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How To Make Sure Your Contact Elements Hit The Target

October 18, 2016 By: Patrick Cunningham

When two independent bodies interact under load in a finite element model, surface-to-surface contact elements are used by the more sophisticated FEA codes to manage the interaction. A typical surface-to-surface contact region consists of a pair of element types that are located on the outer faces the structural finite elements. On one body you will have contact elements whose job is to search for target elements on the opposing body. The contact elements will only search for targets of the same pair. The pairing of contact and target elements is typically established with a shared element attribute. In the ANSYS® finite element program, that attribute is the real table number assigned to the element. 

The contact elements do all the computational work of detecting, evaluating and, if necessary, reacting to the target elements. The target elements are, as the name suggests, simply targets for the contact elements look for. 

So what exactly do these contact elements do, and how do they do it? If you were a contact element your standard work procedure would go something like this:

1. Search a region extending outward from the contact element detection point for target elements of the same pair. 
 
2. If target elements are detected, determine their proximity and if action is required to prevent the outer surfaces of the bodies from passing through each other (interpenetrating). Targets that are deemed far field are ignored. Near field targets must be evaluated to determine if there is still a gap between the elements or a penetration that requires a response.

3. If any penetration is detected with a near field target element, push back against it using a predetermined method. Method options include the use of a stiff spring stiffness and a resulting force and/or a pressure degree of freedom to minimize or enforce zero penetration between the contact and target element.

However, the best methods for keeping the target element at bay are only useful if the contact element is able to detect the target. If detection is not successful, then contact element has no reason to react. In most nonlinear analyses the most challenging part of the solution is the contact detection. Contact detection can be dependent on several aspects of the finite element model such as:

• Finite element mesh size: When attached to a flexible body the contact element size is dictated by the size of the underlying structural elements. The contact elements lie on the outside faces of the solid elements and share the same nodes. If the underlying solid mesh is coarse, the detection points of the contact element may be spread thin and target elements may pass in between them undetected.  

• The search range of the contact element: Some contact elements use a pin ball radius to define the range over which the contact element will search for targets. The search range is essentially a sphere around the contact element detection point. Unless a target element passes through the sphere, it is ignored by the contact element.

• The contact detection location: The gap or penetration between the contact and the target element is calculated with respect to the detection location. There is no optimal location that works best for all problems, so a few codes, including ANSYS® offer several options for contact detection about a point or on a projected surface from the contact element face onto the target element.

Since the contact detection location can have a big impact on the solution, it is important to understand the mechanism behind the different approaches that are available. In most cases the contact detection is located at the integration points of the contact element. A quad shaped element with eight nodes will therefore have four detection points on the element face following the 2x2 integration scheme of the element. 

If you have a model with an edge or corner in contact you may need to consider contact detection at the node locations. In Figure 1 the red circles represent pin ball radius around the detection point. With integration point detection option, the element corner penetrates into the target element before contact is detected.
 

Figure 1 – Integration Point Versus Nodal Contact Detection Location


A third option is surface projection contact detection. With this method, the contact detection points are located at the nodes but gap and penetration are calculated as an average across the overlapping region of the projected contact surface onto the target face. While this method involves more computation (and hence more solution time) it has several advantages:

• The averaging effect tends to smooth out the penalty load used to keep the contact and target from interpenetrating.

• It results in a less dramatic status change when a contact element node slips off a target face.  This is useful because sudden changes in the contact status effect the force equilibrium of the system and can cause convergence problems.  

• It performs much better than point detection when the contact and target mesh sizes are dissimilar.

Consider a simple model with two 1” blocks being pressed together. With a 100 psi load on the top face of the upper block we should expect to see a compressive normal stress in both blocks of -100 psi. On the left side of Figure 2 the contact is defined with integration point detection. While the average stress in the two blocks is around -100 psi the stress field varies around the detection points by almost a factor of 2. Using the same model with surface projection detection on the right side of Figure 2 displays the uniform stress across the contact interface and throughout both blocks, as expected.
 

Figure 2 – Integration Point Versus Projected Contact Detection For Two Blocks Under In Compression



For many cases the standard method for point detection will do the job, if you are not overly concerned with detailed results at the interface. If you do find yourself in a situation where point detection is affecting the results, I hope your tool offers other options like the projection method. Has anyone run into this issue or others when using contact elements? If so please post a comment. We would love to hear how you dealt with it.