Interstitial Iterations

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THIN | THICK SHELL - PROPOSAL

LEARNING FROM NATURE - NUT SHELLS LEARNING FROM NATURE - CELLULAR STRUCTURES - FOAM

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RETICULATING THE VOLUME

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PACKING INVESTIGATIONS

48 52 58 70 78

CELL CONFIGURATIONS GEOMETRICAL ARRANGEMENT RANDOM DISTRIBUTION PACKING SIMULATION

LIQUID SIMULATIONS

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TOWARDS THE THICK SHELL

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SPHERES ARRANGEMENT ON THE SHELL FORM - FINDING METHODS ON MEMBRANES FABRICATION PROPOSAL

178 198 206

THICK SHELL

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FORM - FINDING MEMBRANES DETERMINISTIC AND STOCHASTIC LEVEL POURING CONCRETE ON SHELLS - POURING POINTS

228 240 244

PACING FUNCTIONS

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HETEROGENEOUS SHELL

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THIN | THICK SHELL

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PROPOSAL

interstitial investigation on the relationship of insdide and outside space

Architecture itself provides shelter from capricious environment. The built structure mediates between the environmental conditions of inside and outside. This makes the build structure a connector-interstitial space. The project means to investigate the role of shell in architecture through the new direction of contemporary architecture that is adaptive, autonomous, dynamic and responsive. For the making of architecture, when we come to know that built structure (the shell) is a connector, then our effort to design that connector should be how to make a better connection.

The aim of the project is to challenge the perception of concrete shell structures as a flat thin surface without any openings, as well as their basic forms and the idea of covering big spaces without subdivisions. It seeks to investigate a new methodology that replaces the limited conception of the traditional shell structures in light of the potentials of natural structures.It proposes to create a 3D perforated ‘thick concrete shell’ that generates a system and can cover functional, structural and formal needs.

The research started investigating the potentials of natural shells (nuts) and cellular structures as a strategy for design. In particular have been investigated the Foam Structures. All of those structures have different characteristics that could be used for creating 3D perforated structures on a wide range of design scales.

Understanding the cellular structure of the foam allowed us to explore the relation between the solid and void spaces. Designing the voids can lead the way to designate the form that is the by-products of voids themselves. Thus the areas left outside the voids define the negative space which forms the spatiality.

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Project started to investigate the analysis thin concrete shell structures, which began to appear in the 1920s. A thin shell concrete structure, is a structure composed of a relatively thin shell of concrete, usually with no interior columns or exterior buttresses. The shells are most commonly flat plates and domes, but may also take the form of ellipsoids or cylindrical sections.The aim of the project is to challenge the consideration of concrete shell structures as a flat thin surface without any openings, as well as their basic forms and the idea of covering big spaces without any subdivisions. Our intend is to create 3D perforated ‘thick concrete shell’ that acts as structural component which allows openings, surface perforations and space subdivisions.

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LEARNING FROM NATURE NUT SHELLS Shells in nature represent in a intricate way the relationship of outside and inside. The study of nuts through sections shows the differantiation between the two membranes exterior and interior. The formulation of which is directly affected by.

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[Above]

Almond is a monocoque strong single structure. It has crude skin that has porosity.that lets air in and out, keeps water from getting out,while allowing moisture in. Providing nutrients for the developing plant through its interior skin.The interior is really smooth. The seed inside is totally different environment but a very same durable hard preservative material.Walnut structure was much more different then Almond because it has a really hard exterior shell but also a thin interior skin(or membrane ) to form the seed inside. The exterior and interior cover is different material.Brazilnut sections shows three different layers that is serried. The inner layer so smooth and it has reinforcement in the corners.

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The series of cutting sections done on nuts summarize some in testing observations. The nuts structure works on different layers such as; The outside shell-a solid strong skin--The inside-on hollow space. Interior (the seed ) is forming the exterior(shell) in the same time shell shapes the seed.

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LEARNING FROM NATURE CELLULAR STRUCTURE - FOAM The research on cellular lattices explores the idea of heterogeneity in structure. Foam is used as a model that shows those properties in its structure and fabrication.

Foam is a man made cellular structure with entropic qualities and variable properties. It is a multi scale system characterized by heterogeneous geometries and it is created from a non-linear process. Foam is typically a disordered material with a variety of bubble sizes. Furthermore, the study of its structure needs a deep understanding of self-formation in three-dimensional tessellation of the space.

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skull bone

bamboo

iris leaf

bulrush leaf

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“Materials with a cellular structure are widespread in nature and include wood, cork, plant parenchyma and trabecular bone. Natural cellular materials are often mechanically efficient: the honeycomb-like microstructure of wood, for instance, gives it an exceptionally high performance index for resisting bending and buckling. Here we review the mechanics of a wide range of natural cellular materials and examine their role in lightweight natural sandwich structures (e.g. iris leaves) and natural tubular structures (e.g. plant stems or animal quills). We also describe two examples of engineered biomaterial with a cellular structure, designed to replace or regenerate tissue in the body. “ 4 4 Lorna J. Gibson, “Biomechanics of cellular solids.” (Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Journal of Biomechanics 38 ,2005), pp .377–399

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Foams Type: Open Cell Foam

Closed Cell Foam

Reticulated foam

[Above] Furthermore, foam properties are characterized by anisotropy and defects such as its structure is always different, its struts might often be irregular or broken and the cells’ voids have multiple variety of sizes. Nonetheless, foams can be split and divided into categories; they are very efficient for specific applications and can be man made.

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polymer foam

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[fig 6] Scan of Foam

image 12 - Polymer foam----21

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[fig 5] Foam Model , Architecture Investigations

poluretane foam

Foam is a cellular structure , those structures falls into 3 typologies such as: two-dimensional honeycombs, a three-dimensional foam with open cells and a three-dimensional foam with closed cells. The first has solid cells edges and they connect with open faces, the second has both edges and faces solid, so that each cell is closed off from its neighbors.

Furthermore, foam properties are characterized by anisotropy and defects such as its structure is always different, its struts might often be irregular or broken and the cells’ voids have multiple variety of sizes. Nonetheless, foams can be split and divided into categories; they are very efficient for specific applications and can be man made.

Their use and quality is defined through the properties of the solid struts, such as open or closed cells and thickness. For example, a bath sponge is an open cell type, which allows water to flow through the structure. A camping mat is a type of closed cell foam where the cells are sealed off from each other; this does not allow substances to go through and makes the material water repellent.

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[fig 5] Foa

[Above] Studies on the foam structure, the diagram shows the foam’s structures trhough function layers. This was part of the initial studies that were later use to define the rules for the concrete lattice design.

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[Above] Inserting the problematic of defining in-between space in thin concrete shell conception brings the possibility to make more than a thin concrete shell, a skin of concrete. Design a three - dimensional concrete lattice that challenges the perception of concrete shells as large scale objects used for spanning large areas. It inspires the design of a structure that creates openings, space subdivisions and perforations.

Natural Ventilation Space Subdivision

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ventilation

[Above] It inspires thedesign of a structure that creates openings, space subdivisions and perforations (figure11). Various configurations can be also composed for water draining and gardens, in a smaller scale for insulation and ventilation. Multiple functions occur by carving away material to create void.

Water Store

Green landscape Structure

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[Above] It is intented to create a three-dimensional lattice shell that is a densely interconnected architectural structure, which responds to the material and architectural scale as well as the spatial organization. A recursive system is required in order to achieve this desired scale variation.

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RETICULATING THE VOLUME

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RETICULATING THE VOLUME

experimenting on the creation of void in concrete

Initial studies on the reticulation of volumes investigating the potential creation of the inspiring geometry. The reverse conceptual method of creating geometry through the organization of voids is used.

The first physical models for the understanding of reticulation of concrete where based on empirical experiments. Gradually the control of the methodology was acquired. At the beginning polystyrene balls where used inspired from the EPS concrete, scaling up the idea of creating a closed cellular structure in the volume.

The void was not easily achieve with the foam balls so balloons where used for the creation of the required perforation. Air cells - balloons are easily removed and their deformation brings to the reticulation an interesting result. Deformation studies where conducted comparing the foam balls and the balloons on a 2D and 3D grid

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[Left] Perforated rectangle box with the use of foam balls .

[Right] The foam balls are attached on the sides of the box in order to achieve a controlled perforation. The tangency of the foam balls though is not successful since the fixed position is not suitable.

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[Above] Initial physical models using balloons. The struts that are created are really close to the one we observe in the cellular solid study.

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[Above] revealing the interstitial space , process of removing the balloons from the physical model,

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foam balls

balloons

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water balloons

air balloons

foam balls

[Left] comparison different approach for reticulating the volume. Water balloons, air balloons and foam balls are used.

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foam balls -4.5cm

balloons 6cm

balloons 4.5cm

balloons 3cm

foam balls mix sized 6-4.5-3cm

balloons mix sized 6-4.5-3cm

volume

foam balls -6cm

volume

limitation volume

volume

volume

limitation

limitation

limitation

volume

limitation

volume

limitation limitation

regular results of foam balls

comparison between mixed size foam balls and balloons

deformation between the balloons

comparison between same size foam balls and balloons

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foam balls

balloons

[Above] first physical model for the reticulation of a rectangular volume using foam balls and water balloons. The results are similar, though the deformation that is observed in the water balloons case is intriguing and challenging.

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foam balls

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balloons

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PACKING INVESTIGATIONS

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PACKING INVESTIGATIONS

reverse conceptual methodology - design space through voids

Sphere packing studies are essential to the understanding of the intricate organizational behavior of the spheres. The two main characteristics of a sphere packing is the geometrical configuration and the packing density. The creation of the optimum packing has long been an issue for mathematicians. The optimum packing of spheres is of immediate interest with the research on the organization of spheres as it provides the smaller negative space and therefore the minimal volume.

The geometrical configuration of sphere packing resulted to the understanding of the reticulation of volume following a recurisvity during the process. The geometrical definition though is not viable for the arrangement of ballons.Therefore a stochastic,more random distribution is preferable. Adding to this complex reasoning the behavior that the materiality of the spheres introduces an additional element to the process. Finally through physics simulation various packing configurations can be investigated using different proportions and size of spheres.

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CELL CONFIGURATIONS Looking in the cellular topology of the polymer foam, a configuration of cell is identified.Cell configuration studies are conducted through the process of understanding and replicating.

Specifically smaller spheres are arranged around a bigger cell and the reticulated volume is studied. The big cell is called parent cell and the orbiting smaller cells around, child cells.

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rotation on xy axis

rotation on z axis

rotation on xy axis

unit cell rotation on z axis

rotation on xy axis

instertitial space between cells rotation on z axis

[Left ] 1. highly controlled arrangement of child cells around parent cell with various rotations on x, y and z axis.

2. child cell size and position is adapted to the radius and the center point of the closest child cell

looking for the closest point

creating sphere according to tangency with closest point

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[Left ] geometrical arrangement of child cells around the parent cell with angles of rotation 900 and 60 0

[Above] physical model of one of the configurations of child and parent cell

[Below] The interlocation of the cells between them is a subject of investigation and is driving the further research on the configuration of the child cells around the parent cell.

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left view

front view

section

reticulated volume = 0.00045 m3

left view

front view

section

reticulated volume = 0.00031 m3

= =

+ =

+

1st iteration

+

2nd iteration

=

== 16 spheres

++

+=

=

++

== 25 spheres reticulated volume 0.00056m3

front view

+

+ 58

left view

=

section

=

section

reticulated volume = 0.00032 m3

volume = 0.00052 m3

reticulated volume = 0.00031 m3

section

volume = 0.00052 m3

[Right] Geometrical arrangement of child cells around the parent through a recursive procedure.

Fractal organization of spheres is achieved through endless iterations [Left] random arrangement of the child cells around the parent cell with two lapses of iterations

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GEOMETRICAL ARRANGEMENT OF SPHERES Packing with geometrical configuration is the way to highly control the process of arranging spheres in a volume. Various geometrical arrangement have been investigates, packing on a grid, appolonean gasket, etc.

These studies bring a better understanding of the geometry of the spheres and the interlocation of various sizes that can be achieves through recursivity.

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A

B

Area - A

Area - B

Circles arranged on grid

Area - C = Perforated Volume

A Circle packing is a configuration of circles with a specified pattern of tangencies. Circles can touch each other, leaving little space between them, unlike tessellation, which tile the space.

Area - A = Area B = Area C

rectangular grid sphere

negative space

diagonal grid

hexagonal grid

Basic 2D configuration of circles on a rectangular, diagonal and hexagonal grid. Observing the interstitial space optimization.

grid type K

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For a given grid type K there exist multiple packing arrangements, which imply various possibilities to use this system on different level of geometrical studies.

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connection of equal spheres

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equal sphere packing - close packed structure

connection of unequal spheres

perforation of cube lattice with variation in intersection of the balls

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iteration 01 27 spheres Cumulative spheres’ volume = 0.39m3 Interstitial volume = 0.016m3

iteration 02 8 additional spheres Cumulative spheres’ volume = 0.45m3 Interstitial volume = 0.006m3

iteration 02 59 additional spheres Cumulative spheres’ volume = 0.52m3 Interstitial volume = 0.003m3

iteration 03 288 additional spheres Cumulative spheres’ volume = 0.60m3 Interstitial volume = 0.002m3

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[Left] In mathematics, an Apollonian gasket or Apollonian net is a fractal generated from triples of circles, where each circle is tangent to the other two.

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[Above] A particular interest is found in the apollonian gasket packing as there is a close connection to the reference image of polymer foam that leads the investigation for the concrete lattice of the thick shell. In three dimensional space

+ 01

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[Right] There are endless iterations of placing smaller and smaller spheres, with an endless recursivity showing that the negative resulting lattice could be minimised in a big extend.

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total sphere volume Volume = 3.4 m3

total sphere volume Volume = 3.4 m3

top view

axonometric view

top view

front view

left view

top view

total sphere volume Volume = 3.4 m3

+

+

+

total sphere volume to reticulate 3.4m3 top view

+

axonometric view

top view

front view

left view

+

+ +

interstitial volume 16 spheres Volume = 1.0 m3 Cumulative spheres’ volume = 2.8 m3 Interstitial volume = 1.0 m3 + +

+ +

++

+

interstitial volume 21 spheres Volume = 0.6 m3 Cumulative spheres’ volume = 3.2 m3 Interstitial volume = 0.6 m3

iteration 03

+ +

+ +

+ +

++

+

+

Iteration 02 Iteration 01 21 spheres total 16 spheres total Cumulative sphere Volume = 3.2 m3 Cumulative sphere Volume = 2. interstitial volume Volume = 1.0 m3

+

+

+

+

front view

iteration 01

+

iteration 02

+ +

Iteration 01 left view 16 spheres total Cumulative sphere Volume = 2.8 m3

Iteration 02 Iteration 03 21 spheres total 45 spheres total Cumulative sphere Volume = 3.

Cumulative sphere Volume = 3.5 m3

interstitial volume Volume = 0.4 m3 45 spheres Cumulative spheres’ volume = 3.5 m3 Interstitial volume = 0.4 m3

interstitial volume Volume = 0.6 m3

+

+

+

Iteration 03 Iteration 04 45 spheres total 147 spheres total Cumulative sphere Volume = 3.

Cumulative sphere Volume = 3.5 m3

iteration 04

+ +

+

++

+ +

++

+

Towards Recursion 147 spheres total Cumulative sphere Volume = ? interstitial volume Volume = ?

+

+

+

interstitial volume Volume = 0.2 m3 147 spheres Cumulative spheres’ volume = 3.5 m3 Interstitial volume = 0.2 m3 + +

Towards Recursion

+

+

+ +

Towards Recursion 147 spheres total Cumulative sphere Volume = ?

+

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interstitial volume Volume = ?

interstitial volume Volume = 0.4 m3

+

Iteration 04 147 spheres total Cumulative sphere Volume = 3.

Towards Recursion interstitial volume 147 spheres total Volume = 0.2 Cumulative sphere Volume = m3 ? interstitial volume Volume = ?

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RANDOM DISTRIBUTION OF SPHERES Sphere packing is a space filling process and can be approached in a non geometrically defined methodology. The random distribution studies are based on the principle of placing the maximum number of balls in a given space.

Certain rules are imposed during the generation of the spheres like minimum and maximum radius and tangency tolerance between them.

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tangent circle packing with random center points for certain radius size limitations

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[Left] Random points are created in sequence in the limits of a cubic lattice. Every frame a sphere is created as well which is tangent or non intersecting with the already existent within a radius or maximum and minimum values. If these conditions don’t apply another random point is selected until the fulfillment of the requirements.

Iterations are continuous until the cubic lattice is filled in the maximum capacity with spheres of the minimum radius.

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not tangent spheres

tangent spheres

intersecting spheres

[Above] Random selection of points in a cubic volume.

Using those points non tangent, tangent or intersecting spheres are created in order to understand the difference sin the random reticulation of the volume.

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PACKING SIMULATION The materiality of the spheres that are arranged is an important input in the quest for the optimum packing. Physics engines give the opportunity to simulate the behaviour of balloons. Through simulation a range of studies is conducted trying to find the right parameters of elastic material and the conditions in which they self organise. Accurate statistical results are acquired about the void volume and the size of spheres simulated when poured in a an empty box.

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material systems _ designed Particles Aggregations ( Eichi Matsuda, Uniy 4, AA London)

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Architectural systems commonly seek to form clearly defined and seemingly permanent material assemblies. Loose granulates in concrete can be considered and researched as material systems.

A large arrangement of components can complete architectural tasks. The architect’s role is to modulate and observe their behavior on the particle and system level. To observe how a shapeless material generates form and geometry and finally space.

These elements have the ability to adjust to the internal and external system influences.

Material systems bring suggestions, maybe even solutions in the query for interstitial space.

When architecture is designed in the conceptual boundaries of material systems interstitial space emerges. It becomes the space between the aggregates, the void in their arrangement.

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[Left] studying the behavior of balloons on physical models comparable to the simulations wiith physics engines

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[Left] digital simulation of pouring spheres in a box.

Stiffness, elasticity mass and other parameters are simulated with precision until a similar behavior to the physical models is achieved.

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1.5

0.72

0.84

0.88

0.97

1.04

1.09

1.20

1.20

1.5

1.5 1.25 1.02 0.81 0.56

size 2

size 3

size 5

[Left] Same pressure is applied on the packing of sphere size 2, 3,5 for the same amount of time. The deformation is measured reflecting the stiffness of the packing agglomeration. The bigger the size of the spheres the smaller the deformation.

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sphere volume 125 spheres - size 3

437 sphere - size 2

1.76

1.72

1.59

1.42

0.77

28 spheres - size 5

1.67

1.60

1.53

1.43

1.26

1.72

1.62

1.56

1.49

1.38

[Right] Quantification of the void volume in the packing at each frame of pressure. This study gives the understanding of how the application of force on the agglomeration increases the intersection of spheres, the contact between the soft-bodies.

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0.6 0.52

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70KN / frame

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70KN / frame

0.48 0.47

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Through the simulation of same size spheres void volume ratio and deformation ratio a clear understanding of how the size of the sphere affects the packing characteristics is acquired. Size 2 packing has the highest deformation ratio which means the smaller the elastic spheres the easier they can be deformed when pressure is applied on them. For the void ratio size 2 has the biggest ratio as well.

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The reticulating spheres can be inspected as aggregates in the mixture of concrete with the particularity that the particles create voids in the concrete volume. The particle packing between coarse and fine aggregate elements has been a engaging subject of study by material scientists in order to recognize the behaviour of components in the liquid concrete.

Computational simulations on this subject represent and calculate the aggregates particles as spheres. Precisely the packing density of coarse and fine aggregate has been catalogued in a methodical way in order to anticipate the behaviour of such particles in concrete mixtures. The importance of predicting such mixtures is essential for the production of sustainable concrete mixtures that require less water and less cement paste, therefore reducing the CO2 emission (figure 34). The optimum packing of aggregates is also crucial since it directly affects the strength modulus of elasticity, creep and shrinkage of concrete.

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20-20-60 self-organizing behavior

33-33-33 self-organizing behavior

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20 - 40 - 40

33 - 33 - 33

40 - 20 - 40

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3.09

3.25

3.63

4.42

20 -20 - 60

sphere proportions

1.83

2.16

2.50

14 - 28 - 56

60 - 20 - 20

1.99

40 - 40 - 20

20 - 60 - 20

filling measurement

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no pressure

14-28-56 | 537 spheres

applied pressure

9.83 0.43

9.10 0.39

20-20-60 | 217 spheres

void volume void ratio

8.21 0.35

7.16 0.31

20-40-40 | 253 spheres

void volume void ratio

8.91 0.38

7.95 0.33

20-60-20 | 364 spheres

void volume void ratio

void volume void ratio

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9.03 0.39

8.24 0.36

applied pressure

33-33-33 | 277 spheres

no pressure

void volume void ratio

10.04 0.43

void volume void ratio

9.54 0.41

8.18 0.35

void volume void ratio

9.82 0.42

8.72 0.38

60-20-20 | 497 spheres

40-40-20 | 382 spheres

40-20-40 | 275 spheres

9.12 0.39

void volume void ratio

9.67 9.42

8.21 0.35

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studies on boxes without pressure

studies on boxes with pressure

[Above] Section studies of aggregate packing configurations

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8.21

packing 02

Digital and analogue simulations of particles in aggregates studies for concrete mixtures give interesting results helping identify the optimum packing. Based on studies made for aggregates similar studies are made for the proportions of elastic spheres that can be used for the reticulation of concrete volume. The results are interesting since the proportion of size 20-20-60 with the biggest majority of big spheres has the lower void volume. Consequently this proportion will result to the thinnest concrete lattice.

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[Left] digital simulation of pouring elastic spheres with air pressure in order to achieve certain patterns [ Right] analogue simulation of pouring elastic spheres with air pressure in order to achieve certain patterns

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[ Left] _ [ Right] experimenting on the control of the packing of elastic spheres by injecting elastic spheres in a box in order to achieve gradient pattern.

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LIQUID SIMULATIONS

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LIQUID

Understanding of liquid behaviour , towards the heterogeneus lattice The geometrical studies revealed interesting results and many lattice typologies.

However, they always generated a regular mesh, which is fully controlled with geometrical laws.

At this point, the research shifted to simulation studies, as it was understood that mathematical rules couldn’t replicate the heterogeneity of the foam without the variability involved in self-organizing structures.

Moreover, boolean geometrical operation works in a static frozen environment that could not reflect the physics dynamic that the system needed.

Simulations allowed observing the packing self-arrangement. Balls were set as soft bodies, rubber balloons filled with air, and thrown in to same size boxes.

The system was studied mainly during the liquid phase of the cast.

There is a true challenge for the designer to develop new structures that are themselves product of variations. We then return to the question: could architectural form reflect more the heterogeneous properties of those found in nature and expand them as concrete structures?

“And we may now be in a position to think about the origin of form and structure, not as something imposed from the outside on an inert matter, not as a hierarchical command from above as in an assembly line, but as something that may come from within the materials, a form that we tease out of those materials as we allow them to have their say in the structures we create.”12

12 Manuel DeLanda “Uniformity and Variability - An Essay in the Philosophy of Matter” (presented at Doors of Perception3: On Matter Conference, Netherlands Design Institute, Amsterdam, Holland, 1995) p .8

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THICK LIQUID //// CONCRETE Density parameters Software //// Realflow

Density

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Density

Density defines the particles mass per volume. (kg/m3)

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[Above] Liquid parameters for Realflow fluid simulation settings. Different parameters were tested , density was one of the main setting to be changed. (refer to graph above) 113

LIQUID //// WATER Liquid simulations tests on density and viscosity Software //// Realflow

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F1

F 10

F 20

F 30

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F 50

F 60

F 70

F 80

[Above] The images above show simulations of the liquid with water settings.

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THICK LIQUID //// CONCRETE Liquid simulations tests on density and viscosity Software //// Realflow

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F1

F 10

F 20

F 30

F 40

F 50

F 60

F 70

F 80

[Above] The images above show simulations of the liquid with water settings.

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The liquid Cast Initially the cast is a non-form liquid material that fills the formwork and it will transform until it will reach its point of solid equilibrium.

At the liquid state, the material can take any shape and can adjust to various systems.

The proposed system is a dynamic field of air and liquid, characterized in fact by air (inflated balloons) and liquid (concrete).

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[Above] Many packing options were tested to reveal variety of lattice configurations that they could produce. First it was tested a series of same size spheres packing and later mixed sizes sphere packing. A series of sections were used to visualise the lattice internal structure and to identify where it was continuous or broken.

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LIQUID STUDIES / LATTICE STRUCTURE The lattice structure is created by a reverse conceptual method such as the negative space, or else the interstitial space of Boolean sphere packing configurations.

The study has been done with a revrse conceptual method such as Different packing options have been used to reveal the variety of lattices configurations that they can produce.

The first study was donewith a size 5 packing spheres, refer to image on the left.

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Lattice sections

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SIZE 5 This page shows sphere packing size 5 casts.

The lattice morphology has been studied with a series of sections. In this case we can see that top and bottom lattices sections are more regular while in the center the ball layout is more irregular.

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Lattice sections

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SIZE 2 Size 2 studies result very different and revealed interesting observations.

Such as the smaller are the balls the less are the perforations.

Smaller size balls increase the packing dynamics and therefore the segregation of spheres in the liquid and decrease perforations in the cast.

To increase perforations of the cast we test more squeezed packing options, but the result was a super packed option that does not allow liquid to get through the packing.

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- 01 - 02 - 03 - 04 - 05 - 06 - 07 - 08 - 09 - 10 - 11 - 12 - 13

Lattice sections

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SIZE 3 Size 3 resulted to be the a good option that allow more perforations of the lattice and continuity.

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Size 5 F 222

Size 5 F 223

Size 5 F 224

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Lattice deformation studies on size 5 General casting technique creates uniform solid structures.

The elastic cast system of balls has shown a capability to adapt and create singular structures. Every one of the casts either simulated or real models created a structure that is similar to the others but never the same.

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[Above] This study shows an overview of all sections.

In size 3 and 5 we have performed a study on 3 squeezed options. The more we squeeze the more the lattice is perforated, but also hier the risk of broken struts.

Interesting was to see the lattice morphology, such as top and bottom sections are very regular, while middle zones are more heterogeneous and open.

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[Above] Size 5 liquid simulation studies 135

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[Above] Size 3 liquid simulation studies 137

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[Above] Size 2 liquid simulation studies 139

Spheres size 0.5 /0.3/ 0.2/0.1 m box size = 1.5 m spheres number = 111 box volume = 3.375 cubic meters spheres volume = 1.6842 cubic meters for 111 solids

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Above We have analised some options with mixed size spheres.

These studies revealed more intricated and heterogeneous meshes, that would have reflected more the type of packing needed for the concrete shell.

The image above shows the mixes size option with sphere sizes 5/3/2/1.

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Continuity of the lattice was a challenging parameter to meet. In fact as observed in metal foams currently only regular foams structures show full continuity of struts. In fact, common irregular foams are characterised by anisotropy and defects such as big difference in cells size and broken struts. The self-organizing packing should be defined with some rules that could help to avoid such problems.

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[Above] Studies on heterogeneus lattice, with mixed size spheres , testing the struts continuity on the model size 60-20-20 aggregate packing type.

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[Above] Zoom of heterogeneus lattice, with mixed size spheres , testing the struts continuity on the model size 60-20-20 aggregate packing type.

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[Above] Particles moving around the packed spheres.

Model 60-20-20 aggregate packing type.

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[Above] Frame sequence of particles moving around the packed spheres.

Model 60-20-20 aggregate packing type.

F 220

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Mapping Liquid Liquid simulations were used to predict optimum lattices results. The aim was to map the liquid patterns to predict the areas where packing was too dense and liquid did not have any interstitial space to fill.

Liquid speed mapping system was used to study each liquid cast, colours of the map highlighted the speed of the liquid while it finds its way around the balls.

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[Above] Frame sequence of Liquid speed mapping on particles moving around the packed spheres.

Model 60-20-20 aggregate packing type.

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size 3

size 2

Aggregate section - 20-20-60

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Anysotropic Lattice Deforming the balls - like bones structure A load deformed the packing; the weight was kept over the cast until it changed to solid. With the rubber balls elastic system the liquid cast can be used for all its potentials.

The idea is that if the packing was good, liquid always found its way around the spheres. The test created an anisotropic structure that shows structure direction variety according to loads.

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Anysotropic Lattice and singularity The elasticity and variability of this casting system allow the designer to use dynamic potentials in the cast, while also creating a cellular cast. To take the system towards heterogeneous lattice structures, a new model was tested. It was intended to replicate bone structures behaviour in a way that the structure orientation reflects the direction of the loads. This was to further study the dynamical qualities that this system.

The elastic cast system of balls has shown a capability to adapt and create singular structures. Every one of the casts either simulated or real models created a structure that is similar to the others but never the same.

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THICK SHELL Concrete has fully been used as a structural material and using DeLanda ‘s terminology, it has been part of a “linguistic standardization” for designing efficiency.

During the last century, architects have started the race for designing with minimum use of concrete and to achieve maximum coverage area. The modernist movement has created extremely light and thin varieties of concrete structures that work upon performance such as the Isler’s Deitingen Service Station shell . [Deitingen, Solothurn, Switzerland, Europe] Concrete shells have not yet been tested to become something different. The modernist structures have been carried for years as a standard model for production.

The heterogeneous qualities of cellular structures could bring a new concept in shell’s architecture: shell is seen no more as a surface but as a three Dimensional heterogeneous concrete thick skin.

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[Above] The Isler ‘s shell has been taken as a model to be challanged and redesigned with the perforated shell structure.

The image on the left shows particles going trhough the shell generating the lattice.

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Top view Particles going trhough the shell , generating the concrete lattice.

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[Above] Side view Particles going trhough the shell , generating the concrete lattice.

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ANALOGUE

DIGITAL

ANALOGUE / DIGITAL Experiments have been compared between concrete casting and liquid simulations.

The models that have been simulated have been reproduced as concrete cast.

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[Below] Model A size 5 Model B size 3 Model C size 2 Model D Aggregates 20-20-60 Material: Plaster + Water

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[Below] Model type Aggregates 20-20-60 Material: Plaster + Water

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[Below] Model type Aggregates 20-20-60 Material: Plaster + Polymer+ Water

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TOWARDS THICK SHELL

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TOWARDS THICK SHELL

investigations on the formulation of a procedure for the creation of thick shells

A series of investigations were conducted with an ultimate goal to create a precise procedure for the design and fabrication of thick concrete shells. The attempt to arrange spheres on a curved membrane is achieved,through physical models and empirical tests.

One of the first inspirations was the already existing fabrication process of Dante Bini who used two inflated membranes to cast concrete in between and created domes. The agglomeration of balloons is placed between two membranes and through experimentation, various configurations are tested. Additionally studies on pneumatic structures has been done. Taking inspiration from the work of Frei Otto form - finding methods are applied on inflated membranes in physical models and with digital simulation in order to answer to certain architectural requirements. Springs and anchor points are used for the creation of subdivisions and the formation of space

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SPHERE ARRANGEMENTS ON THE SHELL The studies on arranging the balloons on a curve surface where realised through analogue and digital simulation. For physical models the main goal is how to arrange the elastic spheres between two membranes and pour liquid, which forced us to deal with pouring points and techniques of inflating membranes. For the digital part a regular arrangement of spheres on a curved surface was the initial point of study. Further investigations brought into the research more complex parameters like attractors and forces.

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Dante Bini developed a system that transforms the pneumatic structure of a simple dome membrane to a form work for the creation of concrete shells. Dante Bini pioneered ‘air structures’: gigantic balloons that could be covered with a thin layer of concrete then inflated to form domes in a matter of hours (figure 25).

Bini Dome fabrication involves the construction of a ring beam and ground floor slab.

The ring beam cleverly contains a ‘cast in’ eggshaped void to hold the main membrane in place during inflation, as well as air inlets and outlets.

The internal pneumatic form Pneumoform of nylon-reinforced neoprene is then laid over the slab on top of which a complex network of crisscrossing helical springs is stretched across the diameter. A top layer of membrane is rolled on the poured concrete, the bottom membrane is inflated with air and the whole system rises up to the final position where vibration is applied until the air is fully dissipated from the concrete mixture.

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bini shell construction process (The Architectural Review, January 2013, www.architectural-review.com )

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ANALOGUE

DIGITAL

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vacuum bag

bag with concrete

balloon aggloemeration

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frame

latex sheet

agglomeration

mdf base 187

frame

latex sheet

aggloemeration

latex sheet aggloemeration

base

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[Left] Through experimentation a sequence of construction steps is defined. Two membranes are enclosing the reticulating agglomeration of elastic spheres and various pouring points are defined. Pressure is applied by stretching the two membranes so the agglomeration is tangent to the latex membranes.

[Above] Pressure is applied on an agglomeration of elastic spheres in order to prove that the weight of concrete or the pressure from the inflated membranes will not damage in any way the elastic spheres.

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ANALOGUE

DIGITAL

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[Above] Spheres are placed on the curved membranes following a grid. The grid can be deformed with multiple variations and parameters giving a different unique result of packing.

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Boolean operation of the volume of the curved shell with the agglomeration resulting from the grid arrangement of the spheres.

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FORM FINDING METHODS ON MEMBRANES Form finding methods have prior been applied on inflated membranes by Frei Otto but they also represent an extensive field of studies by other architects and engineers. For the creation of a thick shell which is not a simple dome like Bini -shell experiments of form - finding on the membranes are necessary. Lower membrane is the main concern for formulating the interior space of the building creating subdivisions and structural guides. The upper membrane is mainly following the lower membrane guides trying to control the packing and the thickness of the concrete shell.

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Frei Otto was one of the pioneers in pneumatic structures investigations. His curiosity led him in creating numerable models experimenting on the potentials of the pneumatic forms. For the study on anticlastic areas different initial plane structures where tested. Very significant is his work on the Investigation of linear reinforcement on pneumatic membranes which fuelled the structural and design problematic.

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membrane guyed with aditional linear elements - Frei Otto

stabilised membrane with additional linear support - Frei Otto

single membrane with additional linear support

multiplicity of possible design s - Frei Otto

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[Left] ANALOGUE various form - finding methods with springs are applied on a circular membrane in order to experiment with the strength of the springs and the possible patterns.

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360 Pa

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720 Pa

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[Above] different pressure in for the option 01

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[Left]

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Form - finding using physic simulation engine - Kangaroo. Different size springs are applied on a rectangle membrane.

anchor points on the edges anchor points in the main area for creating subdivisions free edges for side openings areas with varying topography creating diverse curvatures

anchor points on the edges anchor points in the main area for creating subdivisions free edges for side openings areas with varying topography creating diverse curvatures

[Above] different pressure for the option 01

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FABRICATION PROPOSAL After the experiments of form finding on the membranes and positioning the balloons on the agglomeration, the combination of the results give a viable proposal for the fabrication of thick concrete shells. Digital simulations as well contributed to the better comprehension of the behaviour of the elastic components, spheres and membranes, that interact with each other.

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1. inflatable structure as a formwork

2. cell agglomeration

3. inflatable structure with cell agglomeration

4. exterior membrane layer

4. exterior membrane layer

The agglomeration is attached on an inflated membrane, the bottom mebrane of the system. The upper membrane is laid over and stretched so it is in immediate contact with the agglomeration. The whole structure is inflated together. The agglomeration of elastic spheres is deformed and adapted to the various form finding methods that exist on the membranes. Finally concrete is poured between the membranes from pre- selected pouring points that adapt to the curvature of the total structure.

5. cast

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vector forces creating singularities ( Open processing, http://www.openprocessing.org/sketch/34320 )

points of attraction - springs creating singularities to the agglomeraiton through the membranes

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The spheres are packed between the two membranes using specific pouring points or injecting them with specific air pressure in order to control better their distribution and organization. A first state of equilibrium is reached until the moment the air pressure is applied on the interior membrane. The output of the interstitial system is then placed in a non-equilibrium environment which has the tendency to change until it reaches its stable condition. The “noise” forces the system to deviate from its preferred trajectory and administers impending change. In a smaller extend internal variation processes - fluctuations occur also to the primary deterministic system. Due to the infusion of energy both systems will enter a transient state but the vacillation in the selforganization of the spheres is restricted from their size, initial position and potential stabilization.

Depending on the pressure the strength of the “noise” that is injected in the packing system is different and the consequent deformation of the particles varies. Simulations showed that the deformation of the particles is bigger on the ones that are in immediate contact with the membranes (the object that applies the force – “noise)”. Moreover, the application of same pressure on various packing configurations showed that the bigger spheres size agglomeration shows smaller deformation comparing to the smaller ones. The material stiffness of the particles and the air pressure inside the elastic sphere is the same for all of them. The surface tension changes because of the size of the particles; this phenomenon explains how the bigger balls are stiffer and more tolerant to the forces .

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3 layers of membrane

2. stables and stochastic level of agglomeration

3. inflating with balloons inside

4. exterior membrane layer

5. cast

Different size of spheres (filled with air) are placed in different parts of the structure providing variability in the reticulation where needed.

The in-between space associates an organized system of various sizes of spheres representing the primary reticulation of the concrete volume and a system of smaller spheres with a more stochastic organization.

The primary reticulation relies on a stable organisation of the spheres that follows the architectural requirements of the thick shell. This way the openings, the subdivisions and the formulation of interior space are ensured in combination with the form-finding methods applied on the controlling system. Additionally initial perforation for ventilation, water drain and garden capsules is realised and further completed by the second stochastic layer of spheres.

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THICK SHELL 4 Layers of Organization

The thick concrete shell is the result of the combination different size layers of organisation. Membranes shape the space configuration according to variable architectural requirements, defining the size and geometry through a parametric highly controlled procedure. Elastic spheres formulate the void, carving away material from the concrete volume, resulting in a new material topology this of a reticulated three - dimensional concrete lattice.

The membranes modulate the in-between space where the material – concrete and the reticulating components will attain final shape and position according to the membranes and forces that dominate. The air pressure applied on the interior membrane creates a strong support in order to hold the dead weight of liquid concrete until it goes dry. The membranes are in an immediate interaction with the sphere agglomeration.

The ballons, have two levels of organisation, the stable and stochastic.

The later follows a spontaneous process of organization, the development of new complex structures takes place primarily in and through the packing. All parts contribute evenly to the resulting arrangement. Each component self regulates its position and behaviour and simultaneously affects the adjoining ones.

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FORMFINDING - MEMBRANES The two inflated membranes are designed through a highly controlled digital simulation.

Membranes are simulated as a grid of springs with specific strength and elasticity. They are inflated with a certain pressure in order to obtain the desired form. Springs characteristics can be modified according to the required result. Same with the controlling points of the membranes that can be used with various ways.

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initial curve-rectangle

arches for side openings

free edges for side openings

subdivision-anchor points

[Right] formfinding method and inflation process

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topology-forces apply for creating various curvature

Frame 1

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[Below] One of the options that shows the combination of the different strategies on formfinding process.Circle diameters is parametically changeable depending on design and functional needs.

25

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pressure = 10.7 force on curves = -2 line force 1= 19 line force 2 = 38

pressure = 9.6 force on curves = -5 line force 1= 0 line force 2 = 0

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pressure = 10.4 force on curves = -4 line force 1= 8 line force 2 = 3

pressure = 2.4 force on curves = -5 line force 1= 0 line force 2 = 0

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pressure = 3.5 force on curves = -3 line force 1= 3 line force 2 = 6

pressure = 12.4 force on curves = -3 line force 1= 0 line force 2 = 0

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force:2 force:2 force:2

1st membrane

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force:2

force:2 force:10

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2nd membrane

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1st membrane

2nd membrane

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1st membrane

distances

2nd membrane

Various methods of form finding are applied on the interior membrane. Anchor points that keep the bottom membrane grounded are applied, where subdivisions or inner open space are required. The delineation of the border where the main openings are created is realised by the use of supporting arches between the two membranes. This method allows formulating a kind of a beam that supports the ending of the reticulated volume of the thick shell. Springs are used for the reinforcement of the concrete shell where necessary.

The top layer – exterior membrane acts as an offset of the interior one in order to keep a control of the complex behaviour of the liquid material. The offset form accepts alterations when it is desired to formulate differently the interior and exterior face of the reticulated volume.

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DETERMINISTIC & STOCHASTIC LEVEL The deterministic level of organisation of the spheres is placed following the functions and requirements that are reflected on the lower membrane. Subdivisions, openings, water tanks and vegetation capsules are created from accurately placed ballons. The stochastic level is responsible for the principal reticulation of the concrete lattice. The packing is simulated with soft - bodies interacting between them and the colliding objects of membranes and stable balloons.

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2nd membrane

stochastic level

stable level

1st membrane

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stable(deterministic) level

membranes

deterministic & stochastic level plan

plan

deterministic & stochastic level

stochastic level

section 01

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POURING CONCRETE ON SHELL-POURING POINTS Liquid simulation is used in order to predict and understand the results of the organisation of the components. The pouring points are chosen according to the curvature of the inflated membranes and the packing configurations.

The liquid should reach the lower membranes in approximately the same time lapse so the weight of the concrete is evenly distributed during casting.

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PACKING FUNCTIONS

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PACKING FUNCTIONS

attribution of functions to the packing categories Packing investigations come to use and are applied on the conceptual design of the thick concrete shell. By setting general parameters according to strength and size, balloons can be arranged in the structure and may perform differently. They can change scale, they can be removed or create perforated inhabitable cells. They can be kept inside the structure and perform as thermal insulation depending on site specific environmental needs. They can be filled with water and used as water tank or as holes for mechanical and natural ventilation.

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Insulation function sphere size = 0,005m - 0,05m proportions = same size organization = stochastic material = polystyrene balls

270

[Below] Sections of the shadow packing for studies on the interstitial lattice. Light studies varying on the perforation of the volume and the amount of light that is allowed to go through the voids.

1. polysterene balls_ http://www.abakhan. co.uk/crafts.html 2. eps concrete _ http://ionicbuilder.en.madein-china.com 3. eps concrete _ http://foamliteconcrete.com/ products/foamlite/foam-liteeps-concrete-safe-

1

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3

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shadow function sphere size = 0,1m - 0,5m proportions = 33 - 33 - 33 organization = stochastic material = biodegradable plastic

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[Below] Sections of the shadow packing for studies on the interstitial lattice. Light studies varying on the perforation of the volume and the amount of light that is allowed to go through the voids.

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Volume perforation function sphere size = 0,2m - 0,8m proportions = 20 - 20 - 60 organization = stochastic material = biodegradable plastic - plastic membranes

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[Below] Volume perforation of concrete. For this function the ultimate packing proportion is used, 20 -20 - 60 which was calculated during the packing simulations since the smaller void volume is required in order to have the thinest concrete attic epossile.

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shadow function

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subdivision

openings

vegetation and water tanks

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Vegetation and water tanks sphere size = 2,5m - 5,0m organization = deterministic material = removable plastic membrane

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water tank

garden capsule

http://www.habitatdesign.com/2012/04/spheres-for-the-garden/

http://www.davidharber.co.uk/sculpture/sphere.htm

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Openings sphere size = 0,5m - 2,5m organization = deterministic material = plastic membrane

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http://archinect.com/blog/article/51158693/finland-west-the-sacred-and-the-profane

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Subdivision and openings sphere size = 0,5m - 2,5m organization = deterministic material = plastic membrane

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subdivision

openings

http://www.designboom.com/architecture/toyo-ito-taichung-metropolitan-opera/

http://www.hiepler-brunier.de/overview/213/

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Shadow and light sphere size = 0,5m - 2,5m organization = deterministic material = removable plastic membrane

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openings

http://www.designboom.com/architecture/jean-nouvel-louvre-abu-dhabi-under-construction/

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shadow

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openings

volume perforation

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HETEROGENEOUS SHELL

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[Above] Particles generating the concrete lattice.

F 1350

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Pouring points for concrete casting

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