How can I make a mesh "look 3D printed", i.e. you can see the layers. e.g.:
You see all those layers? How can one do this? Maybe a bump map? or is there an option to separate a mesh into pieces, i.e. explode it?
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Expanding on Leon Cheung's answer, you may want to add a little bit of unevenness to the texture so as to make it look more realistic:
It depends on how much detail you want. There's a very (computationally) expensive method, and there's a very cheap method.
The "expensive" method is to use the blocks mode of the remesh modifier which will give it a stepped look. (You would build the model like normal, and then apply the remesh modifier to it). This has the benefit of being highly controllable and gives you real geometry (which will give you a proper silhouette). But it will create a LOT of geometry, which will increase render times and slow down your viewport, depending on how fast your computer is, and how detailed your model is.
The "cheap" method is to make a bump or normal map. (Bump and normal maps do the same thing in different ways, I find bump maps easier to make because they're just black and white, but normal maps give arguably better results... but that's neither here nor there). A bump/normal map will make the surface appear to have bumps that do not actually exist. This has the benefit of being relatively lightweight (assuming your bump map isn't a 3GB image) with very good detail. But bump/normal maps are arguably more difficult to create from scratch, and if you look at the model closely, especially at the edges, it will become apparent that the surface is actually flat.
There's lots of information out there about how to create & use bump/normal maps, and how to use remesh, so take a look and see which one does what you want it to do.
Alan Warburton released the "3D Print Simulator" texture in 2015 that allows you to use normal maps/bump mapping to simulate the look of a 3D print
3D Print Simulator eschews the tendency to fetishize the 3D print by attending more closely to its most disappointing and tricky formal qualities, specifically its striations and particulate noise. In doing so, it not only focusses on an obvious resemblance to geological sediment that calls to mind the material ancestry of oil and plastic, it also opens up a wider line of questioning to do with the complexities of production.
A sample of the texture
How it looks applied to an object