From a materials-engineering point of view, one of the great benefits of organic and biological materials is their elasticity. Of course, organic elastomers like polyisoprene (the largest component of natural rubber latex), high-molecular-weight polydimethylsiloxane (silicone rubber), and polyurethane exhibit the most extreme elasticity, with elastic (or quasielastic) strains† sometimes exceeding 1000%; but other organic polymers have viscoelastic behavior above their glass transition temperatures, which are often quite low, making them very resistant to shattering in everyday use and often capable of elastic strains over 10% and even larger ductile strains. By contrast, common metals are limited to elastic strains of about 1%, although pseudoelasticity can give shape-memory alloys larger strains closer to those of the plastics mentioned above; and common ceramics are closer to 0.1% to 0.01% strain.
Furthermore, biological metamaterials such as wood and sponge can achieve much greater elastic strains than their component materials can. Similar benefits are achieved with crude synthetic metamaterials such as gels, aerogels, foamed metals, aerated cements, and so on.
This is a potentially serious problem for designing self-reproducing automata working from exclusively inorganic feedstocks, an objective I consider important for three different reasons: first, most of the universe, even most of the earth, does not appear to contain life forms, and thus mostly lacks complex organic molecules that could be used to build the automata needed to mine the asteroids; second, it is desirable that any agent controlling such automata not have an incentive to, e.g., deforest large areas of land, in order to build more automata; third, when automata that consume organic matter in order to operate have appeared in the press, public perception has been extremely negative.
Such plastics and elastomers fulfill several very important functions in existing machinery, including vibration isolation (i.e., couplings with a very low derivative of force with respect to displacement), relaxing tolerances, elastic energy storage, and protection from impacts. Though metals and especially ceramics offer higher ultimate strengths than plastics and especially elastomers, members made from metals and (again, especially) ceramics often must be sized orders of magnitude larger than their static and dynamic loadings to resist impact loadings.
Advances in vibration isolation have long been crucial to demanding apparatus — Michelson and Morley built their interferometer on a slab of rock floating in mercury, as I understand it, and modern inventions were the key advances that made LIGO possible. But many less-exotic machines need to manage vibration, too. Everyday modern motor mounts are commonly made with combinations of elastomeric supports (under compression) and dashpots.
But there are many other things you can do as well. Supports in compression are necessarily sized to have enough rigidity to resist buckling; this means that even small-displacement vibrations can transmit a lot of force, and thus energy, through them. Supports under flexion, like truck-suspension leaf springs, are not subject to this limitation, but suffer a compensating lever-arm disadvantage. Supports in pure tension can supply much more compliance for a given bearing capacity. This is why a tensegrity structure provides so much more compliance, and thus vibration isolation, than a traditional trusswork.
However, although strings in tension can have a great deal of bearing capacity for their rigidity, as the frequency increases, the string’s own density comes into play. This increases the tension on the string for a given displacement whenever the wavelength of the wave (as it would propagate along the string) is comparable to or shorter than the string’s length, enabling more vibrational energy to be transmitted through the string. Moreover, the resonance modes of the string can smear out a short-lived vibration over a longer period of time. LIGO† dealt with this in part by using DSP after the fact to filter out vibrations at the vibrational frequencies of the instruments’ tension supports.
A different approach to the problem, also used in LIGO, is to use giant-compliance mechanisms made by putting a negative-compliance support (such as an Euler column† near its critical buckling force) in parallel with a positive-compliance support (such as any everyday object). The supports are designed to precisely cancel at the load they must support, enabling that load to “float” over a relatively large range of displacements at near-zero net force.
The energy of a vibration is partly reflected from discontinuities in acoustic impedance; discontinuity-rich environments such as a few meters of dirt and rocks are quite good at preventing the propagation of vibrations, to the point that Elon Musk claimed in his TED talk that neither the US Customs & Border Patrol nor the Israel Defence Force were capable of detecting tunnels dug more than three tunnel diameters under, respectively, the Mexican border and the Gaza Strip. So perhaps a string of beads, each bead connected to the next through a short length of cord, could work like acoustic multilayer insulation to exponentially attenuate transmitted vibrations.
Another possible approach — also at play in hiding tunnels from La Migra — is to use nonlinear interactions to transfer vibrational energy to progressively higher frequency bands. Impacts between relatively rigid particles are one example (say, attaching a box of dry sand to soak up vibrations — we don’t normally consider quartz crystals a great damper), but so too are Euler columns crossing their critical stress (which includes ordinary strings alternating between tension and slackness), the thin-shell dynamics of cymbal crashes, and vibrations reaching large stresses in quasielastic substances like rubber.
Metals and especially ceramics are hard to work with because they demand very tight tolerances. Because their limiting strain is so small, they must be very close to the right shape and position before being brought into contact; typical tolerances for steel machine parts are a few microns, and as I understand it, ceramic parts are even more of a motherfucker. (This is worsened by the frequent need to do much shaping of ceramics in a green state before final densification.)
Plastics (and, again, especially rubbers) can simplify this problem enormously. If an engine head can seat on a rubber gasket rather than directly onto the cast-iron cylinder, for example, it need not withstand the large forces that would be needed to seal it against the cylinder directly, compensating not only for its manufacturing imperfections but also its thermal warping. In high-vacuum systems, where organic materials generally outgas too much, this role is often taken up by gaskets made from a malleable metal like indium, thus avoiding the need to apply large stresses to glass to seal it against metal.
In another direction, many RepRaps have been built with bits of plastic hose serving as flexible shaft couplings, to allow for some misalignment of shafts. Nowadays, machined springs are more common for this use, which I think is because they last longer.
As an alternative to using plastic gaskets or flexible shaft couplings to compensate for inaccurate parts or assembly, possibly self-reproducing automata can be made from more accurate parts accurately assembled. As an alternative to using them to accommodate for thermal expansion discontinuities, matching thermal coefficients of expansion is possible (and regularly used to seal metal to glass in vacuum tubes); graded-TCE materials may help here.
For the last few centuries, “clockwork” devices have been driven by elastic energy storage, typically in brass watch springs rather than in plastics. Plastics are actually not very good for elastic energy storage, despite what would appear to be higher energy densities: they tend to be viscoelastic rather than purely elastic, losing stored energy to creep relatively rapidly, and quasielastic elastomers like polyisoprene actually store the energy as easily-lost heat rather than strained bond energy as metals do. (For this same reason, rubber makes better motor mounts than would a steel spring of nominally the same stress-strain curve: the rubber dissipates high frequencies.)
Organic materials are used for shorter-term elastic energy storage, such as in bows, which must be unstrung when not in use to prevent creep.
Impact loadings, as I understand it, are characterized by being limited principally by energy rather than force. If a perfectly rigid sphere of 1 kg is traveling at 1 m/s toward your machinery, it can exert an arbitrarily large pressure or force on the machinery — the collision of two such idealized horrors would produce infinite force and pressure for an instant. But it only has half a joule of energy. If the material it strikes deforms elastically or plastically, the forces actually encountered may be quite low; for example, if it deforms by 1 mm, the sphere stops in about 2 ms, so the force is on the order of 500 N, the weight of only 50 kg. If we suppose that the sphere has a radius of 100 mm, then the pressure is only of the order 30 kPa (5 psi in archaic units). (The precise numbers depend on details of the impact such as the distribution of pressure over the impact area, the stress–strain curve for the impacted material, its Poisson ratio, its density (!), and so on, so in practice the numbers might be a few times higher or a few times lower.) But if the material only deforms by 100 μm, the impact takes on the order of 200 μs, the force is of the order of 100 kN, and the pressure is of the order of 3 MPa. Inversely, if the material deforms by 10 mm, the impact takes on the order of 20 ms, the force is of the order of 5 N, and the pressure of the order of 300 Pa. Thus, by adjusting the rigidity of the impacted material over two very plausible orders of magnitude, we can adjust its stress inversely over four orders of magnitude.
An additional factor is that very rigid impacts will almost certainly have smaller impact areas than softer impacts, because in a softer impact, the colliding bodies come into contact over a larger area than their initial contact. This factor even comes into play for non-impact loadings, such as tightening a spark plug on a car engine, though ductile substances like lead would also help there.
These are the reasons you can lean your full body weight on a car door window though you can shatter it by flicking a fragment of spark plug at it.
The impact energy a material can absorb, either elastically or plastically, is an intrinsic property of the material: it is almost precisely the integral of its stress over its strain to the limiting strain in question. This gives you some number of joules per cubic meter, or per cubic millimeter. In the case of elastic deformation, this is also the energy density of the material when used as a spring. (Small quibbles may attach from the ability of different structures to recruit more or less of the material’s energy absorption capacity, including by way of shear deformations.)
So we have seen that compliant materials are crucial for a variety of reasons. How can we achieve them using inorganic materials? One approach is using metamaterials.
If you make a flat plate from a brittle material with 0.02% elongation at break, such as everyday fired clay, assuming linear elastic stress-strain behavior, it will break upon bending to a position where its inner surface is 0.02% shorter than its midline, while its outer surface is 0.02% longer. If it’s bent into a circle at this point, the outer surface is a circle 0.02% larger than the midline circle and 0.04% larger than the inner-surface circle. So if, for example, it’s 1 mm thick, the radius of the circle is 2.5 m, and its diameter is 5 m. But if you reduce its thickness, the radius of curvature diminishes proportionately.
And that’s why aluminum foil and paper can be bent around much tighter curves before yielding and breaking than aluminum plate and fiberboard.
As you reduce the thickness of the material, the bulk approximation does eventually break down, but, interestingly, at micron scales, the material typically shows greater flexibility than the model would predict, rather than less — perhaps because of fewer surface defects and more consistent cooling — until you get to some kind of grain size of the material, which is on the order of 50 μm for everyday fired clay, but could be as small as dozens of picometers for some atomic and molecular materials.
This is the principle behind the everyday coil spring or knit sock — by structuring ordinary piano wire or cellulose in a particular way, you can get it to yield like rubber, though a steel spring’s behavior is closer to ideal elasticity than rubber’s — but I think we can take it considerably further. If we make 1-nanometer-thick glass foil, which should be feasibility, we can roll it up in a double spiral; if we want the spiral to be able to unroll flat, we can’t exceed the 2500:1 ratio mentioned earlier, so the center of the spiral must be a 5000-nm-diameter circle. If there’s 1 nm of space between the glass-foil layers, in a 1.005-mm-diameter roll we can have 250’000 layers on each side, 125’000 per direction. So our 1-mm-diameter roll can uncoil to hundreds of meters of glass foil!
Because only the glass tangent to the roll is exerting an effective force, this spring is a very good approximation of a constant-force spring, like those used instead of counterweights for some sash windows.
This doesn’t improve the spring energy density of the mass glass (except by reducing surface defects), but it certainly improves the elongation at break of the assembly: it has gone from 0.02% to several hundred million — several tens of billions of percent.
If we continue to use 0.02% as the elastic strain limit, glass foil thin enough to roll up inside 1 mm must be no more than 200 μm thick.
More complex metamaterials could provide not only tailored stress-strain curves (within the total elastic energy capacity of the underlying bulk material) but multidimensional interactions like auxetic materials. As Merkle’s buckling-spring logic thought experiment convincingly demonstrates, the elastic deformation of a massive body with a complex shape can have arbitrarily complex behavior, including Turing-completeness (if the material extends far enough). Recent experiments in computational origami offer promising approaches to this problem.
To look at it another way, much of the problem is that most of the inorganic materials we’re familiar with are brittle at room temperature, while many plastics aren’t. But window glass is a polymer, too; it’s just that its glass transition temperature Tg is higher than what we're used to. Soda-lime glass isn’t just compliant once it's orange-hot — it’s positively gummy. Inversely, we’ve all seen how rubber behaves when cooled below its Tg with liquid nitrogen — it shatters like glass.
Basically the problem is that we’re talking about using materials held together by chemical bonds substantially stronger than many bonds in organic molecules, though not the C-C bonds that hold together blocks of graphite or molecules of polyethylene. So these materials might be more convenient at a higher temperature, perhaps around 400–900 K instead of the 300 we’re used to. (Carborundum and diamond may be more viable semiconductors at these temperatures than silicon or germanium.) From an extraterrestrial perspective, Venus is no weirder than Terra, though a bit more expensive to emulate with MLI.
Going the other direction, at 100 or 200 K, perhaps we could use other unfamiliar materials. Water, of course, forms a crystalline solid at 273 K. I don’t know what materials might form glasses at such temperatures; maybe mixtures of common materials (mixtures generally have less tendency to crystallize), or polymers that I'm not familiar with because they’re too weakly bound to be stable at 300 K.