the tendency to restore a predened relaonal topography.


24



3.2.2 Integrang Constraints

Clearly, the above descripon is abstract and sll inadequate to conceive the micro

scale of material make-up and the macro scale of material assembly. The system must deploy

material processes and to achieve that, a set of constraints have to be computed within the

computaonal design space. Looking into the cell of this structure, the hexagon is a three

dimensional object dened by nodes on each edge and springs that represent the line between

two points. For the purpose of this study, the central point of the hexagon is also dened and

represented as a node from which twelve addional spring connecons are established to

each point on the edge of this paern. Thus, thirty overall spring connecons are developed

in each hexagon. When the paern is repeated to support the aggregate formaon of the

overall structure, some nodes belong to more than one hexagon, thus the average of total

spring connecons is dierenated in each hexagon. Based on the observaon of physical

tesng, during the inaon, the cellular structure is bending towards the strong layer. As the

air pressure increases, its side length expands at dierent rate. For example, the upper sides

expand approximately twice than the lower sides. In addion, the perpendicular sides that

connect the upper and lower base expand less than the previous one.

Aer gathering all these expansion rates for each single connecon, the constraints

that the system requires refer to the variaon on the ideal spring length for the topography

between two nodes. Thus, ve variaons of spring connecons with dierent ideal length

(spring A, spring B, spring C, spring D, spring E ) are programmed as instances of a class that

contains spring aributes. Then, each connecon within a hexagon is assigned to a specic

type in respect to the measurements derived from physical tesng. The gure 22 illustrates

the distribuon of ve variaons of spring connecons within a hexagon.

25

Figure 22. View of the distribuon of ve variaons of spring connecons within the hexagon.




4.0 Tesng and Results

The representaon simulates the process of inaon on the physical model where

the cellular structure from inially planar surface is subjected to a plasc deformaon. Each

digital cell bends according to the local distribuon of dierenated rates of spring expansion.

The result is a double curved membrane that is subjected to uniform ripples which represent

the posive and negave local curvature. By changing the allocated spring expansion rates ineach cell, the algorithm generates the form of the tessellated membrane with dierent degree

of local curvature accordingly. Clearly, the key role of the algorithm is the local distribuon

of dierent spring types in each cell because they are able to control and dene both the

curvature degree and the direcon of the buckling process. The development of this material

system gives the privilege to the designer to explore a range of dierent conguraons within

the design space. In that sense, by aggregang more components to form larger surfaces,

the system can compute the same generave drivers in larger and more complex material

assemblies. Thus, the scale of design is exible according to the designer’s intent.

Physical experimentaons point out that under inaon physical components are

subjected to a wrapping moon into themselves forming an upward or a downward trend

according to their allocated dierent spring types. In both cases, the maximum deviaon

is occurred at nodes posion in Z, the horizontal projecon of the curvature and its height.

For this reason, the measurements that were taken on the individual component and each

aggregate cellular paern focus on the 3 main dierent aspects:

1. Deviaon of nodes posion in Z

2. Horizontal projecon of the curve

3. Height of the curve

The maximum deviaon occurred on each spring length between the equilibriumstate and the state under inaon is represented on the column bar of gure 23. However,

the performance of bend formaon on physical model is the result of numerous factors

that make the material system so intricate and hardly predictable. For example, the varied

amount of inserng air corresponds to dierent inaon rate and the resulng thickness of

silicone layers inuences dierently the tensile strength of each cell, thus in every iteraon

the system deviates from the previous statement. For this reason, four observaons were

carried out that refer to dierent resulng ideal lengths for each spring type with values that

slightly deviate from the real values ( gure 24). Each of these observaons comes up with

dierent results about the horizontal projecon of the curve and its height for each unit. The

purpose is to nd the ideal combinaon of digital values of spring lengths to correlate with

minimum deviaon with the physical deformaon. This method aims to nd the minimum

error occurred among these observaons when considering aggregates.


26



Figure 24. Column chart for the case of four observaons that refer to dierent resulng spring lengths.


27

Figure 23.Column chart of maximum deviaon on each spring length (mm) for equilibrium and inaon.



4.1 Tesng on Single Unit

The inial tesng of the algorithm was performed on a single component which is

the three aached hexagons in a way that form 120 degree angle. The digital inaon was

simulated with high rate of correlaon between arfact which raonalizes the represented

topographies within the framework of material logics.

More precisely, each observaon comes up with results that refer to the length to

height rao of the curve. Comparing these results with the physical rao, the aim is to nd

the observaon that corresponds to the minimum deviaon, thus minimum error recorded

between physical and digital inaon ( gure 25). Based on the graph of gure 26, the least

deviaon corresponds to observaon 1 and the maximum deviaon refers to observaon

2. In addion to that, the following graph of gures 27 , 28 illustrate the minimum and

maximum deviaon of nodes posion in Z that correspond to observaon 1 and observaon

2 accordingly compared to physical model. Clearly, the model so far is considered reliable

enough to measure accurately and predict with minimum rate of error the inaon on single

component. The gure 29 illustrates the digital deformaon of single material componentbased on measurements of observaon 1. It can be seen that the single component is

subjected to a signicant buckling formaon towards its lower layer. Comparing the result

with the physical reacon of single unit in gure 11, the digital material system can compute

the ancipated deformaon.

Figure 25. Column chart for length to height rao of curvature measured in mm for each observaon.

Figure 26. Column chart for average error of each observaon compared to the physical values.

0.2

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observation 1 observation 2 observation 3 observation 4

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Figure 27. Minimum Deviaon of nodes posion (mm) in Z between Physical and Observaon 1.

Figure 28. Maximum Deviaon of nodes posion (mm) in Z between Physical and Observaon 2.

Figure 29. Views of digital buckling formaon of single component towards its lower layer.

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Physical Observation 1


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4.2 Tesng on Double Component

The same procedure as previously was carried out for the double component. The

chart of gure 30 shows the length to height rao of the curvature developed on a and

b component measured in millimeters for each observaon. Based on the chart of gure

31, observaon 2 corresponds to minimum error compared to the physical rao values and

observaon 4 comes up with maximum error. Comparing the previous minimum value oferror displayed on single component with the current value on double component, it can be

seen that the error remains surprisingly constant without any change on its value. This means

that the digital system can compute and predict accurately the reacon of both single and

double component under inaon. The graphs of gure 32 and 33 illustrate the minimum

deviaon of nodes posion in Z for observaon 2 and the maximum deviaon for observaon

4 accordingly. Moreover the following gure 34 represents the digital reacon of double

component under air pressure that corresponds to results of observaon 2. Clearly, the

dome formaon of the double physical inatable component can be correlated accurately to

the digital one.

Figure 30. Column chart for length to height rao of the curvature (mm) developed in a and b component for each

observaon.

Figure 31. Column chart for average error displayed on a and b component for each observaon compared to the

physical values.

2.3

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Error a Error b

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a a b b a a b b a a b b a a b b


30



Figure 32. Minimum Deviaon of node posion in Z between Physical and Observaon 2.

Figure 33. Maximum Deviaon of node posion in Z between Physical and Observaon 4.

Figure 34. Views of digital buckling formaon of double component towards its weak layer.

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Figure 35. Aggregate system of four adjacent components

with reversed bending aributes.

4.3 Tesng on Aggregate System of four components

The aggregate system composed of four adjacent components with reversed curvature

as it is illustrated in gure 35 becomes more intricate, thus less predictable than the previous

stages. The results outline a considerable increase on the deviaon of resulng length to

height rao. Each observaon comes up with values referring to rao that are considerably

dierenated from the real values. The minimum error is presented in observaon 3 and themaximum error refers to observaon 1 ( gure 37 ). From the chart of gure 36, it can be seen

that observaon 1 comes up with high rates of curvature height for all the four components.

Given the fact that this observaon represents also the highest deviaon, this means that

maximum bending induces the system to greater rate of distoron, thus maximum error. On

the other hand, observaon 3 with minimum average error ,displays uniformly distributed

values concerning the length to height rao of curvature of four components.

Figure 36. Column chart of length to height rao of the curvature (mm) developed in four components for each

observaon.

125130

110

140

74.5

45

30

40

165160

138

165

3531.5

28

20

154147

140

168

45

3037

28

160

150154

160

28

36

10

64


Length Height

a a b b c c d d a a b b c c d d a a b b c c d d a a b b c c d d


32



The gure 38 illustrates the equilibrium and deformaon state of the digital aggregate

system of four components. The digital simulaon produces blended curvature and remains

proximate to the original prole. The blended curvature is triggered by the local distribuon

of dierent spring connecons within each cell. The result of blended curvature conveys the

impression of a membrane being subjected to a double uniform ripple.

Figure 38. View of digital simulaon of the inated aggregate system based on 4 components.

Figure 37. Column chart for average error displayed on four components for each observaon compared to the

physical values.

3.44

1.5

1

2

3.53.14

0.2

2

4

1.52 1.6

2.4

2.8

0.6 0.5

6.4


Error a Error b Error c Error d


33



4.4 Tesng on Aggregate System of six components

The previous procedure on aggregate system based on four components points

out the fact that by aggregang components the system becomes more complex, thus less

predictable. Combining six components with reversed layout of spring connecons as it is

illustrated in gure39, the result is less accurate to the physical reacon of material system.

More precisely, the average error outlines an upward trend between the current stage andthe previous with minimum value presented in observaon 2 and maximum error presented

in observaon 3 ( gure 40 ). Observaon 2 represents an overall uniform distribuon of

average error occurred in each component. Unlike observaon 2, the rest of other cases

represent non uniform distribuon of error values within each component which implies

that the aggregate inatable model presents less similarity among each cellular curvature,

thus less similarity to the inatable physical model. More precisely, gure 41, documents the

actual values of length to height rao for all components in each observaon case. Clearly,

observaon 2 has the least deviaon among the other cases which means that it represents

the opmal soluon that best correlates to the physical model deformaon.

Figure 40. Column chart for average deviaon displayed on six components for each observaon.

Figure 39. Aggregaon with 6 components of reversed bending behavior.


34



1, 0.2 2, 0.2

4, 0.8

6, 2.3

y = 0.0025x3 + 0.0825x2 - 0.265x + 0.38

R² = 1

0

2

4

6

8

10

12

14

16

0 2 4 6 8 10 12 14

E r r o r

Components of Aggregate System

ERROR

Poly. (ERROR)

Figure 41. Column chart of length to height rao of the curvature (mm) developed in six components for each

observaon .

Figure 42. Trendline for average error displayed by dierent aggregate paerns.

Each level of complexity represented by dierent aggregates with varied number of

components is documented within the framework of this study. As the number of elements

increases, the average error of digital simulaon compared to physical deformaon follows

an upward trend. Based on the previous measurements, the trend of average error which is

the degree to which this error will connue to increase in future, can be esmated accurately.

The graph of gure 42 illustrates the trendline of average error in dierent aggregate

paerns. The trendline is polynomial of degree 3 and its R squared value or coecient of

determinaon has value equal to 1 which provides a measure of how well future outcomesare likely to be predicted by the model. In our case an R

2 of 1.0 indicates that the regression

line perfectly ts the real data points. Thus, a remarkable clue derived from this graph is

that the trend line of average error shows a slight increase unl the level of six components,

followed by a bigger rise on its value as the number of elements increases more.

164

154

138 140

44

22.5

36.5

45.5

164158 155

146

42.5

2630

26

165 165 165160

18 21 1824

165 168

147 150

10

26.532

36.5

128

145

160

150

2529

42

62.5

158165

133

145

25 28 25.533


Length Height

a a b b c c d d e e f f a a b b c c d d e e f f a a b b c c d d e e f f a a b b c c d d e e f f


35



Consequently, it can be esmated with high accuracy that as the prole geometry

becomes more complex, the aggregate system is considered inadequate in ancipang the

physical reacon of the arfact. For instance, when the prole geometry doubles its size

up to 12 components, the average error rises to 13. In that case, the model is not able to

accurate predict the physical reacon of material system under certain inuences. The strong

semanc properes established between representaon and arfact in smaller systems, lose

their validity as the aggregates increase their size. The following gures illustrate the digitalrepresentaon of inatable aggregate of six components.

Despite the gradual increase on error rate as the system aggregates to six components

with higher level of complexity, the digital deformaon outlines the overall shape of

ancipated buckling. The wrapping moon towards the springs with minimum expansion

rate is successfully correlated to the physical one. Moreover, the overall system is subjected

to a rotaon over itself which is also occurred to the physical model. Obviously, the intricate

material system can be correlated up to a level. Over this level, this methodology based on

a parcle spring system is not able to accurately predict in detail the bend formaon in each

aggregate component.

Figure 43. Digital representaon of inatable aggregate system composed of 6 elements.


36



5.0 Discussion

5.1 Overview of ndings

Regarding the results documented in the previous secon, it is evident that

computaonal design has been able to be embedded with material properes to generate

relaonal topographies of the inatable aggregate cellular structure. The model, implementedthrough a parcle spring system, was capable to simulate the bend formaon of silicone cells.

The categorizaon of springs ideal length and their local distribuon within each hexagonal

cell, played the key role to control the bending behavior of its cellular structure. Inializing

the simulaon with the case of a single unit and then going through the same procedure

by aggregang components, the results show that the algorithm performs more opmally

in terms of smaller aggregate system rather than in larger assemblies where the error

proporonally increases as the number of elements is mulplied.

One of the signicant ndings refers to the two dierent methods of measuring the

system deviaon from the physical one. The simulaon of bend formaon was assessed

according to the rao of the horizontal projecon of the curvature to its height and the

deviaon of nodes posion in Z. The opmal soluon that refers to the observaon that

provides the minimum error for each aggregaon, is crosschecked by both of these two

dierent measurements. This nding conrms the validity of the implemented tests, thus the

credibility of their results.

Concerning the results derived from each case of Observaon, it can be seen that

there is not a single Observaon that represents the opmal soluon for all the stages of

aggregaon. For every stage that corresponds to dierent amount of elements tested, there

is a dierent opmal result. One of the persistent ndings was with the increase of expansion

rate on perpendicular spring connecons (spring type C ) and together with the decrease ofspring ideal length of central upper connecons (spring type B), the generated local curvature

within each cell came closer to the ideal one with minimum distoron rate. However, the values

of length to height rao that describe the degree of bend formaon are lower in that case.

On the other hand, the case when the perpendicular springs (spring type C ) expanse less with

minimum length deviaon from the equilibrium state combined with maximum expansion

rate on central upper connecons (spring type B), the buckling level is higher. However, the

values that refer to length to height rao are mainly disproporonate to physical ones, thus

maximum error from the physical model. Moreover, the results pointed out that the case of

observaon 4 where both the perpendicular and central upper connecons are subjected to

maximum deviaon from their equilibrium state, is not able to meet the requirements for

being opmal soluon in any aggregate system.

The tests on single unit showed that the algorithm is able to predict accurately with

negligible average error the ancipated deformaon of single cellular structure. Surprisingly, in

the next stage when aggregang two components, the average error remained stable without

any increase in its value. The algorithm is considered to provide valid results and predict

with high accuracy the bend formaon of the double cellular structure. Unlike the previous

small aggregate system, when the number of elements is mulplied, the four components are

subjected to higher deviaon from the ideal ones, thus the result of simulaon is less valid.

Clearly, this nding was ancipated, as the local transforms impact upon the whole. The global

deformaon ends up based on the interacon of spaal forces developed in each cell. Thus, the

exact behavior is less predictable as the system becomes more intricate. In that sense, when

aggregang six components, the system is providing with less accurate results. However, the

overall bend formaon presents high rate of similarity with the physical outcome. Each cellular


37



structure based on its local distribuon of dierent ideal spring lengths performs the

ancipated posive or negave curve with varied values of length to height rao. Mainly, the

middle units are subjected to higher loading forces, thus there the deviaon rate is higher

than the rest. Opmal soluon is considered the case where there is an uniform distribuon

of length to height rao within the overall range of aggregate system. In the case of aggregate

system being composed of six components, the opmal soluon is achieved with minimum

average error of 2.3. The trend line of average error shows a slight increase unl the level ofsix components, followed by a bigger rise on its value as the number increases more. When

aggregang twelve elements, the system behaves far more complex with resulng error to be

six mes bigger than the previous result.

Based on the trend line of error occurred in each aggregate system, it can be esmated

with high accuracy that as the prole geometry becomes more complex, the aggregate

system is considered inadequate in providing accurately results upon the physical reacon

of the arfact. The strong semanc connecons developed between the representaon and

the represented when considering small aggregate systems, are not applicable as prole

geometry becomes more intricate.

5.2 Crical Assessment

The proposion of this study is to explore an alternave design approach that allows

the inherent aributes and behaviors of complex material system to play a more acve role

in computaonal design process. Employing computaonally Hooke’s law, the parcle spring

system generates relaonal topographies that are subjected to tension or compression. In

that sense, the representaon incorporates a process of negoaon in which the form is

directly connected with the inuences of forces exerted within the system. In respect of the

inial design intenon, the performance of the generated topologies have been considerablyexamined and assessed towards the physical outcome of fabricated aggregate system.

Based on the previous ndings, it can be asserted that the parcle spring system

can provide sucient measurements to achieve a reliable simulaon concerning the inaon

of aggregate material system. However, the performance of the algorithm decreases as the

prole geometry becomes more intricate. Obviously, this is a logical consequence as the

deformaon is computed without taking into consideraon some signicant aspects such

as the gravity or the physical reacon of system when it interacts with other surfaces. The

biggest amount of measurements was carried out while the inatable aggregate system was

standing on the ground. Apparently, the resulng deformaon may change considerably in

case the model is hanging and oang without being interacted with any exterior to thesystem factor.

Moreover, silicone rubber as most material, is complex and displays non-linear

behavior when exposed to dynamic environmental inuences. In our case, building a scale up

model with inatable rubber components poses mulple challenges concerning its opmal

structural performance. Considering the fact that silicone rubber has low tensile strength

and is considered sensive to fague from cyclic loading, the fabricaon process took into

consideraon various aspects in order to build the cellular structure with less structural

damage when it is subjected to inaon for the purpose of this study. For instance, the shape

of moulds plays a fundamental role in fabricaon. Moulds specify the resulng thickness of

both silicone layers thus the rate of sness and elascity is also inuenced. In addion to that,

moulds provide the internal channel which controls the elasc bending of each pneumac

cell. The preferred input channel triggers a maximum inaon on upper layer and a slight and


38



gentle curve in overall range. This study didn’t take into consideraon the emergence of the

inated bubble of upper layer into the computaon design thus the overall deformaon was

computed without being esmated the impact of the upper inaon upon itself. Clearly, if

this aspect had been considered, it would have altered the results.

Despite the dicules of working on silicone rubber anisotropic aributes, the

physical model of aggregate pneumac cellular structure was successfully implementedand displayed high rate of tensile strength during successive inaon. This accomplishment

facilitates the experimentaon and the overall process. Moreover, regarding the computaon

part, it can be asserted that one of the most important features of the proposed algorithmic

method is the use of generave process for adjusng the specied spring lengths within

each cellular structure in order to display various bending behaviors. Employing this feature

computaonally on the overall aggregate system, the result is the transformaon of its inially

enrely planar surface to a double curved membrane with uniform wave ripple shape based

on the assigned bend behavior in each cell. In other words, the use of parcle spring system

provided a simplied method to generate reciprocal connecons between the arfact and the

digital model in order to update the design intent directly through feedback.

5.3 Future Developments

The study presented in this thesis can be regarded mostly as a preliminary invesgaon

for modeling material properes and behaviors within the digital model. Although the

implemented algorithm achieved to accomplish the thesis objecve, some aspects need to

be further explored for further advancements of the algorithm.

A high level of accuracy requires solving physical problems that can involve analysis

of uid mechanisms, thermodynamics and chemical kinecs. A beer understanding of these

topics would drive to more accurate models, thus to beer design and control. This entailed

the advance of computaonal design by embedding material logics and calibrang these with

nite element methods (FEMs) for simulaon. Combining the feedback from the fabricaon

process with the compared results of both generave computaonal design model and the

FEM model simulaon, it can be argued that material design computaon can explore higher

levels of complexity of aggregate systems and provide reliable results.


39



6.0 Conclusion

The framework of this study examines the case of engaging material properes

and capacies within the computaonal design in order to create a reliable model that can

predict accurately the behavior of a complex material system. The proposed method involves

a generave algorithm that establishes relaonal topographies based on a parcle spring

system and the material research is based on elasc inaon of silicone cellular structures. Theaim of this thesis was to determine rst the tness of the method on a single cellular structure

and then to test its eciency on more complex systems when aggregang components. The

tesng was carried out in four stages where the exploraon of dierent spring lengths within

each cell was conducted to nd the opmal soluon with minimum average error reported

in respect to the physical model. The inial tesng of the algorithm on single component

showed that it was able to generate the bend behavior with high rate of accuracy. The average

deviaon of the system form the ideal one remained constant without any change within the

next stage of tesng on double component. So far, the evaluaon of the results conrmed

the validity of the algorithm to simulate accurately the bend formaon. When the prole

geometry becomes more complex by aggregang more components together, the trend line

of average error showed a slight increase unl the level of six components, followed by a

bigger growth on its value as the number of elements increases more. Thus the algorithm

provided less reliable results when aggregang larger assemblies.

Despite the ancipated limitaons of the algorithm, the outcome of this study is

a design tool that constantly updates its role through feedback derived by physical tesng

on real model. Clearly, the key role of the algorithm to assign various bend behaviors by

changing the local distribuon of varied spring lengths within each cell, gives the privilege to

the designer to control the resulng form of the inatable double curved surface structure.

In this way, the algorithm sets the basic parameters that can be further developed in order

to provide more reliable results when it is tested on larger aggregates with higher complexitylevel.

In respect of the challenge to fully control the shape of deformaon on so robocs

which are considered the new shi to an innovave generaon of robocs cra, it can be

argued that by employing the proposed computaonal method to explore the performance

capacity of the intricate structure and elasc behavior of each cell, the study achieved the

challenge to control its deformaon and moreover to scale up the physical model producing

larger inatable silicone aggregates.


40



Web Documents:

M. Calis, M. Giorelli, G. Levy, B. Mazzolai, B. Hochner, C. Laschi ,P.Dario. An octopus-bioin-

spired soluon to movement and manipulaon for so robots [online].Available from:

< hp://www.octopus.huji.ac.il/site/arcles/Calis-2011.pdf> [Accessed June 2011].

Deepak Trivedi, Christopher D. Rahn, William M. Kier, Ian D. Walker.So robocs: Biological

inspiraon, state of the art, and future research [online]. Available from:

<hp://labs.bio.unc.edu/Kier/pdf/Trivedi_Rahn_Kier_Walker_2008.pdf> [Accessed Septem-

ber 2008].


42



Figure 50. Aggregate System of six components.




45







46



DIGITAL SIMULATION:

Illustraons of dierent digital aggregate systems

SINGLE UNIT:

DOUBLE UNIT:

Figure 56. Digital Simulaon of single unit.

Figure 57. Digital Simulaon of double unit.


47



AGGREGATE SYSTEM OF FOUR COMPONENTS:

Figure 58. Digital Simulaon of Aggregate System of four components.


48



Appendix IIPseudocode (aer Processing API)

Basic functions of the Particle Spring System:

//Create five different connections within hexagonal pattern

Spring [] springA; // Central Connection A

Spring [] springB; // Central Connection BSpring [] springC; // Perpendicular Connection

Spring [] springD; // Lower Side Connection

Spring [] springE; // Upper side Connection

int num1;

int num2;

int num3;

int num4;

// Declare different Arraylists to assign spring connections among their numbers

int [] central= new int[num1];

int [] centralConnectToDown=new int[num1];

int [] centralConnectToUp=new int[num1];

int [] perpendicularDown= new int[num2];

int [] perpendicularUp= new int[num2];int [] chain1a=new int[num3];

int [] chain1b= new int[num3];

int [] chain2a=new int[num4];

int [] chain2b= new int[num4];

String [] data;

Node [] nodes;

float mass; // Insignificant Value

float k; // Spring Constant

float d; // ID spring Length

void setup(){

frameRate(100);

size(1300, 800, OPENGL);

smooth();

font =loadFont( “Candara-Bold-14.vlw”);

textFont(font);

data= loadStrings( “File.csv”); //Read nodes position from a csv file

num=data.length;

nodes= new Node[num];

for ( int i=0; i<num; i++)

{

nodes[i]= new Node (); //Initialize nodes

}

insertData(data);

// Initialize the input values of arraylists

int[]central= {7, 7, 7, 7, ...... ....,131, 131, 131};

int[]centralConnectToDown= {1, 2, 4,...... .,129, 128, 127};

int[]centralConnectToUp= {8, 9, 11,..... ..,134, 133, 132};

int[]perpendicularDown= {1, 2, 3,.........,128, 129, 130};

int[]perpendicularUp= {8, 9, 10,..... ..,132, 133, 134, 135};

int[] chain1a= {1, 2, 3,....., 110, 109, 151};

int[]chain1b= {2, 3, 4,....,109, 78, 150};

int[] chain2a= {8, 9, 10,.....,134, 133, 132};

int[]chain2b= {9, 10, 11,......,133, 132, 123};


50



springA=new Spring[num1];

for ( int i=0; i<num1; i++)

{

springA[i]= new Spring( nodes[ central[i]], nodes[ centralConnectToDown[i]]); // Assign connecons of

Spring A type among certain nodes

}

springB=new Spring[num1];


{springB[i]= new Spring( nodes[ central[i]], nodes[ centralConnectToUp[i]]); // Assign connecons of

Spring B type among certain nodes

}

springC=new Spring[num2];


{

springC[i]= new Spring( nodes[ perpendicularDown[i]], nodes[ perpendicularUp[i]]); // Assign connecons

of Spring C type among certain nodes

}

springD=new Spring[num4];


{

springD[i]= new Spring( nodes[ chain1a[i]], nodes[ chain1b[i]]); // Assign connecons of Spring D type

among certain nodes

}

springE=new Spring[num3];


{

springE[i]= new Spring( nodes[ chain2a[i]], nodes[ chain2b[i]]); // Assign connecons of Spring A type

among certain nodes

}

}

void draw()

{

translate(width/2, height/2); lights();

background(86, 85, 90);


{

nodes[i].draw();

}


{

nodes[i].move();

}

drawSpring();

inate();

}

void insertData( String[]sarray)

{

for ( int i=1; i<sarray.length; i++)

{

String[]line=split( data[i], “,”);

nodes[i].posion.x= oat ( line[0]); // Read the csv le and assign posion x to the rst number of row

nodes[i].posion.y= oat ( line[1]); // Read the csv le and assign posion y to the second number of row

nodes[i].posion.z= oat ( line[2]); // Read the csv le and assign posion z to the third number of row

}

}


51



void drawSpring() // Draw the ve dierent spring connecons based on their assigned color aributes

{


{

springA[i].draw(120, 120, 120);

}


{

springB[i].draw(120, 120, 120); }


{

springC[i].draw(0, 0, 0);

}


{

springD[i].draw(140, 0, 0);

}


{

springE[i].draw(0, 0, 140);

}

}

void inate() // Adjust spring connecons with dierent expansion rates for the state under inaon

{


{

springA[i].computeLength(41.5, 3.0);

}


{

springB[i].computeLength(50, 3.0);

}


{

springC[i].computeLength(25, 3.0);

}


{

springD[i].computeLength(40, 3.0);

}


{

springE[i].computeLength(50, 3.0);

}

}

void balance() // Adjust spring connecons with dierent expansion rates for the equilibrium state

{ for ( int i=0; i<num1; i++)

{

springA[i].computeLength(41.5, 1.0);

}


{

springB[i].computeLength(41.5, 1.0);

}


{

springC[i].computeLength(20, 1.0);

}


{ springD[i].computeLength(40, 1.0);

}


52




{

springE[i].computeLength(40, 1.0);

}

}

Basic funcons of the parcle class:

class Node

{

PVector posion;

PVector velocity;

Node()

{

posion=new PVector ();

velocity= new PVector();

}

void move()

{

posion= PVector.add(posion, velocity);

velocity= new PVector(0, 0, 0);

}

void draw()

{

pushMatrix();

stroke(255);

strokeWeight(3);

point(posion.x, posion.y, posion.z);

popMatrix();

}

}

Basic funcons of the spring class:

class Spring

{

Node a;

Node b;

oat length1;

oat realLength;

PVector dir1= new PVector(0, 0, 0);

PVector dir2= new PVector (0, 0, 0);

oat g;

oat ID_springLength;

Spring(Node n1, Node n2)

{

a=n1;

b=n2;

length1= PVector.dist (a.posion, b.posion);

}

void computeLength(oat d, oat k) // calculate the length of springs by adgusng an ideal length ‘d’

ID_springLength= d;

realLength= PVector.dist ( a.posion, b.posion);

dir1= PVector.sub(b.posion, a.posion);

dir2= PVector.sub(a.posion, b.posion);

dir1.normalize();

dir2.normalize();

dir1.mult((k*( abs(realLength- ID_springLength)))/mass); //Hooke’s law of elascity

dir2.mult((k*( abs(realLength- ID_springLength)))/mass);


53



if (realLength< ID_springLength) // If the real length is smaller than the rest length of spring then push the

connected nodes apart from each other

{

a.velocity = PVector.sub(a.velocity, dir1);

b.velocity= PVector.sub(b.velocity, dir2);

}

if (realLength>ID_springLength) // If the real length is bigger than the rest length of spring then move the

connected nodes close to each other

{

a.velocity = PVector.add(a.velocity, dir1);

b.velocity = PVector.add(b.velocity, dir2);

}

if (realLength==ID_springLength) // If the real length is equal to the rest length of spring no forces are ap-

plied. the system is in equilibrium

{

a.velocity = new PVector(0, 0, 0);

b.velocity = new PVector(0, 0, 0);

}

}

void draw(int c, int v, int k)

{

realLength = PVector.dist (a.posion, b.posion); //Actual length

ID_springLength= d;

stroke(c, v, k);

strokeWeight(1);

line( a.posion.x, a.posion.y, a.posion.z, b.posion.x, b.posion.y, b.posion.z);

}

}


54