I would like to construct the deformation gradient tensor from two set of coordinate data. I have two sets of 3D Cartesian coordinates for a 3x3 grid. The first set is the reference configuration and the second set is the deformed configuration.

In particluar how do I calculate the $\displaystyle \frac{\partial x}{\partial X}$ terms?

Am I right in thinking that $\displaystyle \partial x$ terms are the changes in the coords from the reference state to the deformed state? In which case what do the $\displaystyle \partial X$ terms represent?

Thanks for any help with this, I feel like I know the answer but for some reason cant see the trees for the woods.