From material to structural complexity: A cross-related system

2.5. From material to structural complexity: A cross-

natural mechanisms and structures may actually function. Manuel De Landa²⁷ makes a very interesting point towards this direction through a relative comparison between the progress of mathematics subjected with material science attempting to give an interpretation of “material complexity”, or the complexity of material structures. It all comes with the advances made in the way natural events and mechanisms are perceived in relation to equilibrium thermodynamics mostly used in classical mathematics. The action of an event was believed to be relative to the reaction of a material deformation, but this conclusion proved to be rather simplified and clearly not giving answers to most of the reactions concerning materials. Technological and scientific advances have shown that they preserved much more complex behaviour and there are indeed many cases and material examples, where this linearity is far from typical. Indeed, equation, such as Hooke’s law, which is one example where the stress was linked with deformation, was a major belief in science and physics. In fact, classical mathematics were dealing with linear equations for shallow waves, low-amplitude vibrations, small temperatures gradients, so they were trying to divide/fragmentize events in smaller events in order to explain them linearly, thus linearize non-linearity, as they were not able to do otherwise. Therefore, the attempt to apply linearity through the fragmentation of complex events could become a fraudulent for scientists and misleading, as it could not provide solid results at the end.

27 De Landa, M. (2004), “Material Complexity” in Leach N., Turnhill D. & Williams C, “Digital Tectonics”, University of Bath, UK.

Although we do observe materials in which they deform linearly, meaning that when the load increases, so do material deformation proportionally increases and vice versa; even these materials exhibit a certain threshold, where their deformation behaviour changes, evolving from elastic to plastic, whereas any further increase of load, changes the shape irreversibly. Plastic behaviour is but one example of nonlinear behaviour. Indeed, many materials behave nonlinearly even without critical loads. Some examples of biomaterials, such as organic tissues, display a J-shaped stress-strain curve: Mammalian skin and flesh are two of the many biomaterials that exhibit a J-shaped curve.

Loading and unloading occur along the same curve, i.e. the loading is completely reversible and elastic. This ensures that all the energy used in extending the system is returned once the load is removed. It is clearly important that there should not be too much energy absorption in arterial walls. The elastic properties of arterial wall are important not only to protect against aneurysms but also to smooth out variations in blood pressure and blood flow rate.

Organic tissues, for example, display a J-shaped reaction curve: a small load causes a large deformation at first, but even large loads cease to have much effect. Rubber and other materials display an S-shaped reaction curve: a load fails to have any effect at all up to a point beyond which rubber stretches linearly but only to stop reacting to further loads beyond yet another point. Since a material’s capacity to bear loads is directly related to its capacity to deform, rubber’s inability to further deform under heavy loads makes it very fragile under

those conditions. At any event, J- and S- shaped reaction curves, as well as many others, are examples of nonlinear, complex material behaviour.

Additionally, there are several more examples that can justify this view on non-linearity of the material inert organisation. The material system of metals is another example that recent scientific developments have revealed of being more than static systems.

Although metallurgists and blacksmiths have empirically learned how this metamorphic mechanism works, scientists have recently unravelled that their strength is derived from their atoms chemical bonds and their links between them, being at the same time an

example of the complex dynamical system. Particularly, the system comes to motion when bifurcations occur in the relationship of matter and energy, like presenting cracks, ruptures, and fractures through the structure of metals. These bifurcations in components like the crystalloid structure of metal are called dislocations, endowing a metal

Figure 3: Relation between various metals alloy, with emphasis in acquiring more strength.

with its properties, such as being more or less rigid and so on. It can

be deducted that these emergent properties are the result of this inner dynamic system with material complexity.

This significant assumption on using techniques that utilised constraints away from equilibrium thermodynamics set forward the invention of new material structures, with better properties and resistance to fatigue or fracture, such as nano- and quasi-crystal structures, superlattices and many types of glasses (Figure 4).

Notwithstanding, as we have already analysed in the previous chapter, today’s complexity has the need to be expressed with more than non-linearity, as recent developments in mathematics have proven, such as those towards theories on chaotic systems.

Particularly, he quotes that “(…) we are beginning to understand that any complex systems, whether composed of interacting molecules, organic creatures or economic agents, is capable of spontaneously generating order and actively organising itself into new structures and

Figure 4: Morphologies of faceted single grains of icosahedral quasicrystals.

forms. It is precisely this ability of matter and energy to self-organise that is of great significance to the philosopher. (…)”²⁸.

Moreover, material complexity and its awareness of self- organisation capabilities become the rule, resulting to the distinction between homogeneous and heterogeneous materials, depending on the inner bond relationship and the way they respond to several actions. French philosopher Gilles Deleuze also argues that this homogenization which for centuries was prevailing in the matter-form model was, in particular, technological insufficient. He argues “(…) it is the law that assures the model’s coherence since the laws are what submit matter to this form, and conversely, realise in a matter a given property deduced from form. (…) (p.450); and proceeds to the deconstruction and critique of the Platonic idea on the genesis of form, expressed through the hylomorphic scheme, that “(…) the hylomorphic model²⁹ leaves many things, active and inactive, by the wayside. On

28 De Landa, M. (2004)

29 ‘Hylomorphism’ is simply a compound word, deriving from the Greek terms for matter (hylê) and form or shape (morphê); thus one could equally describe Aristotle's view of body and soul as an instance of his “matter-formism.” That is, when he introduces the soul as the form of the body, which in turn is said to be the matter of the soul, Aristotle treats soul-body relations as a special case of a more general relationship, which obtains between the components of all generated compounds, natural or artefactual.

The notions of form and matter are themselves, however, developed within the context of a general theory of causation and explanation which appears in one guise or another in all of Aristotle's mature works. According to this theory, when we wish to explain what there is to know, for example, about a bronze statue, a complete account necessarily alludes to at least the following four factors:

the statue's matter, its form or structure, the agent responsible for that matter manifesting its form or structure, and the purpose for which the matter was made to realize that form or structure. These four factors he terms the four causes: material, formal, efficient, final cause.

(Accessed: http://plato.stanford.edu/entries/aristotle-psychology/#2)

the one hand, to the formed or formable matter we must add an entire energetic materiality in movement, carrying singularities and haecceities that are already like implicit forms that are topological, rather than geometrical, and that combined with process of deformation; (…) on the other hand, to the essential properties of the matter deriving from the formal essence must add variable intensive affect, now resulting from the operation, now on the contrary making it possible; (…).³⁰

Can we actually reconstruct the way matter and energy re-flow in material systems, imposing themselves upon the creation of form;

to the way a larger in scale structural system can impose an architectural form itself? Could we perhaps re-think our understanding of structure and form through the importance of parameters, such as stresses, prescribed by the environment itself on that form?

Nevertheless, material complexity and the relation matter-form or matter-energy cannot be excluded from a more crucial aspect, probably directing these relationships, the universal forces that can elaborate as guidelines for the dynamical material systems to function.

Deleuze argues the constant deterioration of material and that “(…) it is now a question of elaborating a material charged with harnessing forces of different order: the visual material must capture non-visible forces (…)”³¹. Indeed, when we refer to dynamical systems and to energy flow between the different states of a material organisation, we

30 Gilles Deleuze, A thousand Plateaus, p.450.

31 Gilles Deleuze, A thousand Plateaus, p.516.

must definitely take into consideration what are the principles directing this organisation “in motion”, this dynamical organisation.

Undoubtedly, material systems that are part of Cosmos should be in accordance with rules governing this Cosmos. Deleuze also argues that apart from a capture of forces, a form is also a capture of densities and intensities in time and when Earth comes to take on the value of pure material, the forces become the forces of gravitation and other forces that are of our knowledge, in the sphere of physics or chemistry and so on. Therefore, we may not only speak of a matter-form relationship, but rather of a matter-forces relationship.

Indeed, the force factor is a guiding rule, taking place in the outer or inner environment of all complex systems, material and even structural. Thus, we may understand that material and structure of form are cross-related. So, if placed in the perspective of structures in architecture, how can structural complexity be interpreted and defined?

In response to the analysis of material complexity, the discovery of non-linearity governing the laws of material systems was an aspect of “complexity” that was part of them. Additionally, it is also the great number of laws and elements collaborating together inside the system itself. Structures in nature and, to our interest in architecture, are systems composed of several parts, functioning as a whole organisation. Given that the roles that a structure may play can be highly heterogeneous, the repertoire of materials that a designer uses should reflect this complexity. Additionally, much as in the case

of biological materials like bone, new designs may involve structures with properties that are in continuous variation, with some portions of the structures better able to deal with compression while others deal with tension.

The structural analysis of a typical and rather simple geometrical structure could indeed need linearity to be solved by the engineer. (state which method it is, Hooke’s first method of structural analysis, perhaps even Gaudi. In fact, before the advent of computers, most of the structures were discretized in the two main directions (x, y) and solved linearly, providing acceptable approximated solutions.

Nevertheless, for more complex structural configurations the problem would become impossible to solve, as it would involve a lot of calculations that by hand would need an innumerous amount of time.

What began to change is our perspective on the structural behaviour of a form? Natural structures themselves function non- linearly and most structures, are considered to be composed of several parts of two, three, or perhaps more materials, proving a certain combination of material and structural ‘complexity” in their behaviour.

What is more, in computational architecture and even before, within the Post-modern movement, the idea of the architectural form would become more organic and non-geometrical, affecting at the same time the way that structures become part of the morphogenetic idea itself and adding more complexity to the architectural geometry.

Therefore, structural analysis could require adequate methods in order to respond to those challenges posed by the ongoing design

principles of contemporary architecture. Finite Element Analysis is a very recent method that has become a tool for many engineers towards this direction, with structures of arbitrary size and complexity.

In fact, it has become the most acceptable way and with more solid results when having to engage with highly complex geometry and loading conditions. Historically, engineers were reluctant to use nonlinear analysis, because of its complex problem formulation and long solution time. That is changing now, as nonlinear FEA software interfaces with CAD and has become much easier to use. In addition, improved solution algorithms and powerful desktop computers have shortened solution times. A two decade ago, engineers recognised FEA as a valuable design tool. Now they are starting to realise the benefits and greater understanding that nonlinear FEA brings to the design process.

Therefore, having observed that material systems function non- linearly and have emergent properties as a system, structural complexity is an idea that exists and in fact taking place in most of the buildings conceived presently and by contemporary and in turn computational architecture. It is a very important parameter and part of the architectural concept functioning as a candidate of some sort of

“generative agent” that aids morphogenesis with the emergence of form and structure in the architectural idea.

2.6. Non-standard architecture, the Non-Euclidean