Contact algorithm

The contact algorithm in Abaqus/Standard, which is shown in Figure 1, is built around the Newton-Raphson technique discussed in Nonlinearity.

Figure 1. Contact algorithm in Abaqus/Standard.

Abaqus/Standard examines the state of all contact interactions at the start of each increment to establish whether secondary nodes are open or closed. If a node is closed, Abaqus/Standard determines whether it is sliding or sticking. Abaqus/Standard applies a constraint for each closed node and removes constraints from any node where the contact state changes from closed to open. Abaqus/Standard then carries out an iteration and updates the configuration of the model using the calculated corrections.

In the updated configuration Abaqus/Standard checks for changes in the contact conditions at the secondary nodes. Any node where the clearance after the iteration becomes negative or zero has changed status from open to closed. Any node where the contact pressure becomes negative has changed status from closed to open. If any contact changes are detected in the current iteration, Abaqus/Standard labels it a severe discontinuity iteration.

Abaqus/Standard continues to iterate until the severe discontinuities are sufficiently small (or no severe discontinuities occur) and the equilibrium (flux) tolerances are satisfied. Alternatively, you can choose a different approach in which Abaqus/Standard will continue to iterate until no severe discontinuities occur before checking for equilibrium.

The summary for each completed increment in the message and status files shows how many iterations were severe discontinuity iterations and how many were equilibrium iterations (an equilibrium iteration is one in which no severe discontinuities occur). The total number of iterations for an increment is the sum of these two. For some increments, you may find that all iterations are labeled severe discontinuity iterations (this occurs when small contact changes are detected in each iteration and equilibrium is ultimately satisfied).

Abaqus/Standard applies sophisticated criteria involving changes in penetration, changes in the residual force, and the number of severe discontinuities from one iteration to the next to determine whether iteration should be continued or terminated. Hence, it is in principle not necessary to limit the number of severe discontinuity iterations. This makes it possible to run contact problems that require large numbers of contact changes without having to change the control parameters. The default limit for the maximum number of severe discontinuity iterations is 50, which in practice should always be more than the actual number of iterations in an increment.