In How large a bioengineered mobile lifeform could exist on Earth?, I asked how big my nanoassembled war beasts could be, and it was suggested that I make my question more specific.
I am designing a large autonomous or semi-autonomous war beast that is intelligently designed (not evolved) and constructed by - and to a degree made from - self-replicating nano-assemblers. I want this critter to be as large as possible while still able to function in its role as a weapon of war. Its intended target is Earth or other earth-like worlds, so it should be able to support itself and function in any oxygen-bearing atmosphere at up to 1.3 standard gravities.
Based on this answer to my question, I have made the decision that the war beast will be a fairly short, thick serpentine being that can roll itself into a torus where the diameter of the central hole is approximately equal to that of the average diameter of the roughly circular cross-section of the body. In this configuration, it can move rapidly by rolling, providing impetus by distortions of its toroidal shape from a circle to an oval. When in its serpentine configuration, it would also be able to move by undulatory locomotion, sidewinding, concertina locomotion, Rectilinear locomotion and rolling on its side, forming a curve that it distorts circularly.
In order to make this critter as large as possible, I need to know what to make it from. The material needs to be very strong, in elastic compression, shear and tension. Since this is a war beast, whatever material it is made from also needs to be very tough, and not prone to fracturing at points of damage (as materials such as graphene are prone to doing).
Additionally, the beast must be armoured to withstand as much physical damage as possible, from modern conventional weapons including kinetic penetrators and high explosives, as well as atomics. The best armour materials are very tough, very dense and have a very high melting point to minimise thermal ablation from the high temperatures of atomic explosions. High strength is a bonus allowing greater size.
What materials would best be used for the internal, load-bearing structure of the beast, and what materials would best be used for the external armour plating, and how large a creature (in its toroidal configuration) would they support? Assume that the critter is effectively solid material, though in practise this would not be the case. If the materials are readily available in the earth's crust, that is a bonus, but not a necessity.
I'm looking for an answer backed up by numbers, but I'm also willing to entertain reasonable educated speculation regarding composites and compounds for which no hard figures can be found.
The terms "war beast" and "battle robot" should be considered to be interchangeable. This is intended to be an artificially designed and constructed mechanism that is intended to function like an independent living organism, and it is not based on Earth's biological organisms. It need not be carbon-based at all, and given that it needs to be as big as possible, it is most likely that only metals will have the required strengths simultaneously in tension, compression, shear and torsion, as well as having high density (to resist kinetic penetrator damage) and a high melting point (to resist energy or atomic weapons).