By John CrawfordConsulting Analyst

Demystifying Contact Elements

If you analyze enough problems,chances are good that sooner orlater you’ll run across one thatrequires the use of contact elements. Contact elements areused to simulate how one ormore surfaces interact with each

other. For most analysts, our first exposure to contactelements can be a little confusing because of the variety of elements and the multitude of special features that are available.

We have to determine which contact elementsare appropriate for our problem, resolve any convergence problems that might arise during solution, and check the results for reasonable andaccurate answers. Let’s see if we can clear up some ofthe mysteries that surround the use of contact elements. We’ll begin by talking about the elementsthemselves.

Node-to-Node Elements

In the early days of finite element analysis, there wasone type of contact element: the node-to-node variety.The early versions of node-to-node contact elementswere CONTAC12 (2-D) and CONTAC52 (3-D). Morerecently, CONTA178 (2-D and 3-D) was introduced toencompass the capabilities of both of these elementsand also introduce some new features, such as additional contact algorithms. Node-to-node contactelements are simple and solve relatively quickly. Theirbasic function is to monitor the movement of one nodewith respect to another node. When the gap betweenthese nodes closes, the contact element allows loadto transfer from one node to the other. What does thisreally mean and how does ANSYS know when thenodes are touching?

Remember that an analysis is made up of one ormore load steps, and each load step has one or moresubsteps. Within each substep there can be severalnested layers of equilibrium iterations. The precisenumber and manner in which they are nested isdependent on the solver, how many nonlinear featuresare being used and several other things. Contactanalyses are nonlinear and therefore require their ownequilibrium iteration loop. At the end of each contactequilibrium iteration, ANSYS checks to see if the status of each contact element has changed. It alsocalculates a convergence value (usually force equilibrium) and compares it to the convergence criteria. If the element status has not changed and theconvergence criteria has been met, ANSYS determines that the solution for this iteration has converged and moves on to the next outer iterationloop, the next substep or the next load step, or stopssolving altogether if the analysis is now complete.

If at this point you’re a little confused, don’t worry. The critical ideas to remember from this are the following:

• Contact analyses are nonlinear in nature

• ANSYS performs a special equilibrium iteration “loop” when doing a contact analysis

• Contact elements have a “status” that indicates if they are open, closed, sliding, etc.

• ANSYS checks the element status and theconvergence criteria at the end of each contact equilibrium iteration to determine ifequilibrium has been achieved

Part 1 of 2:What they are, how they work and when to use them.

Tech File

33

www.ansys.com ANSYS Solutions | Summer 2004

34

Tech File

These characteristics are true for all types of contactelements. While they may seem a little primitive whencompared with the newer contact elements, node-to-node contact elements have a lot going for them.They’ve been around long enough to have had theirbugs worked out many years ago, and their extensiveuse over several decades means that there is a vastexperience base to draw upon when setting up anddebugging an analysis. CONTAC12 and CONTAC52can have nodes that are either coincident or non-coin-cident. While the majority of applications involve usingnon-coincident nodes, coincident nodes can be use-ful for certain analyses. If coincident nodes are used,the orientation of the contact “surface” that existsbetween the two nodes must be defined. The initialcondition gap or interference can be provided by theuser as being either positive (gap) or negative (interfer-ence), or automatically calculated from the relativepositions of the nodes.

Node-to-node contact is also available in COMBIN40. COMBIN40 is a rather unique elementbecause it also includes a spring-slider, a damper(which works in parallel with the spring-slider) and a mass at each node. Any of these features can beused alone or simultaneously with any or all of theother features.

While node-to-node contact elements are veryuseful, there are some limitations that must be kept inmind when using them. One limitation is that the orientation of the gap is not updated when largedeflection analyses are performed. Another limitationis that these elements do not account for momentequilibrium. This does not present a problem when aline drawn between the nodes is normal to the contactsurface because in this instance the moments arezero, but care should be taken in each analysis to recognize whether this is the case or not. If not, it isimportant to consider what effect this might have onthe results. It is the responsibility of the analyst to recognize whether this condition is present andwhether it introduces an unacceptable error that invalidates the usefulness of the analysis.

Node-to-node elements can always be generatedmanually, and, depending on the model, you can oftenuse the EINTF command to make them as well.

Node-to-Surface Elements

The next evolution in contact elements was the introduction of node-to-surface contact elements,such as CONTAC26 (2-D), CONTAC48 (2-D), CONTAC49 (3-D), and the recent addition ofCONTA175 (2-D and 3-D). The major enhancementoffered by node-to-surface contact elements is thatthey allow a node to contact anywhere along an edge(in 2-D) or a surface (in 3-D). Rather than a node beingconfined to contacting a specific node, a node cancontact the edge of a certain element. This has significant benefits when objects translate or rotaterelative to each other. Node-to-surface contact elements are capable of simulating large relativemovements with accuracy.

Because CONTA175 includes all the capabilitiesof the other node-to-surface contact elements andhas other features that these elements do not have,CONTA175 will replace the other node-to-surface elements in future versions of ANSYS. Beginning inANSYS 8.1, CONTAC26, CONTAC48 and CONTAC49will be undocumented, and they will eventually beremoved from ANSYS.

There are several ways to generate node-to-surface contact elements. They can be made manually, but this becomes impractical when makingmore than a few elements. GCGEN and ESURF arecommands that are frequently used to generate node-to-surface contact elements, with GCGEN beingthe easiest and quickest way to make CONTAC48 andCONTAC49 node to surface contact elements, whileESURF is used to make CONTA175 node to surfaceelements. To use GCGEN, you make two components,one that contains the nodes from one of the contactsurfaces, and another that contains the elements fromthe other contact surfaces, and then use GCGEN toautomatically generate node-to-surface contact ele-ments between every node and every element that arein these components. To use ESURF, you select theelements that the CONTA175 elements will beattached to and their nodes that are on the surfaceyou wish to place the contact elements onto, makingsure that you have the proper element attributes active(TYPE, REAL and MAT), and then issue the ESURFcommand.

Last but not least, the Contact Wizard can beused to generate node-to-surface contact elementsand is usually the easiest and quickest way of makingthem.

www.ansys.com ANSYS Solutions | Summer 2004

By John CrawfordConsulting Analyst

Demystifying Contact Elements

My last column talked about the different types of contact elementsavailable in the ANSYS product:node-to-node, node-to surface andsurface-to-surface. Each type hasunique qualities, and, depending onthe analysis, you may find one type of

contact element better suited to the problem at hand thananother. Now that the types of available contact elementshave been introduced, let’s talk about how best to use them.

Simulating Real-World Contact

An important idea to keep in mind is that, unlike most otherelements, contact elements do not have an analogous entityin the real world. A solid element represents solid material,but what does a contact element represent? Contact elements don’ represent a unique physical object, they represent a physical phenomenon: contact. In the realworld, contact exists everywhere. But in the finite elementworld, contact is only present if we specifically “create” itwith contact elements.

To use contact elements effectively, you have to under-stand the differences between how nature works and howfinite element analysis is used to simulate physical phenom-ena. It is common practice in finite element analysis to makesimplifying assumptions. You can think of the real world ashaving all analysis “options” turned on all the time. But infinite element analysis, these options are activated one byone. When doing a contact analysis, you have to make surethat all the options are used that are appropriate for theproblem. This can be more difficult than it sounds becausewe sometimes fail to recognize some of the small but signif-icant factors that are part of the problem.

You need to consider how loads and other boundaryconditions are applied in the real world and use this insightwhen setting up a contact analysis. For example, supposeyou want to simulate lowering a block onto a table and thenapplying a vertical load to the block that pushes it into thetable. In the real world, you would pick up the block and useyour eyes to guide your hands as they move the block clos-er to the table. You control the position and the orientation ofthe block as it is lowered. And as the block approaches thetable, you might decrease its speed a bit until the blockmakes contact with the table. You would then push down on

the block with the desired force, deforming the block andthe table beneath it.

The finite element load steps that mimic this scenariowould be the application of a series of displacements to theblock that control its position and orientation in space as itmoves closer to the table. After each solution, results wouldbe checked to see if the block has made contact. You loopthrough a series of analyses and post-processing sessions,and as the block gets closer to the table you might decreasethe displacement increments until it gently touches thetable. Once the block comes into contact with the table, thevertical displacement is removed and replaced with thedesired force.

Friction might also be included in the simulationbecause it will stabilize the model, especially if you removedthe lateral displacements that are holding the block fromsliding off the table. If friction were ignored, there would be atendency for numerical errors in the solution to apply a smalllateral load to the block that could cause it to slide acrossthe table if it were not restrained. This would probably resultin an error message that would say “Maximum degree offreedom limit exceeded,” which means that the block isunrestrained and is either spinning wildly or flying throughspace (well, finite element space, anyway).

While you may not consciously think of it, the presenceof friction in the real world stabilizes the problem and keepsthe block from sliding off the table. The finite element modelmight benefit from this stabilizing action as well. An addi-tional benefit of using friction in finite element analysis is thatit will provide a more accurate simulation of the interfacebetween the block and the table, which may be somethingof interest in the problem.

One complexity of introducing friction is that it makesthe problem “path dependent,” which means that the orderin which the loads are applied has an effect on the finalresults. Problems that are path dependent (which includecontact with friction, plasticity, creep and others) need tohave the load history applied in a way that corresponds tothe manner in which the loads are applied in the real world.

Most contact analyses require a series of load steps toset up the initial conditions, guide the components towardeach other in a gradual and controlled manner, and thenapply any additional external loads. While there will alwaysbe cases in which it will be appropriate to simplify the loadhistory to a single load step, it is useful to think of contactanalyses as requiring multiple load steps and then removeunnecessary load steps when you can prove to yourself that

Part 2 of 2:How best to use them in solving real-world problems

35

www.ansys.com ANSYS Solutions | Fall 2004

Tech File

Don’t Oversimplify Load History

The most common mistake in using contact elements isinappropriate simplification of the load history. It is useful toset up your contact analyses using the following steps.

1. Thoroughly understand the real problem. Understandhow the components are assembled, how each compo-nent is held in its initial position, how friction stabilizesthe system, how the operating loads are applied, etc.

2. Tabulate a series of load steps that mimic the progres-sive application of these loads

3. Simplify load steps as appropriate.

4. Use the tricks of the trade to help the finite elementsolution yield a reasonable answer. These tricks includeusing soft spring elements to loosely tie the compo-nents together, varying the contact element stiffness,load steps, initial conditions, etc.

5. Review the results for reasonability and accuracy.

6. Tune the model to give you an accurate answer. “Tun-ing” means varying mesh density, contact element stiff-ness, coefficient of friction, element options, etc.

Remember that the real world is always transient and hasfriction, plasticity, large angle geometry and all other analysis“options” active. Your finite element model will probably notinclude all of these characteristics. Make sure that youunderstand the impact of the simplifications you make.

36

Tech File

www.ansys.com ANSYS Solutions | Fall 2004

it is appropriate to do so. Perhaps the most important ideato keep in mind when doing a contact analysis is to think ofthe load history the real-world problem experiences, convertthese loads into finite element analogous load steps, andthen simplify the analysis by reducing the number of loadsteps when it is reasonable to do so.

Stiffness: How Much is Enough?

Because contact elements are “elements,” they must pos-sess stiffness, and the amount of stiffness that is appropriateis problem-dependent. If contact element stiffness is toolow, the results will not accurately represent the true behav-ior of the system. If contact element stiffness is too great, thesolution may oscillate (which is often referred to as “chatter,”and convergence will be difficult or impossible. During solution, the ANSYS product calculates a force convergencevalue and compares it with the criteria. You can monitor thisin the output window as shown in the example below.

LINE SEARCH PARAMETER = 0.5000E-01 SCALED MAX DOF INC = 0.1121E-02

FORCE CONVERGENCE VALUE = 0.4042E+6 CRITERION= 499.3

When convergence is reached for this iteration, you will seesomething like the following.

LINE SEARCH PARAMETER = 1.000 SCALED MAX DOF INC = -0.1087E-04

FORCE CONVERGENCE VALUE = 23.07 CRITERION= 520.0 <<< CONVERGED

>>> SOLUTION CONVERGED AFTER EQUILIBRIUM ITERATION 9

The ANSYS product also plots the calculated conver-gence value and the convergence criteria in the graphicswindow as it progresses through the solution. This lets youmonitor the convergence history and possibly detect anyproblems that might occur.

While no foolproof method exists for calculating theoptimal value of contact element stiffness for all problems,the ANSYS product calculates default values that work quitewell for most problems. It is common practice to begin ananalysis with the default value for stiffness and then adjust itup or down as needed. If the problem converges to a solu-tion without any difficulty, try increasing the contact elementstiffness and see how it affects the results you are lookingfor from the analysis.

Tricks of the Trade

As more experience is gained in using contact elements,you will develop tricks and techniques to help use themmore efficiently. One age-old trick is to use soft springs likeCOMBIN14 to tie various components together and keepthem from flying apart when computational instabilitiesintroduce “chatter.” Another trick is to begin a contact analy-sis with a relatively soft contact stiffness that allows for quickconvergence, and then increase the stiffness to achieve a

solution that is accurate enough for your needs. This tech-nique is applicable when friction effects are not included inthe problem, but can lead to inaccuracies in the final resultwhen friction or other nonlinear behaviors (such as plasticity)are present. Increasing the number of load steps and sub-steps is sometimes helpful in achieving convergence, espe-cially when using node-to-surface and surface-to-surfacecontact elements.

The ANSYS product has a wide selection of contactelements, each of which are appropriate for certain applica-tions. When in doubt, surface-to-surface contact elementsare a good starting point, especially for fine meshes andcomplicated geometries. Node-to-node contact elementsare very useful for instances in which the mesh is relativelycoarse and sliding motion is minimal. Node-to-surface ele-ments are useful when modeling point-to-surface phenome-na, such as a corner of an object contacting a surface or thetip of a beam sliding across a surface.

While using contact elements can be a little intimidatingat first, if you are careful in how problems are set up, you’llfind that they are relatively easy to use and offer an insightthat you can’t get any other way. n

Part one of this article, which appeared in the last issue of ANSYS

Solutions, discussed some of the basics of contact elements, includ-

ing what they are, how they work and when to use them.