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How to get inside the ABAQUS incremental/nonlinear static solver

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Hi guys,

I'm working on an ABAQUS extension/plug-in of a sort and I'd like to replicate results for a single 4-node plane stress element produced by the ABAQUS incremental/nonlinear static solver.

I assumed the relationship is:
t[K] {Δx} = t+Δt {P} - t{F}

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