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Where can I find info on the partial derivative of elastic energy wrt position?

datahead8888

New member
Jul 24, 2013
4
I've been studying a version of the finite element method.

The author of a paper I was reading refers to the partial derivative of total elastic energy wrt position, partial derivative of surfacic energy wrt position, and partial derivative of strain wrt position.

Does anyone know of a good resource that explains these concepts?

I'm not as skilled with vector calculus, so a less aggressive reference is good.
 

Ackbach

Indicium Physicus
Staff member
Jan 26, 2012
4,197
If elastic energy is
$$\frac{1}{2} k x^{2},$$
then its derivative w.r.t. position is just the negative of the force:
$$ \frac{ \partial}{ \partial x} \left( \frac{1}{2} kx^{2} \right)= kx = -F.$$

I've never heard of "surfacic energy". Could you define that, please?

As for the derivative of strain w.r.t. position, you could probably find that in a book on material science.