Hi Fellow Pioneers,

I would like to improve my understanding on the various convergence conditions in an implicit finite element simulation. I mostly use the Abaqus solver so terminology and convention of this post is following that of the solver.

I can understand the residual force condition. It is for static analysis. The residual force is like the summed total force on the system, which should be zero for a static problem. Since the computation cannot give an exactly zero residual force, the solver will accept it if it is small enough.

However, there are a few other conditions out there I do not fully understand. One is the displacement/rotation correction condition. I know that the solver typically adjust the deformation of the bodies to satisfy the field equations. However, I'm not sure why the displacement/rotation correction is compared against the displacement/rotation increment and the solver will not accept the result if the correction is larger compared with the increment.

Another condition I do not understand is the contact conditions. For example, max penetration error. I can understand that it is impossible to have an excatly zero penetration at contact interfaces so the solver will have to accept a sufficiently small penetration. However, I do not understand is why the condition the solver uses is the ratio between the max penetration error and the displacement increment. Why does the penetration error needs to be small not against an absolute tolerance but the dsplacement increment?

If possible, please share your insight on these convergence conditions so we may better address convergence issues in the future.

Thank you.