I understand the "large strain" option in nonlinear (specifically for a von Mises material such as steel) is used when there is an "updated Lagrangian" formulation. If I am following the theory, its essentially the element is distorted by the applied deflections in Step n, and in step n+1 a new strain is calculated based on the strain that occurred from n to n+1. This is opposed to total Lagrangian modeling, which is there is the initial shape at n=0, and the strain is calcualted at n, n+1, n+2, etc. from n=0, which is computationally less intensive than updating the matrix each step.

First of all -- am I tracking that much of the theory?

Second -- while I understand that failing to turn on "large strain option" when you have large strain results in inaccuracies, is there an accuracy issue if you turn "large strain option" on and its not needed.

My specific issue is highly localized bending/shear/compression where there is not large displacement but there is large strain (above 5% as a peak value). If I have it turned on, sometimes it doesn't solve all the way to the end whereas if I turn it off, it solves. This is using 10 node tets (high order element). There doesn't appear to be a signficant difference in stress, strain, or deflection in using the two options for the loads that do solve.

One clue here leads me to think your load curve is a pain in the a$$ for the solver. To keep the option turned on AND have it complete, try increasing the loads gradually on approach to the failing time step. Once it gets past that time, you can resume a larger time increment. But if it solved without it turned on with the original curve, then heck, you got the answer. Both options should reveal equivalent results.

The clue is If its turned off, the "max. incremental strain" value is used which might explain why it solves without issue. If its on, the max incre. strain is not used.