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# Determining Inflection Point

## Determining Inflection Point

(OP)
I am calculating the stress-strain curve for a material and I want to find when the curve is no longer linear - aka when it enters the plastic region. I have the function for the curve and I would like to know how to find that point when the slope is no longer constant. I can take the first and second derivative and visually see the slope and change in slope but I do not know how to find the value where it changes.

Does anyone have any recommendations?

Thanks
Replies continue below

### RE: Determining Inflection Point

Presumably, the 1st derivative is showing a relatively constant value, until it deviates. So you need to determine what a reasonable deviation constitutes an official deviation, and you simply need to search for when that happens.

TTFN
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### RE: Determining Inflection Point

(OP)
IRstuff - the first derivative does show a consistent value but I do not know how use that to actually calculate the point where it is no longer consistent.

What I would like to know is how do I calculate the point of deviation - is there a function in mathcad that does it for me or something similar? Is there a mathematical method that I can use the first or second derivative function and find the point that has a reasonable deviation?

Another question in itself is how do you determine what a reasonable deviation is - it is, for the example of the second derivative, where "y" is equal to 0.001?

Thanks

### RE: Determining Inflection Point

Why don't you put a sample function here to try it out?

### RE: Determining Inflection Point

Use the absolute value of the second derivative and compare it to some threshold you choose.

Peter Nachtwey
Delta Computer Systems
http://www.deltamotion.com

### RE: Determining Inflection Point

The point of deviation is not a fixed concept; it's what you need or want, based on your structural requirements and material characteristics. Presumably, you need a certain level at which the material will return to its original condition, and how much margin you want against the threshold where permanent deformation occurs.

TTFN
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