# CONTACT in ABAQUS: HARD and SOFT contact techniques

Hello,

I am using Abaqus for nonlinear FEA of contact between material1 (soft foam like) and material2 (hard plastic type) in vertebrae for my thesis. I have encountered many problems during this exercise, because I have to include the results of various contact conditions in this situation with friction. I am trying to get results for

•  Hard contact (using penalty constraint enforcement)
•  Soft contact (using linear and exponential Pressure-Overclosure relations)

The major problem is convergence during both analyses.

In hard contact the problem was the contact formulation - surface restrictions that limits some connectivity characteristics (e.g  3D solids/faces joined at nodes, or, T-intersections) , it was because of some solid elements (of material2- hard) which were connected via only one node (instead or being connected via edge or face). Mesh refinements were not so much helpful, because they only divide elements, refinement has no thing to do with smoothness of connection of already existing large-sized elements. I was able to get results only with selecting Finite Sliding option, although no sliding occurs in physical model because or interdigitation). This matter put a question mark on my results.

In soft contact, the problem was pressure-overclosure relation. It is really difficult to decide what should be C_o (clearance at zero pressure) and P_o (pressure at zero clearance), because the  nodes and elements faces of material1 and material2 are nearly at zero distance (<10E -4) from each other. By selecting a linear pressure-overclosure relation and setting the value of contact surface stiffness "'K'" roughly equal to maximum value available in the siffness matrix of an element at the contact surface, I started my analysis. Soon I realized that the stresses at contact interface are higher even than stresses of Hard contact. so I reduced the value of "'K'" and re-run the analysis, repeating the analysis and reducing "'K'" till I got interface stresses equal in both cases finally. This value of "'K'" is now  K_o  for my analysis.

I have K_o , but the problem is still C_o and P_o, I can calculate P_o from P_o = (K_o) x (C_o), because C_o is very very small (less than 10E -4) , and if multiplied with (K_o = 350) gives some thing really funny ( i.e Pressure required to clost the clearance will be 0.0017). I have tried to run the analysis with some higher values of P_o  but the analysis is not converging.

### Is that really a meaningfull conversion?

I don't think it can be that easy to translate the linear model into an equal exponential model.

You don't know what kind of overclosure you have from the linear model, and to multiply with the clearance sounds strange.

I don't know how the exponential model looks like, but i'd pick p_0 as roughly the same as the contact pressure (compare with linear and hard contact results, or calculate some rough estimate, even uniform pressure distribution) and put c_0 to something, maybe a fraction of the expected contact patch dimensions.

I'm going to guess a bit here since I don't know how this is implemented in abaqus, but in the end, there is some exponential function that fulfills
f = p0
f[-c0] = 0
and if i were to directly translate the linear model to this, i would put
f' = k
but of course, that would still leave one unkonwn.
If my understanding of the exponential contact model is wrong, please correct me!

### That is right, this

That is right, this conversion is not correct.

The only problem is that I can not get the values of C_o  and P_o  for my model, I have been looking for any method which can give me the contact surface stiffness, so that I can use the exponential model. I have throughly studied the Theory manual and User manual, but there was not a single line about HOW to get these values for a model.

Therefore I tried to get an idea of how much stiffness will give the results equal to Hard contact. I know that doing this will never give correct results because PressureOverclosure relation based contact  and  Hard contact are different, but I am desperately looking for any method which could give me some values for K  and/or  P_o  so that I can start my work. The calculations I wrote above are in Abaqus Theory Manual (Article: 5.2.1 Contact pressure definition)

Please guide me on how to get values for these parameters. I have been trying to do this analysis for last 3 weeks. 