The underlying assumption in my comments has been that 'contact' is of interest and more nonlinearities (large strain, large rotation, finite sliding friction contact, etc.) 'may' come into play at a later time as the modeling progresses. If none of this on the cards, then I am with you; yours is a clever approach. So, again, you may have it right but my understanding comes from the 'math' of contact formulation itself. With that in mind, let me clarify my opinion.
The reason, IMHO, for the high rate of convergence is because you are simply using a 2 node element assigned with linear properties in tension and compression, with the non-smooth character coming into play only when there is a transition. Likewise, gap contact elements, in reality, are non-linear springs, which explains your similar experience with gap elements. I am not sure if the documentation says so but I am quite sure that FEA developers do not recommend gap elements any longer (keeping in mind my assumptions).
The reason why 'contact' takes 'much' longer to converge is because the code has to identify the normals on the master surface. In fact, the space must first be discretized by 'invisible' elements. If the surface isn't smooth or if there is finite sliding or friction, the computational expense increases dramatically. In such a situation, if you add other nonlinearities, the solver *will* have a very hard time to converge to a solution. Indeed, you may even have to switch to Explicit.
However, if you have smooth flat surfaces opposing each other with little to no sliding and frictionless interaction, then the problem becomes *very* simple for the solver to solve.
Section 21.2.2 of the Analysis User's Manual (v6.11):
"
Stability
Using no compression or no tension elasticity can make a model unstable: convergence difficulties may occur. Sometimes these difficulties can be overcome by overlaying each element that uses the no compression (or no tension) model with another element that uses a small value of Young's modulus (small in comparison with the Young's modulus of the element using modified elasticity). This technique creates a small “artificial” stiffness, which can stabilize the model."
This statement, I believe, explains our opinions/experience.
Now, coming to your point, yes, contact is a nonlinearity in itself but there are exponential (soft) contact models available in Abaqus that are 'smooth'. You can assign small parametrized tensile stiffness and an appropriate (chosen by the analyst) compressive stiffness.
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