I want to find the Cauchy stress tensor in certain materials with ab initio methods. I already have the analytical form of my own definition of "energy" and "forces" (not from DFT), and I now wonder how to derive the stress tensor from them? I've checked Kittel's Intro to Solid State Physics and Lautrup's Physics of Continuous Matter, but it's not discussed there.
Any recommendation for the right reference to this specific problem? It can be a DFT textbook if it has some detailed discussion in it about how to obtain the Cauchy stress tensor from a DFT energy and forces.
Dr. Clark's CASTEP workshop lecture 14 seems to have the answer to my question on page 7. But I'm still a little bit confused on how to implement Hellman-Feynman Theorem to get the stress tensor.