11.3 Contact algorithm

Understanding the algorithm ABAQUS uses to solve contact problems will help you understand the diagnostic output in the message file and carry out contact simulations successfully.

The contact algorithm in ABAQUS/Standard, which is shown in Figure 11–9, is built around the Newton-Raphson technique discussed in Chapter 7, “Nonlinearity.”

Figure 11–9 Contact logic.

ABAQUS examines the state of all contact pairs at the start of each increment to establish whether slave nodes are open or closed. In Figure 11–9,

denotes the contact pressure at a slave node and

denotes the penetration of a slave node into the master surface. If a node is closed, ABAQUS determines whether it is sliding or sticking. ABAQUS applies a constraint for each closed node and removes constraints from any node where the contact state changes from closed to open. ABAQUS then carries out an iteration and updates the configuration of the model using the calculated corrections.

Before checking for equilibrium of forces or moments, ABAQUS first checks for changes in the contact conditions at the slave 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 labels it a severe discontinuity iteration and no equilibrium checks are carried out.

ABAQUS modifies the contact constraints to reflect the change in contact status after the first iteration and tries a second iteration. ABAQUS repeats the procedure until an iteration is completed with no changes in contact status. This iteration becomes the first equilibrium iteration, and ABAQUS performs the normal equilibrium convergence checks. If the convergence checks fail, ABAQUS performs another iteration. Every time a severe discontinuity iteration occurs, ABAQUS resets the internal count of equilibrium iterations to zero. This iteration count is used to determine if an increment should be abandoned due to a slow convergence rate. ABAQUS repeats the entire process until convergence is achieved, as summarized in Figure 11–9.

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. The total number of iterations for an increment is the sum of these two.

By separating the two types of iterations, you can see how well ABAQUS is coping with the contact calculations and how well it is achieving equilibrium. If the number of severe discontinuity iterations is high but there are few equilibrium iterations, ABAQUS is having difficulty determining the proper contact conditions. By default, ABAQUS abandons any increment where it needs more than twelve severe discontinuity iterations and tries the increment again with a smaller increment size. If there are no severe discontinuity iterations, the contact state is not changing from increment to increment.