FEA In-Depth:  Contact Stiffness Explained

By Bill Kelly

It’s rare that a structural analyst is tasked with evaluating a single component that’s not part of an assembly.  Understanding how the part interacts with other parts or with the ground can be the difference between a successful design and one that does not meet the requirements.  Engineers like to invoke the Saint-Venant principle to justify ignoring the local details at the contact interfaces.  It says that if you get far enough away from the contact, the stress distribution in the component of interest will not be affected by the simplifying assumptions employed at the interfaces.  Unfortunately, the high stress points are often near or at the interface with other parts, so detailed modeling of the interaction is required. 

Proper modeling of contacting interfaces requires expertise.  It’s easy to get into trouble, specifically convergence difficulties, when introducing this nonlinear behavior to a model.  The behavior of a static FEA model, for example, is defined by the stiffness matrix.  This matrix can be thought of as connecting degrees of freedom together by springs, the stiffness of which depends on the nearby element size, shape and material elastic modulus.  When parts come in and out of contact, most FEA codes account for that by adding or removing fictitious springs between the two parts.  In real life there is no such spring, parts cannot penetrate into each other. The real life contact stiffness is infinite.  Toggling between a super stiff spring and no spring at all wreaks havoc on the FEA solution thereby leading to convergence problems.  To get a proper solution requires judicious selection of the contact stiffness.  It must be low enough to allow convergence, and at the same time be high enough to limit the penetration of the two bodies to acceptable levels.  It’s important for analysts to understand this to ensure proper contact simulations.       

Analysts can also manually specify the contact stiffness, usually a factor of the compressive stiffness of the nearby elements.  Modern FEA codes can also automatically tweak the contact stiffness behind the scenes to achieve convergence.  The results always need to be checked to ensure that only a minuscule amount of penetration is occurring.  There are times the analyst might prefer to manually specify the stiffness.  For example, when trying to get a true apples-to-apples comparison between two slightly different designs, this manual specification ensures that the contact stiffness variable is not tainting the comparison.  The actual number used for stiffness is problem dependent.  A good practice is to start low to avoid convergence problems, and then stiffen from there until the penetration is acceptable.

When bodies come into contact, there is a normal force and a shear force (unless it’s a frictionless interface).  So there is actually a separate normal and tangential contact stiffness.  Too low a tangential stiffness could detrimentally affect the stick-slip behavior and the interface shear forces.  Tangential stiffness is typically a factor of the normal stiffness, but again is problem dependent.    

The actual solution of the contact problem often requires multiple substeps since it’s nonlinear.  Loading typically should be brought on incrementally so that the contact comes on gradually.  Also, rigid body motion should be avoided.  You don’t want the part to fly away if it comes out of contact.       

This discussion is mostly geared toward standard frictional surface-to-surface contact that can open and close.  Other behaviors are available, such as bonded or ‘no separation’.  Consult your FEA user manual, but be careful not to just settle for default values and assume all is well.  Click here to learn more about our FEA capabilities.


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