Digital Architecture

Shi_Ling_Bridge_Tonkin_Liu_Yunnan_model_2

The Shadow Pavilion by PLY Architecture showing how a thin planar surface can be rolled into an element that generates a distinctive building form

The leaf roller caterpillar manipulates flat leaves into tubular forms by attaching threads across the surface and then shortening the threads in a manner similar to a ratchet strap

Transformations of planar surfaces

One of the simplest ways to transform a planar surface into something that provides protection is to roll it. The leaf roller caterpillar (genus Aenea) wraps a leaf into a tube, secures it with silk, and thus makes a structure within which it carries out its metamorphosis.

The caterpillar uses this tube structure for a week, but recent research shows that it is then used by other organisms, and plays a significant role in increasing the density and diversity of arthropods. Similar ingenuity is evident in PLY Architecture’s elegant pavilion in Matthaei Botanical Gardens, Michigan.

Sheets of laser-cut aluminium were rolled into cones and then assembled based on patterns of phyllotactic geometry.

Shadow Pavilion Plan

Shadow Pavilion section and elevation

Plants have had to evolve ways to present large amounts of photosynthetic surface to absorb light. But a larger surface area needs more structuring, since growing bigger leaves by increasing their thickness has significant drawbacks.

Curves and folds have evolved to create stiffer elements out of thin material.

In the case of the Southern Magnolia, the fold occurs along the midrib and each half of the leaf is curved . Both the fold and the curve contribute to the leaf ’s stiffness. In rain forest environments, daylight at forest-floor level is scarce and many plants have responded with large leaves folded into fan forms .

The Southern Magnolia leaf, stiffened through a combination of
a curve and a fold

A stunning example of stiffening a thin surface can be found in the giant Amazon water lily (Victoria amazonica). Leaves of up to 3 m in diameter with smooth top surfaces are strengthened on their undersides by a radial, branching, network of ribs to an extent that can support the weight of a small child.

The principle of using ribs to stiffen a thin surface may well have inspired engineers to design similarly efficient structures, and the concept could be applied widely.

Fan palm leaves – an elegant example of how folds can
transform a large, thin surface into a structure that can
cantilever from a single point of support

Architects Tonkin Liu, working with structural engineer Ed Clark at Arup, were inspired by the forms of marine molluscs and techniques from tailoring to develop a new form of construction derived from planar surfaces. They refer to this as a ‘shell-lace structure’ .

Just as in the molluscs, the structure derives its stiffness from the articulation of a thin surface: folds increase the effective structural depth, curves create added stiffness and twists provide a degree of triangulation.
The end product is an extremely elegant structure, constructed with a minimum of materials, deriving its strength from its shape rather than its mass.

Diagrams by Tonkin Liu Architects showing how structural
principles from shells were analysed

The Shi Ling Bridge designed by Tonkin Liu Architects and structural engineer Ed Clark of Arup – an example of a ‘shell-lace structure’ that achieves efficiency of materials by exploiting vaulted, folded and twisted forms from shells

"Shell Lace Structure is a technique inspired by nature. Seashells gain strength from optimised curvilinear geometry, locking in stiffness with corrugation. Lightness is achieved through perforation, creating highly-efficient and responsive structures with minimum weight and wastage. The technique has been developed through research and experiment with digital modelling, digital analysis, and digital fabrication tools. The design process is intuitive, analytical and iterative. Three-dimensional geometries are built up virtually from conjoined developable surfaces. These surfaces are unzipped at the seams, unrolled and nested allowing efficient computer aided cutting from a flat sheet material. The cut profiles are reassembled to create the final three-dimensional form."
- https://tonkinliu.co.uk/shi-ling-bridge

Resources and further reading:
https://tonkinliu.co.uk/shi-ling-bridge

Book reference:
Biomimicry in Architecture by Pawlyn, Michael

Get the Book on Amazon:
https://amzn.to/3I8RHw0

MX3D Bridge By Joris Larman

Nature makes extremely economical use of materials, often achieved through evolved ingenuity of form. Using folding, vaulting, ribs, inflation and other means, natural organisms have created effective forms that demonstrate astonishing efficiency. The many manifestations of this in natural organisms provide a rich source book of ideas for structures that could be radically more efficient than those found in conventional architecture.

Hollow tubes Nature builds simply and economically, often meeting both goals simultaneously by making hollow tubes. Nature is abundant in examples that demonstrate this structural principle, such as human bones, plant stems and feather quills.

If one takes a square cross-section of solid material with a side dimension 24 mm, it will have the same bending resistance as a circular solid section of diameter 25 mm with only 81.7 per cent of the material.

Similarly, a hollow tube with only 20 per cent of the material of the solid square can achieve the same stiffness. In engineering terms, material has been removed from areas close to the neutral axis and placed where it can deliver much greater resistance to bending – achieving the same result but with a fraction of the material.

Sketch showing how four equally stiff structural elements can
be made with varying degrees of efficiency. By using shape and
putting the material where it needs to be, it is possible to use
only 14 per cent of the material of a solid square section (after
work by Adriaan Beukers and Ed van Hinte in Lightness: The
Inevitable Renaissance of Minimum Energy Structures)

One plant in particular shows how hollow tubes can be applied at larger scales in nature. Bamboo species can reach 40 m in height.

How do they maintain strength over this length?
One of the ways in which a tubular element can fail under loading is through one side of the tube collapsing in towards the central axis, leading to overall buckling. Bamboo solves this by interrupting smooth tubular growth with regular nodes, which act like bulkheads .

The nodes provide great resistance to structural failure, and are part of what has facilitated bamboo’s lofty accomplishments.
Bamboo is, by strict taxonomy, actually a species of grass which has achieved such wild success that it resembles the scale of a tree. This plant’s solution seems to apply so widely that it begs the question: why aren’t more trees hollow tubes? The answer derives from the different forms that they strive to grow into: trees generally create a canopy of cantilevering branches, rather than the multiplicity of stems characteristic of grasses.

Bamboo offers solutions to tubular structural elements, while trees offer a biomimic further solutions to holistic structural issues, since they face different pressures than grasses.

Trees: solid forms

Our understanding of trees and how lessons from them can be applied to engineering has developed enormously in recent years, particularly with the work of Claus Mattheck.

In nature, biological forms follow a simple rule, which he describes as the axiom of uniform stress. In locations of stress concentration, material is built up until there is enough to evenly distribute the forces; in unloaded areas, there is no material.

Trees also demonstrate the idea of optimized junction shapes that avoid stress concentrations and can adapt over time. The result approaches optimal efficiency, in which there is no waste material and all the material that exists is carrying its fair share of the load.
By contrast, many steel and concrete structures are designed so that the most onerous load conditions (which only occur in specific locations) determine the size of the whole beam or column.

With his team at Karlsruhe Research Centre, Mattheck developed a design method that utilizes two software processes to create forms of biological design that are effectively identical to the refinements found in nature.
The program allows designers to subject a rough structural computer model to the kind of forces that would be experienced in reality.

These include snow, wind and seismic loading, as well as loads imposed by the building’s use.

The first stage uses ‘Soft Kill Option’ (SKO) software to eliminate material in zones where there is little, or no, stress. Then a ‘Computer Aided Optimization’ (CAO) program refines the shapes and, where necessary, builds up material at the junctions to minimise stress concentrations that could lead to failure.

The designer is free to decide whether they like the output and find alternative ways to achieve structural integrity. Mattheck likens this process to starting with a roughly axed piece of timber, which is then carved to the near-final shape (the SKO stage) before being sanded and polished (CAO). The results can be surprisingly organic in form, and far more efficient than conventional structures. The designer Joris Larman used this to develop a number of elegant pieces of furniture and a bridge that is to be 3D printed and will span over a canal.

Diagram showing Claus Mattheck’s design refinement process using ‘Soft Kill Option’ (SKO) and ‘Computer Aided Optimization’ (CAO) software

We could do the same with buildings and achieve huge increases in material efficiency while producing more elegant and structurally legible forms.

3D-printed bridge by Joris Larman Lab demonstrating the expressive and material efficient results of designing with SKO software

The key difference between trees and bones is that, in the former, material cannot be removed whereas in bone tissue it can be.

Trees consequently grow as solid forms. This might seem surprising, given the hollowness of many bones. The explanation probably lies in the fact that there is not the same selective pressure for lightness in stationary trees as there is in animals that must move at speed to either catch, or avoid becoming, prey.

Most of the bulk of a tree is dead material (only the outer layers remain alive), whereas bones are continually being reformed and recycled.

One other possible explanation is that the solid core of trees functions to some extent as a compression core to resist the tension created by the outer sapwood, which grows in helical patterns up and around the trunk. This structural form has some similarities with Future Systems’ Coexistence Tower.

Coexistence Tower by Future Systems. The compression core and the helical arrangement of tension members around the perimeter have functional similarities with the structure of tree trunks

Trees growing in the shallow soils of rain forests have evolved buttress roots that resist overturning

The root forms of trees could also inspire new approaches to creating foundations for buildings.

The formation of a wide, stiff base effectively moves the pivot point some distance from the trunk and, on the opposite side, a branching network of roots mobilizes a vast amount of soil as ballast to resist overturning.

In rain forests, where soils can be relatively shallow and therefore cannot provide the same resistance as those in temperate climates, trees have evolved pronounced buttresses which actually work in tension to prevent overturning.

Book reference:

Biomimicry in Architecture by Pawlyn, Michael.

Get The Book on Amazon:

https://amzn.to/32F79jb

Cellular biological materials have intricate interior structures, self-organised in hierarchies to
produce modularity, redundancy and differentiation. As Michael Weinstock explains, the
foam geometries of cellular materials offer open and ductile structural systems that are
strong and permeable, making them an attractive paradigm for developments in material
science and for new structural systems in architecture and engineering.

Scanning electron micrograph of cancellous (spongy) bone tissue. Bone can
be either cortical (compact solid) or cancellous, with cortical usually forming
the exterior of the bone and cancellous tissue forming the interior. The

In recent years, new strategies for design and new techniques for making materials and large constructions have emerged, based on biological models of the processes by which natural material forms are produced.

Biological organisms have evolved multiple variations of form that should not be thought of as separate from their structure and materials.

The self-organisation of biological material systems is a process that occurs over time, a dynamic that produces the capacity for changes to the order and structure of a system, and for those changes to modify the behaviour of that system.

The characteristics of self-organisation include a

3-D spatial structure.
redundancy and differentiation.
hierarchy and modularity.

Studies of biological systemic development suggest that the critical factor is the spontaneous emergence of several distinct organisational scales and the interrelations between lower or local levels of organisation, the molecular and cellular level, and higher or global levels of the structure or organism as a whole.

The evolution and development of biological self-organisation of systems proceeds from small, simple components that are assembled together to form larger structures that have emergent properties and behaviour, which, in turn, self-assemble into more complex structures.

The geometry of soap foams is a model for the cellular arrangements at all scales in natural physical systems.

Natural Constructions

Natural materials develop under load, and the intricate interior structure of biological materials is an evolutionary response.
At the level of the individual, there is also an adaptive response as, for example, bone tissue gets denser in response to repeated loads in athletic activities such as weightlifting. Bone is a cellular solid, a porous material that has the appearance of mineralised foam, and its interior is a network of very small and intricately connected structures. When bone becomes less dense, due to age or prolonged inactivity, it is the very small connective material that vanishes, so that the spaces or cells within the bone become larger.
The loss of strength in the material is disproportionate, demonstrating the importance of the microstructure: larger cells make a weaker material. Cellular materials are common at many scales in the natural world, for example in the structure of tiny sea creatures, in wood and in bones. What they have in common is an internal structure of ‘cells’, voids or spaces filled with air or fluids, each of which has edges and faces of liquid or solid material. The cells are polyhedral, and pack all the available arranged space in a 3D pattern. Foam has cells that are differentially organised in space, whereas honeycombs are organised in parallel rows and tend to have more regular, prism-like cells. In all cellular materials, the cells may be either regular or irregular shapes, and may vary in distribution.

D’Arcy Thompson discussed the mathematical expressions for the shapes of growing cells in 1917, arguing that new biological structures arise because of the mathematical and physical properties of living matter.
His chapter on ‘The Forms of Cells’, when read in conjunction with the ‘Theory of Transformations’, has been extended today to patterning and differentiation in plant morphogenesis. The problem of mathematical descriptions of foam has a long history , but it can be observed that foam will comprise a randomised array of hexagon and pentagon structures.

Diatoms and radiolara are among the smallest of sea creatures, and the intricate structures of their skeletons have fascinated, among others, Frei Otto and his biologist collaborator JG Helmke. It has been argued that the formation of these tiny intricate structures is a process of mineralised deposits on the intersection surfaces of aggregations of pneus or bubbles.

Soap bubbles
A naturally produced foam of soap bubbles, demonstrating the differentiation
of polyhedral cells in an intricate geometry of foam architecture, including the
basic Plateau rules for the intersection of three ﬁlms.

The Construction of Materials

In the industrial world, polymer cellular foams are widely used for insulation and packaging, but the high structural efficiency of cellular materials in other, stiffer materials has only recently begun to be explored.

Comparatively few engineers and architects are familiar with the engineering design of cellular materials, and this has contributed to the slow development of cellular structures in architecture.

Industrial and economic techniques do exist for producing foams in metals, ceramics and glass.

Foamed cellular materials take advantage of the unique combination of properties offered by cellular solids, analogous properties to those of biological materials, but they do not share their origin. They are structured and manufactured in ways that are derived from biological materials, but are made from inorganic matter.

The production processes for metal foams and cellular ceramics have been developed for the simultaneous optimisation of stiffness and permeability, strength and low overall weight.

This is the logic of biomimesis, abstracting principles from the way in which biological processes develop a natural material system, applying analogous methods in an industrial context, and using stronger materials to manufacture a material that has no natural analogue.

Polyurethane foam wound dressing
Scanning electron micrograph of polyurethane foam, showing the porous
structure of differentiated open and partially closed cells. Magniﬁcation x 20
when printed at 10 centimetres wide.

Biomimetics is essentially interdisciplinary, a series of collaborations and exchanges between mathematicians, physicists, engineers, botanists, doctors and zoologists. The rigid boundaries between the inherited taxonomy of ‘pure’ disciplines make little sense in this new territory. Similarly, the traditional architectural and engineering ways of thinking about materials as something independent of form and structure are obsolete.

New research into the molecular assembly of structures and materials in what were previously thought to be homogenous natural materials has led to ‘biomimetic’ manufacturing techniques for producing synthetic materials, and new composite materials are being ‘grown’ that have increasingly complex internal structures based on biological models.

The fabrication of composites relies on controlling structure internal to the material itself, at molecular levels.
Here, processing is the controlling parameter and growth is more than a metaphor.

‘Grown’ materials are layered, molecule by molecule, to create distinctive micro-structures in thin films, making new combinations of metal and ceramic that are produced by design rather than ‘nature’. New composites such as flaw-tolerant ceramics and directionally solidified metals might seem to be a long way from the materials available to architects, but they are already in use in many other fields.

Sponge spicule
Scanning electron micrograph of the endoskeletal component of a sponge
made of calcium carbonate. When assembled, the skeleton forms either a
mesh or honeycomb structure. Magniﬁcation x 210 when printed at 10
centimetres wide.

Thomas Von Girsewald and Juan Subercaseaux, centroidal Voronoi
tessellation and boundary optimization in close-packing systems,
Emergent Technologies and Design programme,
AA Graduate School
of Architecture, 2005

Kevlar

Kevlar is perhaps the best-known manufactured organic fiber and, because of its unique combination of material properties, it is now widely used in many industrial applications. It has high tensile strength (five times that of steel), low weight and excellent dimensional stability, and so has been adopted for lightweight cables and ropes in many marine and naval applications.

Kevlar has high impact resistance, so it is the major fiber constituent in composite panels in military and civil aircraft, and in sporting equipment such as canoes, skis, racquets and helmets.

However, it has yet to be used widely in architectural construction.

Liquid Crystals

Liquid crystals have the flow properties of a conventional liquid, and the molecular structure of a solid crystal. This is a phase change occurring between the crystalline and isotropic liquid states.

Kevlar is produced, in part, by manipulating the liquid-crystalline state in polymers.

Spiders use the low viscosity in the liquid crystalline regime for the spinning of their silk.

Spider silk is as strong as Kevlar, which means that it has superior mechanical properties to most synthetic fibers and can stretch up to 40 per cent under load. This gives it an unusual advantage, in that the amount of strain required to cause failure actually increases as deformation increases, an energy-absorbing ability that allows the web to absorb the impact of flying prey.

Read more about Liquid Crystals :
https://www.cs.mcgill.ca/~rwest/wikispeedia/wpcd/wp/l/Liquid_crystal.htm

Ceramics

There is new interest within the material sciences and industry in the use of ceramics as a structural material. Ceramics are very light, but their compressive strength matches, or exceeds, that of metals.

They are hard and durable, resistant to abrasion and noncorroding as they are chemically inert. Ceramics are good insulators (both electric and thermal) and can resist high temperatures.

However, they have one major disadvantage: their lack of tensile strength. The solution to this problem is being sought in biological models – the forming of complex structures internal to the material – and as new production facilities come online ceramics may become the most ubiquitous of new materials for built structures.

Cellular ceramics are porous and can now be manufactured in various morphologies and topologies, ranging from honeycombs and foams to structures woven from fibers, rods and hollow spheres.

Substitutes for human bone and the coating of orthopedic prostheses are produced by similar methods.

Read more about the usage of ceramics in architecture:

https://www.architonic.com/en/story/dominic-lutyens-out-on-the-tiles-ceramic-architectural-facades/7000794

SMO Architektur and Arup, Bubble Highrise, Berlin, 2002
Experimental design from which the design approach to the Watercube was
evolved. The structure is produced by running a packing algorithm to ﬁll a
notional high-rise volume with differentiated spheres, which are then cut at
the surface intersection.

PTW Architects, CSCEG Design and Arup, ‘Watercube’ National Swimming
Centre, Beijing, due for completion 2007
Competition model showing overall scale: 177 x 177 metres and more than 30 metres high, with an entirely column-free
interior space.

Watercube digital structural model. The mathematics of foam geometries are
used to produce the structural array, ensuring a rational optimised and
buildable structural geometry.

Injecting a stream of gas bubbles into liquid metals is the basic technique for producing foamed metals, but preventing the bubbles from collapsing is difficult.

Adding a small quantity of insoluble particles to slow the flow of the liquid metal stabilises the bubbles in the production of aluminium foam sheets, produced with open or closed cells on the surface. Aluminium foams can be cast in complex 3D forms, are stronger and more rigid than polymer foams, can tolerate relatively high temperatures, and are recyclable and stable over time.

They are very light, nominally about 10 per cent of the density of the metal, and are currently used as a structural reinforcement material, particularly in aerospace applications, though they have not yet reached their full potential in lightweight architectural structures.

Closed-cell aluminium honeycomb is widely used as the core material of panel structures, conventionally with other materials as a surface. This is no longer strictly necessary, as new advanced processes produce ‘self-finished’ surfaces of high quality.

Cellular metals including, but not exclusively, aluminium, are being deployed for applications such as acoustic absorption, vibration damping and innovative thermal regulation. As the frequency and range of applications increases, data accumulates for the relationship between the topology of cells in the foam and the subsequent performance of the cellular material, so that improved and optimised cell topologies can be produced.

Another new open-cell foamed material, made of a glass-like carbon combining properties of glass and industrial carbons, can be used for biological ‘scaffolding’. Reticulated vitreous carbon has a large surface area combined with a very high percentage of void spaces, is sufficiently rigid to be selfsupporting, and is biologically and chemically inert. Cellular glass structures are used in medical applications for bone regeneration.

The bioactive glass acts as a scaffold to guide the growth and differentiation of new cells, and this requires an open-cell structure that is highly interconnected at the nanometre scale. The cells must be large enough to allow the bone tissue to grow between the cells, yet fine enough so that the ‘bioglass’ material can be absorbed into the bone as it is replaced by living tissue.

Watercube Resin Model

Watercube Digital Model

Material Constructions Design and construction strategies based on space-filling polyhedra and foam geometries offer open structural systems that are robust and ductile.

Control of the cell size, the distribution and differentiation of sizes within the global structure and the degree and number of connections are variables that can be explored to produce strength and permeability.

SMO Architektur and Arup designed the Bubble Highrise by packing a notional structural volume with bubbles of various sizes, then used the intersection of the bubbles and the exterior planes of the notional volume to generate a structure that gives entirely column-free interior spaces.

The ‘Watercube’ National Swimming Centre, Beijing, to be finished in 2007, was designed by PTW Architects and Arup using a structural design developed from Weaire and Phelan’s soap bubbles arrays. Despite the appearance of randomness, the elements of the structure are highly rational and so economically buildable.

The Watercube is an enormous building, 177 metres (581 feet) on each side and more than 30 metres (98 feet) high.

The network of steel tubular members is clad with translucent ETFE pillows. Over such a wide span of column-free space, the need to minimise the self-weight of the structure is paramount, as most of the structural work involves ensuring the roof can hold itself up. The steel tubes are welded to round steel nodes that vary according to the loads placed upon them.

There is a substantial variation in size, with a total of around 22,000 steel members and 12,000 nodes. There is a total of 4000 ‘bubbles’ in the Watercube, the roof being made of only 7 variant types (of bubbles) and the walls of only 16 variations, which are repeated throughout.

The geometry was developed by extensive scripting, using the Weaire and Phelan mathematics, with a further script required for a final analytical and geometrical correct 3D model. Scripts that run in minutes can deal with the tens of thousands of nodes and beam elements, and scripting was also used to develop structural analysis models and models from which drawings were automatically generated.

The ETFE cushions make the building very energy efficient, and sufficient solar energy is trapped within to heat the pools and the interior area, with daylight maximised throughout the interior spaces.


Watercube physical prototype; cells and ETFE cushions fabricated for the testing of environmental and structural behaviour, and conﬁrmation of production logics.

Book Reference:

Techniques and Technologies in Morphogenetic Design (Architectural Design March April 2006 Vol. 76 No. 2) by Michael Hensel, Achim Menges, Michael Weinstock

Link on Amazon :
https://amzn.to/3pbnKmj

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