On the Functions of Cellular Structures in Nature

WHY did nature evolve cellular structures?

In a previous post, I laid out a structural classification of cellular structures in nature, proposing that they fall into 6 categories. I argued that it is not always apparent to a designer what the best unit cell choice for a given application is. While most mechanical engineers have a feel for what structure to use for high stiffness or energy absorption, we cannot easily address multi-objective problems or apply these to complex geometries with spatially varying requirements (and therefore locally optimum cellular designs). However, nature is full of examples where cellular structures possess multi-objective functionality: bone is one such well-known example. To be able to assign structure to a specific function requires us to connect the two, and to do that, we must identify all the functions in play. In this post, I attempt to do just that and develop a classification of the functions of cellular structures.

Any discussion of structure in nature has to contend with a range of drivers and constraints that are typically not part of an engineer’s concern. In my discussions with biologists (including my biochemist wife), I quickly run into justified skepticism about whether generalized models associating structure and function can address the diversity and nuance in nature – and I (tend to) agree. However, my attempt here is not to be biologically accurate – it is merely to construct something that is useful and relevant enough for an engineer to use in design. But we must begin with a few caveats to ensure our assessments consider the correct biological context.

1. Uniquely Biological Considerations

Before I attempt to propose a structure-function model, there are some legitimate concerns many have made in the literature that I wish to recap in the context of cellular structures. Three of these in particular are relevant to this discussion and I list them below.

1.1 Design for Growth

Engineers are familiar with “design for manufacturing” where design considers not just the final product but also aspects of its manufacturing, which often place constraints on said design. Nature’s “manufacturing” method involves (at the global level of structure), highly complex growth – these natural growth mechanisms have no parallel in most manufacturing processes. Take for example the flower stalk in Fig 1, which is from a Yucca tree that I found in a parking lot in Arizona.

Figure 1. The flower stalk (before bloom) of a Yucca plant in Arizona with overlapping surface cellular structure (Author’s image)

At first glance, this looks like a good example of overlapping surfaces, one of the 6 categories of cellular structures I covered before. But when you pause for a moment and query the function of this packing of cells (WHY this shape, size, packing?), you realize there is a powerful growth motive for this design. A few weeks later when I returned to the parking lot, I found many of the Yucca stems simultaneously in various stages of bloom – and captured them in a collage shown in Fig 2. This is a staggering level of structural complexity, including integration with the environment (sunlight, temperature, pollinators) that is both wondrous and for an engineer, very humbling.

Figure 2. From flower stalk to seed pods, with some help from pollinators. Form in nature is often driven by demands of growth. (Author’s images)

The lesson here is to recognize growth as a strong driver in every natural structure – the tricky part is determining when the design is constrained by growth as the primary force and when can growth be treated as incidental to achieving an optimum functional objective.

1.2 Multi-functionality

Even setting aside the growth driver mentioned previously, structure in nature is often serving multiple functions at once – and this is true of cellular structures as well. Consider the tessellation of “scutes” on the alligator. If you were tasked with designing armor for a structure, you may be tempted to mimic the alligator skin as shown in Fig. 3.

Figure 3. The cellular scutes on the alligator serve more than just one function: thermal regulation, bio-protection, mobility, fluid loss mitigation are some of the multiple underlying objectives that have been proposed (CCO public domain, Attr. Republica)

As you begin to study the skin, you see it is comprised of multiple scutes that have varying shape, size and cross-sections – see Fig 4 for a close-up.

Figure 4. Close-up of alligator scutes (Attr: Hans Hillewaert, Flickr, Creative Commons)

The pattern varies spatially, but you notice some trends: there exists a pattern on the top but it is different from the sides and the bottom (not pictured here). The only way to make sense of this variation is to ask what functions do these scutes serve? Luckily for us, biologists have given this a great deal of thought and it turns out there are several: bio-protection, thermoregulation, fluid loss mitigation and unrestricted mobility are some of the functions discussed in the literature [1, 2]. So whereas you were initially concerned only with protection (armor), the alligator seeks to accomplish much more – this means the designer either needs to de-confound the various functional aspects spatially and/or expand the search to other examples of natural armor to develop a common principle that emerges independent of multi-functionality specific to each species.

1.3 Sub-Optimal Design

This is an aspect for which I have not found an example in the field of cellular structures (yet), so I will borrow a well-known (and somewhat controversial) example [3] to make this point, and that has to do with the giraffe’s Recurrent Laryngeal Nerve (RLN), which connects the Vagus Nerve to the larynx as shown in Figure 5, which it is argued, takes an unnecessarily long circuitous route to connect these two points.

Figure 5. Observe how the RLN in the giraffe emerges from the Vagus Nerve far away from the thorax: a sub-optimal design that was likely carried along through the generations in aid of prioritizing neck growth (Attr: Vladimir V. Medeyko)

We know that from a design standpoint, this is sub-optimal because we have an axiom that states the shortest distance between two points is a straight line. And therefore, the long detour the RLN makes in the giraffe’s neck must have some other evolutionary and/or developmental basis (fish do not have this detour) [3]. However, in the case of other entities such as the cellular structures we are focusing on, the complexity of the underlying design principles makes it hard to identify cases where nature has found a sub-optimal design space for the function of interest to us, in favor of other pressing needs determined by selection. What is sufficient for the present moment is to appreciate that such cases may exist and to bear them in mind when studying structure in nature.

2. Classifying Functions

Given the above challenges, the engineer may well ask: why even consider natural form in making determinations involving the design of engineering structures? The biomimic responds by reminding us that nature has had 3.8 billion years to develop a “design guide” and we would be wise to learn from it. Importantly, natural and engineering structures both exist in the same environment and are subject to identical physics and further, are both often tasked with performing similar functions. In the context of cellular structures, we may thus ask: what are the functions of interest to engineers and designers that nature has addressed through cellular design? Through my reading [1-4], I have compiled the classification of functions in Figure 6, though this is likely to grow over time.

Figure 6. A proposed classification of functions of cellular structures in nature (subject to constant change!)

This broad classification into structural and transport may seem a little contrived, but it emerges from an analyst’s view of the world. There are two reasons why I propose this separation:

  1. Structural functions involve the spatial allocation of materials in the construction of the cellular structures, while transport functions involve the structure AND some other entity and their interactions (fluid or light for example) – thus additional physics needs to be comprehended for transport functions
  2. Secondly, structural performance needs to be comprehended independent of any transport function: a cellular structure must retain its integrity over the intended lifetime in addition to performing any additional function

Each of these functions is a fascinating case study in its own right and I highly recommend the site AskNature.org [1] as a way to learn more on a specific application, but this is beyond the scope of the current post. More relevant to our high-level discussion is that having listed the various reasons WHY cellular structures are found in nature, the next question is can we connect the structures described in the previous post to the functions tabulated above? This will be the attempt of my next post. Until then, as always, I welcome all inputs and comments, which you can send by messaging me on LinkedIn.

Thank you for reading!

References

  1. AskNature.org
  2. Foy (1983), The grand design: Form and colour in animals, Prentice-Hall, 1st edition
  3. Dawkins (2010), The greatest show on earth: the evidence for evolution, Free Press, Reprint of 1st edition
  4. Gibson, Ashby, Harley (2010), Cellular Materials in Nature and Medicine, Cambridge University Press; 1st edition
  5. Ashby, Evans, Fleck, Gibson, Hutchinson, Wadley (2000), Metal Foams: A Design Guide, Butterworth-Heinemann, 1st edition

Cellular Design Strategies in Nature: A Classification

What types of cellular designs do we find in nature?

Cellular structures are an important area of research in Additive Manufacturing (AM), including work we are doing here at PADT. As I described in a previous blog post, the research landscape can be broadly classified into four categories: application, design, modeling and manufacturing. In the context of design, most of the work today is primarily driven by software that represent complex cellular structures efficiently as well as analysis tools that enable optimization of these structures in response to environmental conditions and some desired objective. In most of these software, the designer is given a choice of selecting a specific unit cell to construct the entity being designed. However, it is not always apparent what the best unit cell choice is, and this is where I think a biomimetic approach can add much value. As with most biomimetic approaches, the first step is to frame a question and observe nature as a student. And the first question I asked is the one described at the start of this post: what types of cellular designs do we find in the natural world around us? In this post, I summarize my findings.

Design Strategies

In a previous post, I classified cellular structures into 4 categories. However, this only addressed “volumetric” structures where the objective of the cellular structure is to fill three-dimensional space. Since then, I have decided to frame things a bit differently based on my studies of cellular structures in nature and the mechanics around these structures. First is the need to allow for the discretization of surfaces as well: nature does this often (animal armor or the wings of a dragonfly, for example). Secondly, a simple but important distinction from a modeling standpoint is whether the cellular structure in question uses beam- or shell-type elements in its construction (or a combination of the two). This has led me to expand my 4 categories into 6, which I now present in Figure 1 below.

Figure 1. Classification of cellular structures in nature: Volumetric – Beam: Honeycomb in bee construction (Richard Bartz, Munich Makro Freak & Beemaster Hubert Seibring), Lattice structure in the Venus flower basket sea sponge (Neon); Volumetric – Shell: Foam structure in douglas fir wood (U.S. National Archives and Records Administration), Periodic Surface similar to what is seen in sea urchin skeletal plates (Anders Sandberg); Surface: Tessellation on glypotodon shell (Author’s image), Scales on a pangolin (Red Rocket Photography for The Children’s Museum of Indianapolis)

Setting aside the “why” of these structures for a future post, here I wish to only present these 6 strategies from a structural design standpoint.

  1. Volumetric – Beam: These are cellular structures that fill space predominantly with beam-like elements. Two sub-categories may be further defined:
    • Honeycomb: Honeycombs are prismatic, 2-dimensional cellular designs extruded in the 3rd dimension, like the well-known hexagonal honeycomb shown in Fig 1. All cross-sections through the 3rd dimension are thus identical. Though the hexagonal honeycomb is most well known, the term applies to all designs that have this prismatic property, including square and triangular honeycombs.
    • Lattice and Open Cell Foam: Freeing up the prismatic requirement on the honeycomb brings us to a fully 3-dimensional lattice or open-cell foam. Lattice designs tend to embody higher stiffness levels while open cell foams enable energy absorption, which is why these may be further separated, as I have argued before. Nature tends to employ both strategies at different levels. One example of a predominantly lattice based strategy is the Venus flower basket sea sponge shown in Fig 1, trabecular bone is another example.
  2. Volumetric – Shell:
    • Closed Cell Foam: Closed cell foams are open-cell foams with enclosed cells. This typically involves a membrane like structure that may be of varying thickness from the strut-like structures. Plant sections often reveal a closed cell foam, such as the douglas fir wood structure shown in Fig 1.
    • Periodic Surface: Periodic surfaces are fascinating mathematical structures that often have multiple orders of symmetry similar to crystalline groups (but on a macro-scale) that make them strong candidates for design of stiff engineering structures and for packing high surface areas in a given volume while promoting flow or exchange. In nature, these are less commonly observed, but seen for example in sea urchin skeletal plates.
  3. Surface:
    • Tessellation: Tessellation describes covering a surface with non-overlapping cells (as we do with tiles on a floor). Examples of tessellation in nature include the armored shells of several animals including the extinct glyptodon shown in Fig 1 and the pineapple and turtle shell shown in Fig 2 below.
    • Overlapping Surface: Overlapping surfaces are a variation on tessellation where the cells are allowed to overlap (as we do with tiles on a roof). The most obvious example of this in nature is scales – including those of the pangolin shown in Fig 1.
Figure 2. Tessellation design strategies on a pineapple and the map Turtle shell [Scans conducted at PADT by Ademola Falade]

What about Function then?

This separation into 6 categories is driven from a designer’s and an analyst’s perspective – designers tend to think in volumes and surfaces and the analyst investigates how these are modeled (beam- and shell-elements are at the first level of classification used here). However, this is not sufficient since it ignores the function of the cellular design, which both designer and analyst need to also consider. In the case of tessellation on the skin of an alligator for example as shown in Fig 3, was it selected for protection, easy of motion or for controlling temperature and fluid loss?

Figure 3. Varied tessellation on an alligator conceals a range of possible functions (CCO public domain)

In a future post, I will attempt to develop an approach to classifying cellular structures that derives not from its structure or mechanics as I have here, but from its function, with the ultimate goal of attempting to reconcile the two approaches. This is not a trivial undertaking since it involves de-confounding multiple functional requirements, accounting for growth (nature’s “design for manufacturing”) and unwrapping what is often termed as “evolutionary baggage,” where the optimum solution may have been sidestepped by natural selection in favor of other, more pressing needs. Despite these challenges, I believe some first-order themes can be discerned that can in turn be of use to the designer in selecting a particular design strategy for a specific application.

References

This is by no means the first attempt at a classification of cellular structures in nature and while the specific 6 part separation proposed in this post was developed by me, it combines ideas from a lot of previous work, and three of the best that I strongly recommend as further reading on this subject are listed below.

  1. Gibson, Ashby, Harley (2010), Cellular Materials in Nature and Medicine, Cambridge University Press; 1st edition
  2. Naleway, Porter, McKittrick, Meyers (2015), Structural Design Elements in Biological Materials: Application to Bioinspiration. Advanced Materials, 27(37), 5455-5476
  3. Pearce (1980), Structure in Nature is a Strategy for Design, The MIT Press; Reprint edition

As always, I welcome all inputs and comments – if you have an example that does not fit into any of the 6 categories mentioned above, please let me know by messaging me on LinkedIn and I shall include it in the discussion with due credit. Thanks!