If there is a difference between the full N-R (tangent stiffness) and modified N-R (elastic stiffness, update each step), it usually means at least one of these two methods haves convergence problems.
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In most cases, this is due to some problem in the geometry, boundary conditions (supports, loads, master-slave connections), or in cases of extreme material damage. After checking all former possible problem sources, you may also need to shorten the load steps and/or allow more iterations to let the steps converge.