Let's say I have a metal part, which has some internal stress pattern which I don't know, that gets cut by a mill. The part deforms in some way, and I measure how it deforms. Is it possible to recover an estimate of the internal stress pattern which caused the deformation? Is there some way to do this natively in Abaqus?

I'm currently extracting the stiffness matrix (via the command *Matrix Generate, STIFFNESS, etc.) and then (because I have measured the part deformation) multiplying it with a displacement vector I have constructed. Theoretically this should give me a vector containing the forces at each node in my mesh of the part. I can then map the forces to stresses. Is this a reasonable approach?

Also, one other question. Let's say I constructed a part in Abaqus and applied some load to one of the part's surfaces. Does Abaqus use the stiffness matrix internally to calculate how the part deforms? In other words, does Abaqus use the direct stiffness approach internally or does it use some other numerical techniques?