<p>Since I'm running a 3D printing facility of an engineering school, students are always wondering how much infill percentage affects the stiffness of the part. I know that it is impossible to get a numerical solution for this question, but maybe there is an option to simulate in software an already sliced model. I haven't seen in any slicer an option to export as .stl or .step or any other format which can be accepted by simulation software. Has anyone seen or thought about something similar? </p>

I don't believe that slicing engines create any sort of solid model that would be useful for CAD simulation. When a slicing engine slices a 3D model, it's goal is to spit out the preferred machine paths in G-Code (of some kind). However, I've read a few articles, done some tests, and heard through the grape vine that anywhere between 10%-35% is good enough for most applications. I once watched a webinar for understanding the new MakerWare interface that explained how they chose such settings. Although I can't find the clip directly,
here
is the page for all of MakerBot's webinars. I think
this
webinar was the one I watched explaining a little bit about preferred infill percentages.
From experience, anything over 35% doesn't yield much more strength from infill side of things. Beyond 35% and you're going to want to reconsider how you're orienting the print when you print it and what you're printing to utilize the grain structure for proper strength.
However, infill percentage/patterns are not the only variable for creating strong parts. Infill is really just a way to save time and material. Here are some other ways to potentially increase strength:
Increase your shell. Shell is the number of profile patterns per layer. Typically (in FDM/FFF), each shell is
about
the diameter of your extruder nozzle.
Increase your floor/roof. Similar to shell, floor/roof refers to the number of layers that make up the "bottom" and "top" of the part with regard to the build plate.
Print orientation. Pay attention to which areas of the part are susceptible to strain along the "grain" of the layers. Try to rotate your part on the build plate in a way that minimizes potential failure both in print and post-print use.
Post process. Don't be afraid to do some post-processing to increase the strength. There are
some 3D printers on the market
that go as far as including Kevlar strands in the printing process to beef up their prints. However, it may be as simple as just coating the part in an epoxy with some basic finishing techniques. It's a bit more work, but it turns weak 3D printed parts into full production quality prints.
Update:
Based on some of the comments, it sounds like your best bet might be to find a custom application that can either convert the g-code file into a solid model (try CAM software?), or create a plugin for your CAD software (I know Unigraphics NX and Solidworks allow for this) and essentially recreate your own slicing engine that takes your solid model and generates the same infill pattern dynamically inside.
Perhaps look into the works of
Simlab
or similar which has a lot of 3D software plugins. I'm not promoting them and I don't work for them, this is just a reference of what to look for.