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When the giant aliens came lumbering out of the interdimensional fissure, we fought back, building giant robots of our own... which promptly collapsed onto themselves and were unable to move because of (among other things) the square-cube law and lack of materials with adequate tensile strength to stop the damn thing crumpling under its own weight, inertia and torque requirements. We took a step back, mourned our losses, then started using nukes and kinetic missiles on the aliens like sensible people.

A metallurgist studying a crystal of unobtanium diphlebotinide, discovered its unusual property of forming perfectly (down to the near-atomic scale) cylindrical crystals. He found that if he ground the crystal to be within a few nanometres of being exactly 42 times longer in axis than diameter, and waved his hands over it while fumbling his coffee cup, the crystal settled into a phase with (as best they could determine) infinite tensile, compression and shear strength; it is to all intents and purposes indestructible. I believe physically-necessary consequences are an infinite (or at least speed-of-light) speed of sound, and zero coefficient of friction. They subsequently found that if they 'cast' the crystal already having a perfectly cylindrical hole perpendicular to the axis and one-forty-twoth the diameter of the parent cylinder, then it would still set with the hole, allowing them to join crystals together into larger structures.

I think this (long thin spars with the means to fix pinions to transfer force between them) is all you need to use this new material in construction, including superstructures for giant robots. The zero-friction aspect also makes them excellent axles and bearing plates, and I can imagine lots of smart people immediately setting to designing all sorts of complex machines using them (reminds me of childhood construction toys!). But I'm hoping that the nature of the material means they can't be so easily used to create 'armour': you can't weave them or construct any sort of solid plate, for instance, although it could be used as reinforcement behind armour or pressurised enclosures.

Is this material alone enough to 'solve' the standard problems with giant mecha, namely collapsing under their own weight because their legs can't be strong enough, not being able to move their limbs because we can't produce motors with enough torque, and so forth? If not, what problems would remain to overcome?

Let's leave aside the question of why you would choose to attack a giant alien with a giant robot in preference to a nuke even if you could build one. I'm not asking for a mecha that's an appropriate combat weapon, or even humanoid; more like something to compete on a giant version of Robot Wars.

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – Monty Wild Dec 20 '19 at 7:31
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    $\begingroup$ You might be interested in a book called Cannon God Exaxxion which is quite a good look at what you would actually need to make a giant mecha work, which is precision gravity manipulation. It is also a good deconstruction of the giant mecha genre. $\endgroup$ – John Dec 20 '19 at 16:16
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    $\begingroup$ ^one forty-second the diameter $\endgroup$ – CJ Dennis Dec 22 '19 at 3:25
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Is this material alone enough to 'solve' the standard problems with giant mecha, namely collapsing under their own weight because their legs can't be strong enough, not being able to move their limbs because we can't produce motors with enough torque, and so forth? If not, what problems would remain to overcome?

So, the short answer is that this would make it SOMEWHAT less difficult to build a humanoid mecha, but Adamantium would do nothing at all about the REAL Mecha Problem, which is that anything you can build a giant humanoid robot to do, a robot that is NOT humanoid will do better.

Adamantium also isn't going to solve power problems. It will mitigate them by allowing the structure of your mecha to be lighter than it would be, and thus require LESS power in order to move it around, but you're still stuck with electric motors or hydraulics to actually move those limbs, and it's just not a very effective means of locomotion.

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – Monty Wild Dec 24 '19 at 11:57
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No. Wrong strength.

from OP:

stop the damn thing crumpling under its own weight

Your new stuff has infinite tensile strength.

the crystal settled into a phase with (as best they could determine) infinite tensile strength.

But to stop something crumpling under its own weight you need better compressive strength! Tensile strength keeps stuff from being pulled apart.

https://en.wikipedia.org/wiki/Ultimate_tensile_strength

Two vises apply tension to a specimen by pulling at it, stretching the specimen until it fractures. The maximum stress it withstands before fracturing is its ultimate tensile strength. Ultimate tensile strength (UTS), often shortened to tensile strength (TS), ultimate strength, or Ftu within equations,[1][2][3] is the capacity of a material or structure to withstand loads tending to elongate, as opposed to compressive strength, which withstands loads tending to reduce size. In other words, tensile strength resists tension (being pulled apart), whereas compressive strength resists compression (being pushed together).

Emphasis mine.

Maybe your engineer does not have English as his first language? I hope you did not build a whole mecha out of this new stuff before you figured it out.

Should you, like me, be an engineering aficiondo approaching from a position of ignorance, I recommend The New Science of Strong Materials. Easy to follow and well written.

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    $\begingroup$ shear strength is a problem before compressive strength, this thing has to have joints that can move. $\endgroup$ – John Dec 18 '19 at 20:26
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    $\begingroup$ You make a good point, my pseudosciencing of the adamantium is not comrpehensive enough... $\endgroup$ – Stephen Dec 18 '19 at 20:30
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    $\begingroup$ I invalidated your answer by changing the question, but I mean no offence... :-) $\endgroup$ – Stephen Dec 18 '19 at 20:31
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One other problem is ground pressure.

The maximum bearing capacity of the ground is unaffected, and remains relatively low.

For reference, bearing capacity of stiff clay might be 300 kPa, or about 30 metric tons per square meter. (Until everything turns to mud at least!)

This is already a problem for e.g. tanks.

For a given loadout, a tracked or wheeled vehicle would (almost) always end up with an easier time dealing with bearing capacity limitations than a mecha. A mecha's walk cycle would exert significantly higher peak loads then a wheeled or tracked vehicle, and would likely exert significantly higher horizontal forces too. Running would be even worse.

Some of this would be alleviated if the vehicle was lighter, and yes, adamantium would help with structural weight. But it wouldn't help with the weight of everything else (drivechain, controls, pilot, weapons, etc.). And meanwhile adamantium would help with structural weight of the competition (tanks, etc) also.

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    $\begingroup$ What if the 'humanoid' robot had tracks like Johnny Five? $\endgroup$ – Smock Dec 19 '19 at 11:30
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    $\begingroup$ At that point, one would wonder why the rest of it bothered to be humanoid. $\endgroup$ – Keith Morrison Dec 19 '19 at 16:14
  • $\begingroup$ Perhaps because they needed a nuclear powered battering ram at a height capable of smashing Godzilla in the face? $\endgroup$ – nomen Dec 19 '19 at 23:43
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    $\begingroup$ @Smock - then it would have a significantly higher center of gravity than a standard tank, as well having significantly worse armor angles. $\endgroup$ – TLW Dec 21 '19 at 4:39
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Yes, but it comes with more problems than it solves and you don't need it.

Stronger and lighter materials enable you to build larger structures, more effecient engines and power transmission etc etc so bigger robots.

Infinitely strong materials start to break physics. Don't go there

But you really only need a robot as large as the alien monster right? and that's made of flesh and bone. Bone has evolved over millions of years and has about the same strength to weight ratio as steel/titanium/wood etc.

So you can totally make a giant robot on the same scale as large animals, say dinosaurs, without stretching crediblity Maybe you can push it a bit with carbon fiber or metal foams

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Many problems.

First, something that is infinitely (or nearly so) incompressible will be desastrous towards non-soft materials it comes in contact with, and desastrous when receiving an impulse from somewhere (alien punching the mecha?). Remember that your mecha isn't just "hull". There is something inside, too. Either a human, or a computer, or something the like. Gyroscopes, sensors, hydraulic tubes, whatever.
Every impact from the outside (including the effect of Newton's third law when the mecha walks!) will be transmitted one-to-one. So whatever is inside will meet an unpleasant end very quickly (related).

Second, wind. You are able to build a huge thing that has comparatively little weight. Guess what happens when the wind blows.

Third, what's the purpose of a mecha? Well, it's huge and it has huge physical force so it can deliver a big punch. But your mecha doesn't have mega force. Your adamantium makes its exterior indestructible, alright. But that doesn't mean its servo motors are any stronger. In fact, getting over air resistance alone may be a serious problem for such a huge thing, unless slow-mo fights are an option. Also, delivering a big punch (which means impulse) requires a certain weight, too. So, at least the mecha's fists must be heavy, or the whole thing defeats the purpose.
As an analogy, no matter how hard I throw cotton balls at you, the amount of injuries that you will have is rather limited.

Then of course, building something huge from nanutubes is a real challenge. That'll take a few years to build one mecha.

Also, a material with infinite-whatever is not suitable for everything. You need flexible materials to build something that moves. If nothing else, you will need e.g. wires or tubes for electricity or hydraulic fluid. If these are not made of super indestructible material, the first paragraph applies. If they are made of super indestructible material, they're not flexible, and the mecha cannot move.

Does your world have any such thing as dust or sand? If yes, you should seriously hope that none of it gets into some joint or gear. In the real world, this is to some extent tolerable because both the sand and the gear experience a bit of abrasion, and the lubricant does the rest. For a perfectly rigid, indestructible thing, the only option is to grind whatever comes in between down to, well, basically a molecular level. Which may be a challenge.

Also, it's questionable whether the approach of attacking a huge thing with a huge mecha is intelligent at all. You said "leave this out", but it's really something you should consider.
I have no difficulties killing a dog with little or no injuries, while defending against a swarm of bees is much harder. Defending against roughly cell-sized parasites (think malaria, amoebae) or bacteria is even harder, and I may very well succumb to them. Thus, you should ask yourself whether attacking giant-sized aliens with "normal sized" drones may not be a much better approach.

Lastly, seeing how those giant aliens crossed dimensions and can apparently just willfully ignore the square-cube law (and other physical laws?!), it seems that unless your understanding of the inner workings of the universe drastically changes, they are by all means invincible, so actually it might be best to just surrender and leave the planet to them. Maybe they'll be merciful to their eternal slaves...

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  • $\begingroup$ I'm not suggesting to build every part of a machine out of indestructible materials, only the skeletal superstructure and key bearing parts. $\endgroup$ – Stephen Dec 20 '19 at 15:52
  • $\begingroup$ Then the first paragraph applies, the internals will be destroyed. $\endgroup$ – Damon Dec 20 '19 at 15:54
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    $\begingroup$ Why would a material with infinite strength automatically destroy 'ordinary' materials as a matter of course? In comparison to your hand a diamond or a steel bar has 'infinite' strength, yet transmitting force through them to your hand is not automatically destructive; it depends on many engineering factors; and shock-absorbing features could be incorporated perfectly feasibly. $\endgroup$ – Stephen Dec 20 '19 at 16:00
  • $\begingroup$ There is no reason for internal components to be destroyed. A hose or wire is not automatically absorbing all the inertia of the whole mech. $\endgroup$ – John Dec 20 '19 at 16:11

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