I'm a lay-person, so I'd like to add one point. Outside of physics and engineering, strain and stress are used to describe how we are feeling or the effect something is having on us. For example "My kids are stressing me out." or "This job is a strain on my marriage." You could argue that in some small way your definition still works, but people are generally describing feelings which do not correspond neatly to engineering concepts. If I say "All of those trucks are putting a lot of strain on that bridge," I would not be thinking about your definition, but rather the more common definition - the bridge is dealing with something difficult and might break. I might say the same about a relationship "All of those long nights at the office are putting a strain on my marriage." Again, talking about dealing with something difficult (long hours) and something that might break (the marriage).
I agree that way back when, these definitions came from physics/engineering, but now they are in the public domain and so they've taken on a life all their own. The original definitions are just one definition.
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