There are almost as many answers to this question as there are applications for nonlinear contact. In conversations that start with this question, my first response is often “Well, … it depends”. That answer might sound like a vague side step, but truthfully speaking, the answer to solving a nonlinear contact problem really does depend on a number of factors that can vary in importance from one model to the next. In your ANSYS structural mechanics software, you’ll find a rich library of tools in the form of contact element key options and real constants, as well as solution control options, to help you calibrate the program to fit the specific demands of the contact application.

To understand how to converge a nonlinear contact problem, it is helpful to first understand what the software is trying to do when you introduce a nonlinear contact relationship into a finite element model. This contact relationship is an extra compatibility condition that the program must satisfy in order for the model to be declared converged. Consider a frictionless contact relationship in a static structural analysis. In frictionless contact, the compatibility condition states that the contact elements on one surface cannot penetrate across target elements on a mating surface. However, the elements are free to separate and free to slide relative to each other. You can think of this compatibility condition as a nonlinear boundary condition — the distribution of constraints needed on these surfaces to enforce this condition can vary as the program progresses through the load path. Furthermore, the necessary magnitude and location of these constraints is completely unknown at the start of the analysis. Add to this the prospect of adjustments to the structural stiffness matrix to account for changes due to large deflection and nonlinear material and you begin to appreciate the potential challenge involved in resolving a general nonlinear contact relationship.

Arriving at an optimal distribution of forces at a contact interface depends on a number of characteristics that are unique to each application. One key characteristic that influences convergence is the stiffness of the underlying structure behind the contact and target surfaces. Contact between two stiff, linear, elastic geometries that are well-constrained and contacting across a broad flat interface that is initially closed is going to be much more forgiving, in terms of convergence, than two flimsy structures contacting at local points on tight, curved surfaces that are plasticly deforming through a large deflection.  ANSYS contact technology has the tools to meet the demands of both extremes and everything in between.

In a future blog post, we will continue this discussion by focusing on the different formulation options available for enforcing a nonlinear contact compatibility condition.