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Bionics: Branching is Beefy

08/01/05

If there's one thing that you learn after 4 billion years of futzing around it's how to get strength with minimum materials. We designers have the opportunities to use carbon fiber, plastics, metals, and all sorts of other great materials, and often, meticulous minimization of cost is not so important. But in the animal kingdom, where every gram of calcium carbonate that goes into your shell or bones had to be hunted down, chewed up, and digested at great expense, you learn some tricks in using it. Most of these involve branching.
080105_stressmain

Have you ever thought about stress? Not the kind of stress you get when it's valentines day eve and all the flower shops are closed, and you totally forgot... We mean the kind of stress that breaks things. Stress in an object is basically the force in that object, divided by the amount of stuff in the object. For example, a thick string holding up 50 pounds would see much less stress than a thin one holding the same 50 pounds, and would be less prone to breaking.

So why does branching help with stress so much? It's in the way that stress "flows" through objects. If you've got your basic blue brick of stuff (as illustrated below) and you pull on the sides, the brick has stress on it.

Specifically, it has tensile stress, or stress from pulling. And the path of the stress is straight through the brick. Now, if you cut out a dent in the brick, the stress lines re-arrange. The same amount of stress "enters" the brick at the ends, and has to get through the bottleneck in the middle (bear in mind that stress doesn't really flow like this, but it's a convenient way to think of it. The real explanations for this stuff require sitting through a lot of statics lectures, so we though we'd save you the trouble). So, because of the elastic nature of stress lines, they hug the edge of the dent -- the dent has become a stress concentrator. You've seen this kind of thing happen when a dark plastic part gets white around a boss when the boss has too much force put on it, or in cases like this one, where Plexiglass cracks around a screw hole:

A good rule of thumb to remember is that the sharper the transition from thick to thin, the stronger the stress concentration, and the higher the likelihood of a part breaking. So, it seems like the best thing to do is just add fillets everywhere, or make all your shapes blobby, right? But that takes a lot of material, and can make things pretty heavy, both of which aren't acceptable when you're a horseshoe crab trying to outrun enemies.

This page on optimizations of 2D structures should give you an idea of what we mean. In particular, this movie is great at illustrating how an optimal force distribution involves branching. Basically, each branch presents an optimal path for stress to flow. The material in the middle just isn't needed. This movie shows even more branching, and should help you grasp some of these animal solutions to the same problem.

You can find tons of examples of this with a quick trip to the ocean, where the pulsing surf threatens to crush, rip, or pull everything without a sturdy skeleton. One of the coolest is the shell of the Horseshoe Crab. This guy, like other arthropods, has an exoskeleton-style shell with muscles on the inside. And in order to attach muscles with a lot of pull, like those that run his legs, he's grown a series of stumps with webbed support tendrils of shell that grow into the surface of his shell, spreading the force out so that nothing breaks as muscles pull against the thin sheet of calcium carbonate.

The coolest thing is that, while the tendrils are generally symmetrical, they grew in response to differential stresses on either side of the shell, so the ones for the third leg on the left are slightly different from the third leg on the right, because maybe one leg was a little bigger, used more, or something else.

Fish are also a prime example, as this vertebrae demonstrates. Rather than investing in a solid hunk of bone, which would be chemically costly, and heavy as can be, this network of carefully grown bone is a visual indication of just where muscles attach and stress flows through this bone.

Obviously, architects were some of the first to pick up on this idea, when they began building bridges from beams, instead of solid arches of stone. But the design strategy is spreading into design, as some artists, like Marcel Wanders have used new materials and methods of fabrication to create surfaces of minimal material and maximum strength. We can imagine, as SLA and other fabrication technologies take root, these types of high-complexity, but low material designs will become more standard.

So, next time you're at the beach, or anywhere, take a look at the way nature joins its stuff together. You'll find no sharp edges, and very few straight 90 degree joints. Tree trunks spread at the roots for strength, bones have lace work within them for strength. It's all about spreading the stress out. Think about that next time you're putting a shell on something. It might be the inspiration you need.

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Bionics: Branching is Beefy

08/01/05

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