Technically speaking, all rockets are self-consuming, since they are basically tin cans with fuel. And to carry even less weight with then, they have stages. Allowing not only the rocket to go farther, but to change the nozzle engine. The smaller ones are good for atmosphere, while the bigger ones are good for outer space (the atmosphere density is a big factor referring to the rocket engines).
Well, since the rockets won't reach there in a single stage anyway, why do they need to actually reach the space intact?
The idea of a self consuming rocket is that the nozzle and the fuel tank (composing the majority of the rocket body) would be the same thing. Or at least being the less resistant as possible.
My idea, at least, is to use solid rocket fuel in a cone shaped metallic body like a stalagmite, or multiple ones, resembling Sputnik satellite. While the tip and last stage would be responsible for directing the rocket. What could make things easier to control.
The other idea would be to use a series of stacked nozzles and fuel in between them, consuming the fuel and the nozzle in a cascade. Simply put, to make as much stages as possible, increasing the redundancy and the safety of the spacecraft.
The third idea I had was to use a fuel tank that "shrinks" in size while the fuel is consumed. However, the tank would still have weight and the mechanisms too. So I don't know if it would be useful.
However, there is a lot of things to be thought in here. The first one is, ironically, the autophage factor. If the rocket consumes itself to quickly, it won't generate enough thrust. Or simply, the structure would need to be too thick to maintain the combustion, and so, making it unviable due to its own weight.
I "researched" a little prior to this post, and it is said that the UK is instantiating a "autophage" rocket. However, the only thing I could find is just the news of the UK releasing founding. And also an article talking about it, but you need to pay to see it. So I don't know if there is already a design (I found one in google images, but I can't tell if is the official one).
However, it is said that this autophage rocket would be used for small payloads. But I was thinking about normal or even bigger payloads. What is your thoughts on the subject? Do you think this rocket can only be used for small payloads?