My favorite moment in university was in the first class of semester 2, where a prof said "lets look at a really small part of our thing, and assume we apply some force to it. This will make it stretch, lets assume the stretching is linear relative to the applied force". I raised my hand and asked "is this assumption supported empirically?" and he said "no, we know it's not always true, but if we don't make it we can't calculate anything".

At the time I was mad at engineers for being non-scientific, but after a few years I understood the deep wisdom in that. Nonlinear materials exist, and materials we use have nonlinear ranges. We just don't build things from those, because the math is too unwieldy. (except in very very specific edge cases where we spend a lot of money building a very limited thing)