Foam found that archives theorethical bounds for isotropic stiffness

  • 1) Stiffness is a key for advanced positional nano-fabrication.
    2) For some fixed material stiffness falls with shrinking size.
    So this Foam might prove quite useful for structural components in future nanofactories (and other advanced nanosystems).

    The found foam is basically a superimposed union of
    1) trivial cubic foam and
    2) trivial octet foam (out of octahedrons and tetrahedrons)
    nothing fancy - easy to model

    Paper: "Mechanical metamaterials at the theoretical limit of isotropic elastic stiffness"…ent/full/nature21075.html
    UCSB shortnews:…s-first-perform-predicted
    UCSB news full article (linked):

    UCSB news article with video (not linked):
    Author: "... This material is found to archive theoretical bounds for isotropic stiffness. ..."
    He's referring to something called the "Hashin-Shtrikman Bounds" of which probably few people know about.

  • Regarding the topic of material stiffness:
    I've since cleared up a long held misunderstanding of mine.

    While stiffness indeed shrinks with falling size (to levels that make the softest jelly envious - I'm to lazy to dig up example numbers right now) inertial masses shrink in such a way that they exactly compensate this falling stiffness when speeds are kept constant across scales (or equivalently: when operation frequencies rise linearly with falling size - which is a somewhat natural assumption).

    So problems with mechanical ringing stay unchanged from macroscale to nanoscale. But …

    … But one actually wants to slow down since one both can-afford-to and need-to do so.
    – "afford-to" relates to the enormously beneficial scaling law for troughput-density
    – "need-to" relates to surprisingly high friction-losses-per-area of superlubrication even at moderate speeds
    More on that elsewhere eventually … (more cleared up misunderstandings of mine there)
    Anyways, presumably out of these (here not explained, and in the book Nanosystems not explicitely stated) reasons the typical/majority-of operating speeds of nanomachinery in the book Nanosystems are intentionally proposed quite low at around 4 to 5 mm/s.

    So the macroscopic analogy would be a hypothetical …
    – machinery that one can afford to operate 1000x slower while retaining the same product throughput
    – material with stiffness of diamond but two digit prozentual elasticity before a break
    So much for all those saying/preaching that "things change for the worse" when using cog&gear style nanomachinery at the nanoscale . Availability bias at work …

    So keeping macroscopic prototypes for nanoscale target systems conservative in their assumptions on stiffness despite them being made from very low stiffness plastics seems trivial. Not something to worry about.
    Holds for all but the first assembly level. See next paragraph.
    In fact such prototype systems are so far lower in performance against ringing that it might be problematic in the other way.
    That is: Nanostructures could be made much more filigree.
    Macroscale 3D-printed plastic prototypes may suffer from unavoidable over-engineering.
    While they will still work at the nanoscale they will be far from ideal/optimized.

    Well, low stiffness not being a worry only holds as long as there is no piezomechanosynthesis involved.
    (Piezomechanosynthesis as in tool-tip preparation and the first assembly level from moieties to crystolecules).
    Beefy high-stiffness-from-geometry-structures at the nanoscale are really only needed to counter deflections from thermal motion
    since these deflections are many orders of magnitudes larger than the deflections from machine accelerations at the smallest scales.

    At the second assembly level (assembling from crystolecules to microcomponents) deflections from thermal motions
    are already quite probably pretty much negligible. There is:
    – a large number of parallel acting high stiffness bonds
    – only about kT of energy for the lowest order bending modes of the whole crystoleculear structure (typically many thousands of atoms)
    – compensatability by self centering
    So I wouldn't expect a need to focus on choosing maximally stiff geometries there.
    Well, to be absolutely sure I still need to check actual numbers …

    Side-note: There are other reasons beside stiffness to go for parallel manipulators.
    Like e.g. a larger number of pathways for mechanical motion threading via chains or such.

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