Emergent Technologies and Design Biomimetics workshop
Hygromorphic Actuators Arnold Tejasurya Arpi Maheshwari aka Jagetiya Chaitanya Chavan Giulio Gianni January 2015
ABSTRACT
The project explores the effect of different geometries and support conditions on the curvature of sheet of hygromorphic materials inspired by the Banksia’s seed separators. These cone-shaped separators are free to move inside cavities (or “follicles”) within the plant’s inflorescence by reacting to change in moisture content. First, the effect of different material selection (e.g. veneer, polypropylene, paper) for the active and passive layers of the bio-inspired bi-layer are investigated. Secondly, the effects of different geometries of the specimen (e.g. shape, maximum length, etc.) as well as sheet thickness, are explored. Finally, different types of connection of the sheet to create cones and their application on a membrane surface are investigated to understand their effect on the creation of a global curvature using digital tools. Although from this research no specific architectural design was obtained, it was noted that embedding hygromorphic elements within membranes leads to interesting and unseen results in terms of the production of global curvatures.This feature could be adopted in tensegritic-like membranes where the compressive struts are replaced by the hygromorphic actuator and is part of the future advances of the project.
INTRODUCTION The field of biomimetic bi-layers has been explored widely in the recent years within many different fields with a wide range of applications that varied from nanobiotechnology and the study of nanosensors (Martin, 2007) to architecture and the creation of climate sensitive architectural morphologies (Menges et Reichert, 2012). The latter has proved to be indeed a very interesting and contemporary field of work for architects and designers who’s aim is to produce a material system where no external mechanical or electrical imput is required, but were the “material computes the form in feedback with the environment” (Menges, 2012). Other sources of insipration in nature for such features which have also been previously approached range from the weat awns to the Horsetail plant’s spores, to the pine cones (Reyssat, Mahadevan 2009) However, what makes the Banksia’s seed separator hygromorphic behaviour unique and radically different is the restriction and containment of such behaviour not only by the follicle walls (see Section 2 for further details) but also by the unique shape of the separator itself. The first section of this report aims to describe the taxonomy and most importantly the anatomy of a Banksia inflorescence with particular focus on its seed separator.
Then, once the hygromorphic principle is “abstracted” from the Banksia, results and findings of material tests carried out on different types veneer-based bilayers in both a physical and digital context are explained. Finally, these findings are applied to explore different type of surface morphologies.
C+A coelacanth and associates: MOOM tensegritic membrane structure General References: Martin D., (2007) “Nanobiotechnology of Biomimetic Membranes”, Menges A. Reichert S., (2012) “Hygroscope” project in Centre Pompidou, Paris. Accessed 1st Jan 2015 from: http://www.achimmenges. net/?p=5083 Reyssat E., Mahadevan L., (2009) “Hygromorphs: from pine cones to biomimetic bi-layers”,The Royal Society.
Ch.
TABLE OF CONTENTS
Pg.
1
Banksia
08
Introduction Seed Separator
II
Hygromorphism and Material Exploration
13
Veneer and Unidirectional Ply Active-Passive System Material Tests Reversibility of System Geometric Exploration
III
System and Assembly logic
25
Joint Conditions and Surface Exploration Actuators in a System Boundary Conditions Assembly Parameters.
IV
Global Logic, Future Advances, Conclusion.
34
fig.1.1 Banksia Foliage and Inflorescence. Courtesy:Wikipedia
I
BANKSIA: Introduction Order: Family: Genus: Species:
Proteales Proteaceae Banksia Banksia sessilis
fig.1.2 Map of Australia(not to scale) showing the distribution of species of Banksia. Courtesy:Wikipedia
Banksia, a plant endemic to the continent of Australia, comes in a rather variety of sizes and shapes; from short bushes to trees as high as 30m. Ranging within a genus of 170 species, Banksia belongs to the Proteaceae plant family. The tree has long pointy leaves, size of which varies from just over a centimeter long to about 40 cm depending on the type and size of the plant. However, the most noticeable and prominent feature of Banksia is it’s inflorescence. This is a brightly coloured flower of the plant, which turns into a woody centered-seed bearing-pod. Each inflorescence has multiple seed separators- A two flanged chamber which holds the seed inside of it, protected from the elements. The seed dispersal mechanism of the Banksia tree, is rather unique and is the main subject of this documentation and will be further explored in great detail. Page
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Plan
Follicle(Socket)
Section
Section
Seed Separator
fig.1.3 Lateral and longitudinal c/s through a banksia inflorescence showing the position of the follicle(socket) and seed
I.I
BANKSIA: Inflorescence and Seed Separator
From the numerous flowers of the Banksia, which blossom on the hard centered “cone like” inflorescence, only few bear fruit. The fruit of a Banksia is a woody ‘follicle’ consisting of two flanges, which in turn bear the seed for the plant. These follicles are called the “Seed Separators”. The flowers on the inflorescence either dry out to reveal the rough skinned solid interior of the cone, or in some cases remain on the fruit.(See fig 1.3) Banksia has evolved to cope with the regular culling of the plant due to bush fires, however these very fires trigger a physical reaction such that the inflorescence releases the seeds and helps in the regen-
fig.1.3 Diagram showing parts of the Banksia Inflorescence.
fig.1.5 Brightly coloured Banksia Inflorescence. Image courtesy: Wikipedia Page
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I.II
Seed Separator: Working mechanism
fig.1.6 Seed separator of a Silver Banksia (Banksia marginata) with winged seeds still cohering. Courtesy:Wikipedia
The Seed Separator is made up of two flanges of a fibrous woody material. This separator sits inside of a pocket in the inflorescence. When the fire induces heat, there is a contraction of material and thus opening of the socket which holds the separator.
The series of images above show the process of displacement of the seed separator from inside of the socket. Each cycle of wet and dry spell, results in separation. The process is further explained geometrically and forms the basis of this biomimetic exercise.
Due to the Hygromorohic properties of the seed separator flanges, when rain water hits the inflorescence, expansion occurs in the flanges. As a result of the wedge shaped geometry of the seed separator and the joining conditions at the sides, a ‘mouth’ opens up, which is a slit at the top where the two sides of the flanges join. The curving of the free ends pushes the assembly slightly outside of the fixed socket.(Ref, fig. 1.7 below) When it loses moisture, the ends straighten up of again. This repeated Curved cycleEdges of wet and dry, over a few Seed Separator spells of rain,makes the seed separator push itself out Seed Separator-Dry of he socket thus releasing the seeds off the tree.
The diagram below, shows the process in a geometric illustration. The socket(shown in red) holds the seed separator(shown in black).The lateral compression of the seed separator(see plan below) results in an upward movement due to the conical geometry and fricSeparator-Wet Opening/uplift tion of the sidesSeed (ref section below) vs Dry
Lateral contraction
Upward push due to transverse expansion Opening/uplift relationship Curvature 1 W=Wbox @ h1 h1=0
Opening/uplift relationship Opening/uplift relationship
Seed Separator Socket
Force diagram
section:
Upward displaceLateral contraction
Up h2
h1
Curvature 1 W=Wbox @ h1 h1=0
Curvature 2 W=Wbox @ h-h2 h2>h1
h1 Force diagram
Curvature 1 Curvature 1 W=Wbox @ h1 W=Wbox @ h1 h1=0 section:
fig.1.7 Diagrams showing the working of seed separator: Reaction to the bush fire and hygromorphic behaviour of material.
h1=0
Plan
Expansion exerts pressure on the sides of the socket
Test outcomes
h1
PHYSICAL
shell force reaction at socket ridge
Uplift
[Vertical equilibrium] uplift + socket reaction = gravity + [friction] + shell force
Force diagram Force diagram section: section:
shell force
Curvature 3 W=Wbox @ h-h3
h3>h2 [Vertical equilibrium] of traslation (h) = gr uplift +height socket reaction
Curvature VIRTUAL 2
Curvature 2@ Model scale (range) Height of tras W=Wbox h-h2 fig.1.8 Force Material thickness W=Wbox @ Opened h-h2 surfa h2>h1 Optimal design of socket edge translation h2>h1 Socket ridge stiffness Effects of friction diagram.
Test Testoutc ou
shell force
Page reaction at socket ridge
10PHYSICA PHYSICAL
Model scale Model thic sc Material
Geometrical
Geometrical
s
Physical
s
h
Physical
h
c
c
R
R θ
Equations h= R (1 - cos½θ) c= 2R sin(½θ) where: R= s/θ
θ
Equations h= R (1 - cos½θ) c= 2R sin(½θ) where: R= s/θ
anisotropic/inhomogeneousanisotropic/inhomogeneous properties properties [direction of fibres, different[direction thicknesses] of fibres, different thicknesses]
Joint design Joint design [bolted, clipped, glued , taped] [bolted, clipped, glued , taped]
fig.1.9 Geometric explanation of the Test output Test output expansionPHYSICAL mechanism. PHYSICAL Opening/uplift relationship
fig.1.10 Diagram illustrates the difference between geometric andVIRTUAL physical world.
VIRTUAL
Relationship between c andRelationship h given between c and h given curvature model Geometrical Geometrical curvature model specific material and joints. specific material and joints.
I.III
Seed Separator: Geometric Extrapolation
h2
h1
Curvature 1 W=Wbox @ h1 h1=0
relationship
Curvature 2 W=Wbox @ h-h2 h2>h1
Force diagram section:
shell force reaction at socket ridge Uplift
To convert the process into a geometrical height of traslation (h) fixed socket width (W) exercise, we imagined the seed separator to behave Test outcomes isotropically. Fig.1.9 shows that we can achieve a relationship betweenVIRTUAL the radius of curvature R and h, the PHYSICAL Model scale (range) maximum displacement. Height of traslation with opening Material thickness
Curvature 3 W=Wbox @ h-h3 h3>h2 height of traslation (h)
Test outcomes reaction at socket ridge
plift h3
h2
ace area at ridge height
comes utcomes
AL
e (range) cale (range) ckness
However we realised that the material would behave in an isotropic manner and there will h3 always be an in-homogeneous curvatures at the ends, where the two flanges join. The exercise lacks the precise mathematical explanation to this anisotropic behaviour and further study would be needed to fully fixed socket width (W) understand this and to convert it to a decipherable equation.(ref. fig, 1.10)
PHYSICAL
VIRTUAL
Model scale (range) Material thickness Optimal design of socket edge
Opened surface area at ridge height
Socket ridge stiffness Effects of friction h3
fixed socket width (W) + shell force ravity + [friction] h2
slation with opening
Opened surface area at ridge height
Socket ridge stiffness never Effects of friction
Curvature 2 W=Wbox @ h-h2 h2>h1
shell force
Curvature 3 W=Wbox @ h-h3 h3>h2
Optimal design of socket edge
[Vertical equilibrium] h2 uplift + socket reaction = gravity + [friction] + shell force
h1
As mentioned earlier in the document, the conversion of expansion ofh3geometry to vertical displacement is further studied.
h3
Curvature 3
Curvature 3W=Wbox @ h-h3 W=Wbox @ h-h3 h3>h2 h3>h2
Height of traslation with opening
fig.1.11 Diag. Explaining the conical expansion v/s the upward displacement.
height of(h)traslation fixed (h) socket width fixed height of traslation (W)socket
VIRTUAL
width (W)
Page
VIRTUAL
Height of traslation with opening
Height Opened surface areaofattraslation ridge heightwith
A simple way to understand the vertical displacement, is to imagine a super rigid box, containing a conical assembly with two sides. When the distance between the top edges increases, the sides exert pressure on the rigid box. Since the width of the box is a fixed parameter, to accommodate the expansion, the cone will be pushed upwards till the point where the internal distance of the cone(shown in blue) matches with the width of the box.(refer fig.1.11)
opening
11
Images ref. HygroSkin, Developed by architect Achim Menges, David Krieg, Steffen Reichert.
II
HYGROMORPHISM AND MATERIAL EXPLORATION
We see various examples in nature where water ( or the lack of it) makes things behave in a certain way. In addition to Banksia, take for example, the opening of pine cones, formation of cracks in muddy lakes to crumbling of leaves after drying. Hygromorphs, are materials which behave in a certain manner as a reaction to moisture. We, during the course of this exercise, studied materials for such properties.Two of the easily available ones, paper and veneer were subjected to certain tests. The aim of it all was to create a system which reacts to moisture, and to study how a very local action, has a global effect. Also it was desired that the system be completely reversible, meaning over the course of one wet and dry spell, it should return back to it’s original state.
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[mm] 35 30
vertical expansion
II.I
Assembly of Material
25
Bidirectional Ply
20
Multi layer Composition 15
To realise the project in the real world, scalability becomes a pressing issue. One way of achieving 10 this is to imagine a system with more thickness. How5 ever, working with veneer, we realized that to achieve 0 5 10 15 20 horizontal thickness we need to work with a ply. Plywood being contraction [mm] wood gluehas a much lesser curving a bidirectionalevo-stik composition, polyrethane glue capacity. Bidirectional Ply Hence we decided to produce our own “uniBidirectional Ply directional” ply using sheets of veneer. These sheets were glued on top of each other in the same direction of grains using a polymer glue.
Unidirectional Ply Unidirectional Ply
Selection of a suitable Glue.
To achieve the above mentioned ply, we want10 is more flexible 15 20 thus not a glue which when[mm] dry, horizontal contraction hindering the behaviour of the system.We also needed stik wood glue rethane glue a glue which is water resistant and durable. 5 ed
We tried two glues: Evo stick wood glue and a Polyurethane Glue. It was observed that polyurethane glue was best suited for our purposes. Also the layer thickness required by this glue was much thinner when compared to any other glues.
Unidirectional Ply
Polyurethane Glue
Wood Glue performance
[mm] 35
vertical expansion
30 25 20 15 10 5
0
5
10
15
horizontal contraction
20 [mm]
evo-stik wood glue polyrethane glue fig. 2.4 Graph showing the relation between horizontal and vertical displacement from two different glue Page
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II.II
Variation of Material Paper, Veneer, Polypropylene
To arrive at a desired combination of materials, a comparative test was conducted between combinations within three materials viz. Paper, Veneer and Polypropylene. Our conclusion was that although veneer has the best performance on its own, it has scaling issues.
To tackle with the problems, we narrowed down on the combination of veneer and polypropylene, (which is studied further in the document)
01. Paper + Polypropylene Active Layer : Paper Passive Layer : Polypropylene Analysis : In a system with Paper and Polypropylene, paper being the hygromorphic material, behaves as an active layer. By knowing the thickness and absorptive capacity of paper, the system curvature can be controlled. In a triangular shape, the smallest side is the natural curving side, however, it was also observed that after losing moisture, there is a residual deformation which occurs along the longer side of the triangle.
fig. 2.1 image of combination between paper and polypropylene
02.Veneer + Paper Active Layer :Veneer Passive Layer : Paper Analysis : The experiment was to see the behaviour of the system when we use two proven active layers, Paper and veneer. It was observed that veneer having greater reaction to moisture, behaved as an active layer. This combination proved to be giving the greatest curvatures, as bot layers were augmenting the process of curling. The drawback of the combination; it has a greater residual deformation, in the same direction.
fig. 2.2 image of combination between paper and veneer
03.Veneer + Polypropylene Active Layer :Veneer Passive Layer : Polypropylene Analysis : The third combination was with Veneer and Polypropylene.Veneer acting as an active layer, and polypropylene being a hydrophobic material, behaves as a passive layer. The system was obs erved to have a uniform desired curvature, however after loss of moisture, there is almost an equal amount of residual curvature which is in the opposite direction.
fig. 2.3 image of combination between veneer and plypropylene Page
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II.III Comparison between types of Veneers After establishing that we would be working with veneer as a primary material in our system, we tested different types of veneers to see which variation achieves the best suitable results. We subjected six different types of veneers to similar tests for comparison. A strip of 120x30mm was used from each variation, and the grain direction was perpendicular to the longer side. They were then immersed into warm water and set aside. It was observed that Veneer 1,3,4,5, and 6 had the most response to the moisture. However Sample 6 was selected, for its curvature was much more predictable and reproducible to the least error.
[mm] 45
vertical expansion
43 41 39 37 35 33
[material 1] [material 3] [material 4] [material 5] [material 6]
31 29 27 25
0
0.5
1
1.5
2
horizontal contraction
2.5
3
3.5 [mm]
ďŹ g. 2.5 Graph showing the differentiation of horizontal contraction and vertical expansion between each veneer. I t compares various veneers with different properties like hygrosensitivity, density of ďŹ bers, material performance etc. Page
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Curvature
Material Fiber
Experiment Veneer sample 01
maxV=40mm Veneer material sample01.which has a good ratio between the vertical deflection and horizontal displacement, in this case sample01 has good stiffness however it is not suitable for outdoor use for long period because it structurally weak, Veneer sample 02
maxV=10mm Veneer material sample 02, has very little hygrosensitivity, which affects the vertical deflection and horizontal displacement. It was observed that it was too less to be applied in a the real project.
Veneer sample 03
maxV=38mm Veneer material sample03, this sample has good hygrosensitivity behaviour, however it also has asymmetrical curve due to non homogeneous distribution of fibers. Therefore with this material the curve can be rather unpredictable,
Veneer sample 04
maxV=36mm Veneer Material Sample04 was observed to be too thin a material. Even though we achieve a decent curvature, the real world application of such thin material was a concern.
Veneer sample 05
maxV=36.5mm Veneer Material sample05, the grains in this veneer were observed to be not always parallel,which resulted in an uncertainty of the direction of the curvature. We were unable to predict the same beforehand.
Veneer sample 06
maxV=44mm Veneer Material sample06, we observed that this sample had the most uniform grain distribution, of all the other samples. It also showed a rather predictable and reproducible results, which led us to settle on this as our base material for the rest of the project, Page
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II.IV
Material Tests with different
Length of veneers strips
Veneer
[Material 06 ; All strips being 30mm wide] The aim of the experiment was to determine if significant curvature is achieved across a larger length, so as to deal with the scalability aspect. We observed the radii of curvature across various lengths of veneer strips. The conclusions were then plotted in a graph. (ref image 2.6 and 2.7)
As the length of the strip increases, there is a tendency of the system to spiral onto itself. This property can be used for certain purposes, however, which was not much suited for our aim. Hence we can say that for the given material system, a certain ‘golden ratio’ exists in between the range of lenths 100-120mm. Strip_04 L=150mm
Strip_01 L=40mm
R=6.0mm
R=9.6mm Strip_05 L=200mm
Strip_02 L=75mm
R=3.95mm
R=8.1mm
Strip_06 L=300mm
Strip_03 L=100mm
R=7.4mm R=3.9mm
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horizontal/vertical horizontal/vertical def. def.
3 2.5 3 2 2.5 1.5 2 1 1.5 0.5 1 5 0.5 5
[mm] 120
0
50
150
100
200
250
300
strip length y=-0.0015x^2+0.1408x-0.2338
0 R^2=0.956 50
100
150
200
fig. 2.6 Graph showing the relation between the ratio deflection with the strip length
250
300
350 [mm]
200
250
300
350 [mm]
200
250
300
350 [mm]
strip length
Experiment Plots Resultant graph
350 [mm]
RADIUS of CURVATURE 100
Radius
[mm] 120 80 100 60
Radius
] ] ] ] ]] ] ] ] ]
RATIO of DEFLECTIONS
80 40 60 20 40 5 20 5
0
50
100
150
strip length 0
50
100
150
strip length y=0.0096x^2-0.556x+11.803 R^2=0.976 Experiment Plots Resultant graph
fig. 2.7 Graph showing the relation between the radius of the curvature with the strip length
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II.V
Material Tests with various
Layers of veneers strips
As stated earlier, the challenge of scalability of the system was to be tackled. One way of achieving that was to increase the thickness of material. Which led us to the use of an unidirectional veneer ply.
The expirement is based on a uniform size of a strip; 120x30mm. Four different thickness have been compared. The first being only one veneer,then two and so on. Along with One passive layer of polypropylene.
The following experiment aims at recording the effect of the thickening of material to the ability of the system to attain a curvature. By means of having a basic database of different thicknesses, we aim to achieve a fundamental formula to get the optimum layer thickness to any given length of a strip, and vice a versa.
ďŹ g. 2.8 Picture depicting gradation of curvature achieved by strips with incremental thickness difference.
Curvature
Minimum
Maximum
fig. 2.9 graph from the result of different layered veneer experiment
4 layers veneer 1 polypropylene
3 layers veneer 1 polypropylene
4 layers veneer 1 polypropylene
A uniform size of 12x3cm strip was compared across various thickness of veneer.
1 layer veneer 1 polypropylene
Although we were able to achieve a conclusion, we were unable to create an ‘optimum condition’ formula to be applied to the project, We had to rely more on a trial and error basis. However we believe that further research in this aspect can yeild what we were aiming for.
Overall observations led to the conclusion that a system of One Veneer sheet with One Polypropylene layer has a greater achievement of curvature, as more layers are added, there is increased resistance thus reducing curvature.
LAYER TEST [mm] 16
vertical expansion
14 12 10 8 6 4 2 0
0
0.5
1
1.5
2.5
2
horizontal contraction
3
3.5 [mm]
1 active layer 2 active layers 3 active layers 4 active layers
fig.2.10 graph from the result of different layered veneer experiment Page
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II.VII
Material Tests with
Reversible Behaviour
or the lack of it.
With a system of active and passive layers of Veneer and polypropylene, as we start applying moisture, there is a gradual increase in curvature. The experiments were all focused on this behaviour. However, we noticed, that when the process of losing the moisture begins, the system behaves in quite an opposite way.After reaching to the normal (as it were before application of moisture) the system does not stop at that. We observe an opposite curvature, wherein the active layer behaves like a passive one i.e. veneer curves to the inside. This creates a problem for a system which hinges on being reversible. Further chapter deals with tackling this problem, where we see how addition of thickness incrementally over a single surface prevents the system from curving in the opposite direction in case of complete loss of moisture.
+ 4.3 cm
01 L
+4.2 cm
02 L
+3.5 cm
03 L
+-3 cm
04 L
-3.5 cm
03 L
-4.2 cm
02 L
- 4.3 cm
01 L
ďŹ g. 2.11 Effect on curvature with addition and removal of moisture.
2 2 0 0 0 0
0.50.5 II.VII
1.51.5
1 1
2 2
2.52.5
Material horizontal contraction horizontal contraction
3
3.5
3 3.5 Tests with [mm] [mm]
1 active layer 1 active layer 2 active layers 2 active layers 3 active layers 3 active layers 4 active layers 4 active layers
Gradation of thickness in a single member
b
The effect of thickness of material to the curvature being established, we wanted to experiment with the thickness being applied as a gradient to a single system (a triangle). So, taking a base isosceles triangle of 120mm side, layers were added every 2/3rds of the height. In total of 4 such smaller tri-c angles were overlapped creating in technical terms, a ‘unidirectional veneer ply’ with gradating thickness, with a passive layer of polypropylene below.. Uniform overall thickness
1 veneer 1 polypropylene
Variation in overall thickness
4 veneer 1 polypropylene
fig. 2.13 a single layer system
A single layer system with active and passive layers being One veneer and One polypropylene triangle respectively. A curvature was observed where the side curls onto itself. (Ref. fig.2.11) Also after complete loss of moisture, the system reverses it’s curvature (Explained previously in the document; ref chap.II.VI)
A multi-layered system where the active and passive layers are (4)layers of veneer and one polypropylene respectively. The effect of Variation of thickness was observed.The system has an overall curvature which does not curl onto itself. (Ref. fig.2.11)
fig. 2.14 a multi layer system
We could conclude from this that with application of variation of thickness, we could achieve a controlled curvature, and because of the resistive nature, there will always be curvature on the opposite side of which the layers are glued. One more important effect of layering was that it prevented the system to go to a reversed curvature after complete loss of moisture.This can be extremely beneficial for a system which demands reversibility (i.e. coming to the initial state of rest, as it were before application of moisture, after one cycle of wet and dry)
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c
III
SYSTEM AND ASSEMBLY:
The next step was to carry forward the results from the experiments on individual units and assemble them to form a system which can use the hygromorphic behaviour of veneer as an actuator.
III.1
So we set up a model with a 2 materials laminated together forming a bilayer system. Here one of the material is an Active material, with a certain amount of thermal expansion, while the other material is the passive material with zero thermal expansion. When temperature is applied, the system attains a curvature because of the difference in thermal expansion of the 2 layers. This replicates the physical experiments with veneer and polypropelene exposed to humidity.
JOINT CONDITIONS:
We further decided to explore different joint conditions digitally in Strand7 to study the variations in the assembly of 2 triangular units. We carried out 4 different joint conditions. Limitations of using Strand7 is that we cannot set up hygromorphic behaviour of the veneer as the actuator, so we needed to replicate that behaviour by using a material with thermal expansion and using temperature as an actuator.
III.1a PINNED JOINT
Material Properties: Active material: Modulus E : 1000 MPa Poisson’s ratio v: 0.3 Thermal Expansion: 0.005 Thickness: 1mm Temperature: 10 degrees C Passive material: Modulus E : 1000 MPa Poisson’s ratio v: 0.3 Thermal Expansion: 0.000 Thickness: 1mm
Pin joint
fig.3.1 Diagram illustrates Curvature Analysis
The first joint condition we explored was a Pin-Joint where two triangles are bound at the 3 end points. This allows formation of uniform double curvature because of uniform stress along the entire surface. This was one of the computational limitation of observing material oriented curve.
fig.3.2 Diagram illustrates Stress Analysis
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III.1b HINGED JOINT
Hinged joint
fig.3.3 Diagram illustrates Curvature Analysis
fig.3.4 Diagram illustrates Stress Analysis
The second joint condition we explored was a Hinged-Joint where two triangles are bound along the 2 longer sides. This restricts the translational movement along the vertical axis and allows for a rotational movement along the joint between the two sides. It is observed that the stress reduces gradually from the vertex towards the free side of the triangle. This results in a curvature which increases gradually towards the free side of the triangle. Thus it was established that for hinged-joint condition, as the distance between surface and the joint increases, the curvature also increases.
III.1c FIXED JOINT
Fixed joint
fig.3.5 Diagram illustrates Curvature Analysis
fig.3.6 Diagram illustrates Stress Analysis
The third joint condition we explored was a FixedJoint where two triangles are bound along the 2 longer sides.This restricts the translational movement as well as rotational movement along the edge of the triangles. It is observed that the stress reduces drastically from the vertex towards the free side of the triangle. The stress near the vertex is too high which restricts the formation of curvature. However near to the free side of the triangle, we observe a very high curvature in the direction parallel to the grains. This is again because of Computational limitations.
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III.1d PARTLY FIXED-HINGED JOINT
Hinged joint
Fixed joint
ďŹ g.3.7 Diagram illustrates Curvature Analysis
The fourth joint condition we explored was a PartlyFixed and Hinged Joint where 2/3rd of the longer side of the triangles is bound by Rigid Joints and the rest 1/3rd is bound by Hinged Joints. A relatively shallow curvature is observed along the fixed part of the joint. ďŹ g.3.8 Diagram illustrates Stress Analysis
Conclusion The series of digital experiments lead us to derive different curvatures depending on the various joint conditions. From the above experiments we realized that using Hinged-Joints to connect two units generates an assembly which has uniform curvature and stress distribution. Thereby we decided to use this jointing method to carry on with our further explorations.
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III.II
Geometric Exploration
b a
b
02 Triangular:
01 Rectangular:
c
With a rectangular surface, although we achieve greaer curvature height, when the system displaces(curves) it has 4 end points which displace out b of place. pt.s a,b,c, and d seen below. a
3
a With a shape which is triangular, because there is d curvature only on one of the three sides of the triangle, given that the grain direction is along the height of the triangle, there is displacement of only two points c as against to a rectangular shape. pt.s a and b below d
1 active layer 2 active layers 3 active layers 4 active layers c
3.5 [mm]
b
a
b d
a
ctive layer active layers active layers active layers
b b
a c
b
a
d
a
b
b c
b
a
b
a
a a
b
System
03 Rhombus: a
The next best geometry to a triangle was a rhombus, whichchas the same number of displaced points, but is more symmetrical when compared to b a triangle, with a central curving axis. a
To imagine a surface with rhomboid geometry, gave us cmuch freedom and scope to develop a regional system. Using the curving direction b to our advantage, we can have a system with two rhombi which have reverse direction of curvature, thus creating a variation. a
c
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III.III
SURFACE EXPLORATION: Further we decided to study the behaviour of Hygromorphic rhomboid shapes. Experiment setup involved a laminate of Veneer, as active material, and Polypropylene, as passive materials. These rhombus units were assembled with alternate units in opposite directions of curvature while keeping the grain directions constant. These units were connected to each other only at the vertices. This allowed formation of curvature of indiviual units. So we had the white veneers curving in one direction whereas the brown veneers curving in the opposite direction.There is an overall curvature achieved to the system as a whole because of the curvature at local level.
fig.3.9 Physical model of rhombus unit arranged alternatively in opposite direction .
fig. 3.10 Physical model of system using membrane as the passive member
fig.3.12 Physical experiments using evenly spaced veneers as actuators
fig.3.11 Physical experiments using evenly spaced veneers as actuators
Our next step was to introduce a flexible membrane to act as a passive member. Hence we designed a system with equally spaced veneer rhombuses as actuators, connected by a membrane between them (fig 3.10,3.11 and 3.12). Here a Hinged-Joint like connection was established where in translational movement of veneer with respect to membrane was restricted but rotational movement was allowed. So we could observe the formation of uniform curvature in individual rhombus units. It was also observed that after curving, the actuators produced stress in the membrane. Because of fixed boundary conditions, these stresses in the membrane get translated into an overall curvature. Stresses in the membrane was further studied by computational exploration.
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III.IV
SYSTEM ORGANISATION:
The further step was to create digital model and experiments using Strand 7 to help us generate a system where veneer acts as Actuators to put the Membrane in Tension. Due to fixed boundary conditions, the stresses in the membrane are translated into a glogbal curvature
III.IV a Evenly spaced Actuators
As we did in the previous Strand7 experiments, we tried to replicate the hygromorphic behaviour of veneer by applying temperature and using the thermal expansion of the materials as our action. We created a bilayered Actuator where one material (active) has some thermal expansion and the other (passive) has zero thermal expansion. The difference in the thermal expansion leads to the formaion on the curvature when the 2 materials are laminated together
Material Properties: ACTUATOR:
Active material:
Passive material:
Modulus E : 1000 MPa Poisson’s ratio v: 0.3 Thermal Expansion: 0.005 Thickness; 1mm Temperature: 10 degrees C
Modulus E : 1000 MPa Poisson’s ratio v: 0.3 Thermal Expansion: 0.000 Thickness: 1mm
MEMBRANE: Modulus E : 20 MPa Poisson’s ratio v: 0.45 Thermal Expansion: 0.00 Thickness; 1mm Boundary conditions: Fixed to restric translational and rotational movements in all directions. fig.3.13 Diagram illustrates evenly spaced actuators Plate Curvature xx (mm) -2.032
fig.3.15 Diagram illustrates Stress Analysis - Front view Plate Stress (MPa) 3.88
-2.5
2.18
-4.5
0.67
Actuators
Actuators
Plate Curvature xx (mm) 3.6
Plate Stress (MPa) 0.75
2.7
-0.12
-3.4
fig.3.14 Diagram illustrates Curvature Analysis
Membrane
-0.91
fig.3.16 Diagram illustrates Stress AnalysisTop view
Membrane
From the Digital experiments (fig 3.13, 3.14, 3.15 and 3.16) we observed that the Actuators attain curvature when applied temperature and this induces Stress in the membrane. The rhombus units are evenly spaced which results into evenly distributed stress in the membrane.
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III.IV b Stagerred Actuators
Material Properties: ACTUATOR:
Active material:
Passive material:
Modulus E : 1000 MPa Poisson’s ratio v: 0.3 Thermal Expansion: 0.005 Thickness; 1mm Temperature: 10 degrees C
Modulus E : 1000 MPa Poisson’s ratio v: 0.3 Thermal Expansion: 0.000 Thickness: 1mm
MEMBRANE: Modulus E : 20 MPa Poisson’s ratio v: 0.45 Thermal Expansion: 0.00 Thickness; 1mm Boundary conditions: Fixed to restric translational and rotational movements in all directions. Flexible Membrane
Hygromorphic actuators
fig.3.17 Diagram illustrates Staggered actuators system Plate Curvature xx (mm) 9.99
fig.3.19 Diagram illustrates Stress Analysis Front view
2.7
2.89
-5.3
0.31
Actuators
Actuators Plate Stress (MPa) 3.12
Plate Curvature xx (mm) 9.3
1
-1.19
-7.29
fig.3.18 Diagram illustrates Curvature Analysis
Membrane
Plate Stress (MPa) 5.7
-2.70
fig.3.20 Diagram illustrates Stress Analysis
Membrane
Further Digital experiment (fig 3.17, 3.18, 3.19 and 3.20) we carried out was by introducing a staggered row between 2 parallel rows of actuators. The boundary conditions are fixed to restrict both translational and rotational movment. Here the surface area of the membrane decreases and the number of actuators increases. Because of this we observed that the stress in the membrane increases drastically. This leads to formation of a global curvature. Page
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III.IV c Reverse Actuators Material Properties: ACTUATOR:
Active material:
Passive material:
Modulus E : 1000 MPa Poisson’s ratio v: 0.3 Thermal Expansion: 0.005 Thickness; 1mm Temperature: 10 degrees C
Modulus E : 1000 MPa Poisson’s ratio v: 0.3 Thermal Expansion: 0.000 Thickness: 1mm
MEMBRANE: Modulus E : 20 MPa Poisson’s ratio v: 0.45 Thermal Expansion: 0.00 Thickness; 1mm Hygromorphic Flexible Membrane actuators
On the back of Membrane
Boundary conditions: Fixed to restric translational and rotational movements in all directions.
fig.3.21 Diagram illustrates Staggered actuators system
Plate Curvature xx (mm) 6.29
Plate Stress (MPa) 0.30
-2.00
-1.57
-9.38
-3.08
Actuators
Actuators
Plate Curvature xx (mm) 1.40
Plate Stress (MPa) 0.30
-1.77
-1.32
fig.3.22 Diagram illustrates Curvature Analysis
Membrane
Next Digital experiment (fig 3.22, 3.23 and 3.24) we carried out was by introducing a row of actuators on the other side of the membrane.. The boundary conditions are fixed to restrict both translational and rotational movment. Here both the actuators have curvature in opposite direction to each other. It was observed that a global curvature is formed in the direction of the actuators with maximum curvature (fig 3.24)
-1.20
fig.3.23 Diagram illustrates Stress Analysis
-2.70
Membrane
fig.3.24 Diagram illustrates Stress Analysis Front view
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III.IV d Gradation of thickness of Actuators Material Properties: ACTUATOR: 1 layer 2 layers 3 layers 4 layers 5 layers
Flexible Membrane
Hygromorphic actuators
fig.3.25 Diagram illustrates Staggered actuators system
Active material: Modulus E : 1000 MPa Poisson’s ratio v: 0.3 Thermal Expansion: 0.005 Thickness layer1: 1mm Thickness layer2: 2mm Thickness layer3: 3mm Thickness layer4: 4mm Thickness layer5: 5mm Temperature: 10 degrees C
Passive material:
Modulus E : 1000 MPa Poisson’s ratio v: 0.3 Thermal Expansion: 0.000 Thickness: 1mm MEMBRANE: Modulus E : 20 MPa Poisson’s ratio v: 0.45 Thermal Expansion: 0.00 Thickness; 1mm Boundary conditions: Fixed to restrict translational and rotational movements in all directions.
Plate Curvature xx (mm) 1.24
Plate Stress (MPa) 5.79
5.73
2.89
-9.84
0.31
Actuators
Actuators Plate Stress (MPa) 3.12
Plate Curvature xx (mm) 1.07
2.34
fig.3.26 Diagram illustrates Curvature Analysis
-6.10
Membrane
Further Digital experiment (fig 3.26, and 3.27) we carried out was by using layering of veneer increasing gradually. The boundary conditions are fixed to restrict both translational and rotational movment. We observed that as the layering increases the thickness of veneer, stress increases thereby reducing the local curvature. This reflects in the curvature of the global geometry. Thus desired curvature can be obtained by varying the layering of the actuators.
-1.19
fig.3.27 Diagram illustrates Stress Analysis and side view
-2.70
Membrane
In conclusion, we carried out a series of digital experiments to simulate the desired curvature and study the stresses generated in the system. However, due to limitations of the software we had to use temperature as an activator instead of humidity. Also, during the physical experiments we could not devise a method to control or measure the amount of humidity. Also, we would like to take these experiments forward to a larger scale where similar system could be designed to create inhabitable spaces.
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Current
Proposed
Veneer
(active)
Polypropilene
(passive)
Lycra
(membrane)
Existing
Lycra
(Membrane + Passive)
Veneer
IV.1
FUTURE ADVANCES
Given the promising results obtained from the digital explorations the potential uses of this system are numerous. The idea of embedding the hygromorphic elements within a membrane surface immediately triggers the possibility of having a membrane structure held up by the contraction and bending of these elements. Very much like the “tensegritic membrane strcutures” -a great example of which is provided by the MOOM pavilion by Kazuhiro Kojima- the membrane can be put into tension by the environmental esponse of the hygromorphic actuators. However, where in “conventional” tenensegritic membranes the struts act in pure compression, in this case it is not fully undestood if it would be compression, bending, or most likely a combination of the two. Thinking about the way in which the hygromorphic components are embedded in the membrane- an aspect of the project that was not explored thoroughly enough- highlighted the possibility of removing the polypropilene as a passive layer and use the membrane itself as one. In order to do so however it is understood that the amount of pre-tension in the membrane when it is fixed to the veneer component as well as the flexibility of the type of membrane itself would be crucial to obtain a layer which is effectively “passive” and does not stretch.
(active)
Proposed
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IV.II
CONCLUSION
To conclude, we can state that the project has only scratched the surface of what is deemed to be a field of work extremely promosing and rich of potential. It is understood that the interesting results of the research conducted on the system of hygromorph material and membrane are only partial and cannot be used for any architectural design until the upper scalability of this system has been defined. Some studies on the relationship between strip thickness, strip length and radius of curvature have been conducted, however these can only provide us with a qualitative understanding of their relationship and do not provide us with the numbers necessary for such system to be applied on an architectural scale. Indeed, it was also understood that the rhombic shape- one of the most noticeable features in this systemcould provide several advantages in terms of obtaining curvature and in terms of regular disposition on a sheet of material (or membrane). However, these benefits were not compared thoroughly enough against other shapes and geometries. It is also forseeable that these rhomibc components- or indeed any component with sharp angles- can “poke� the membrane. Although this issue has not been tackled, a good solution could be provided by rounding the corners of the components. Finally, when considering the type of membrane to be used, the connection system between the membrane and the hygromorph components, as well as the optimal geometrical arrangement of the components on the membrane a lot of work has to be done before an architectural design can be produced using this system.
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