Iterations for Solving Linear Contact Models

Why does an analysis take multiple iterations to solve, even if it has bonded contact and is linear in nature?

There is a list of features that trigger Newton-Raphson (NR) iterations (i.e., a nonlinear solution), but having any contact elements (even if bonded) will trigger NR iterations. (The other things that trigger NR iterations — plasticity, nonlinear springs, etc. — are usually more obvious.)

In Mechanical software, you can use the following command to force a single iteration:

neqit,1, force.

With this, you will see the following warning:

*** WARNING ***
CP = 2.090 TIME= 12:09:08 Using 1 iteration per substep may result in unconverged solutions for 
nonlinear analysis and the program may not indicate divergence in this case. Check your results.

The warning indicates that if the analysis is truly linear (i.e., small deflection theory), you should have force balance. If the analysis is nonlinear, you will not get force balance.

Now, let’s say the analysis was solved as a linear analysis, but large deflection effects should have been turned on. We would not know this because a linear analysis does not use the NR method. Hence, by specifying "neqit,1, force", we are forcing the solver to assume that it is a linear analysis.

If you want to be safe, use the substep (NSUBST,1,1,1), but this may require multiple equilibrium iterations. If it is linear, it should converge quickly (e.g., two or three iterations), and you can ensure numerically accurate results. If you are confident that the analysis should be run as linear, then use one equilibrium iteration: (NSUBST,1,1,1 with NEQIT,1, FORCE). There will not be any additional checks, but the solution will be just one iteration, like a linear analysis.