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Would it be a cubic/quadratic Bezier curve? Or perhaps (part of an) ellipse?

I am a computer science student who is working on a physics engine using realistic materials, meaning I would like for example wood to bend in a realistic manner when pressure is applied to it at a certain point. When I thought I had found that a quadratic Bezier curve resembled part of an ellipse (if |AB| = |BC|, it seems to be part of a circle), I believed I had the answer, however after some checking this appears not to be the case. So with what kind of curve do materials naturally bend?

My apologies if this is an obvious question, or if this question does not fit this stackexchange, as I have little to no background in physics :) (Just high school and game physics.)

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  • $\begingroup$ I was taught that a cubic spline generally represents a bent rod passing through all the points you want to hit. I'm not sure how physically accurate that was though, since the professor who said that was known to make inaccurate statements. (Also seems like this might be the same as a Bezier curve, but analyzed differently) $\endgroup$ – JMac May 8 '19 at 14:53
  • $\begingroup$ Thanks for your input, I'll look into it :) $\endgroup$ – rvvermeulen May 8 '19 at 14:58
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    $\begingroup$ a sophomore-level strength of materials text will contain exact formulae for the bent shape of the beam of your choice under whichever type of load you wish to impose on it. Handbooks are available with those formulae tabulated. Try to find a copy of Young's formulas for stress and strain for example. $\endgroup$ – niels nielsen May 8 '19 at 17:01
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It is not clear if you are curve fitting data or building a simulator. If the former then the comment regarding a cubic-spline would hold. If the later then you need to go deeper. There is a whole field of study in mechanical engineering devoted to beam bending. For static bending with small deflection, the amount of deflection will depend on the material properties and geometry and there are some famous beam bending equations that you can look up in a mech. eng. text like Strength of Materials, etc. For larger bending these equations do NOT hold. A well known scientist, Timoshenko, worked on exact solutions and solving methods for large scale beam deformations. You can look up his work. If you really want "realist" bending profiles you may have no choice other than to start working with finite element methods (FEM) for solving the partial differential equations (PDE) that govern the balance of internal stress with gravity and other external loads. This is really the only way to do it. There is no general solution that always works.

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