[SonOfLilit]

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)

[olivierduval]

It's funny: I had the EXACT SAME PROBLEM !!!! Like "how is it science when a prof says: "this equation is too complicated too solve so let's erase these third and forth derivatives and pretend that it's the same - even if it's not - because that's all that we can do"

So I left the "physics" courses and went the "math" courses... only to learn 3 years later how to prove that this kind of approximation is mathematically sound indeed :-D

[AstralStorm]

Should have taken one more course about chaos theory which is the special case when this approach fails.

[bongodongobob]

Can you give some examples of linear and non-linear materials?

[pistachiopro]

Practically all materials behave nonlinearly when stretched or compressed a visible amount. For certain structural applications, though, if that happens we've already failed. Linear models work really well for designing big concrete structures and certain metal structures. Sometimes we try to apply linear models to other things, but that's always kind of fishy.