Engineering vs True Strain

As Engineers, we like to assume. I didn't appreciate it much earlier, but I will tell you why we do that. 

Most of the formulas we study during our Bachelors, well I have only completed my Bachelors yet, there's always some assumptions mentioned before a formula, Always. 

Thin Beam Model


Critical Buckling Load


Now why do we assume if it's not the actual response. It makes our life easier, by that I mean the calculation time and effort for getting into something. And it gets the job done. As I earlier once wrote in my blog : Acceptable within the Engineering world, due to certain circumstances. Does it mean we are wrong, NO! Most of the assumptions give the limits too.

One such assumption is the Engineering Strain. 

A comparison.

Engineering Strain is a straight line which indicates that the strain in a structure varies linearly although that is far from actual scenario. In actual life, or per experimentation, the strain doesn't vary linearly. It sorts of curve down as we increase the load. Take an example of a rubber band, it will keep increasing until it doesn't. After a certain limit, the increment in length on stretching it won't be significant and it will break. That is the true strain. In the engineering world, of course within a limit, the stretch increment would be same.

What causes this difference? 
You can look at the formula and tell. Engineering strain is the ratio between the change in length to the original length, while true strain is the change in length to the instantaneous length. In actual life, as we stretch a band, its thickness decreases. This affects its resistance to the later stretch it will bear. Thus, the strain increase will be less in the later part. This whole thing is ignored in the case of Engineering Strain.


But I just proved that both are different in the first place, why use it then? See, till a certain point, the increase in true strain is also linear. This region is called the Elastic region. If you pull a band slightly, it will just return to its original state. Hence, for analysis within the elastic region, we do the Linear analysis.

So what if the load is increased and it crosses the elastic region. Don't fret, we got it covered too. The big Brother comes, the non-linear analysis. Although it covers a lot of other non-linearity, large displacements is covered by it too. 

Conclusion: Yes, we do assume. That within acceptable limits. One more reason is the difficulty in measuring each increment every time, so we generalise it. 





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