Finite Element Analysis of Elastomeric Materials used in Medical Device Development
Welcome to the start of a multi-part blog series based on an actual case of Finite Elemental Analysis (FEA) used in the development of a silicone rubber medical device balloon.
A Medical Device company wished to improve the cycle life of an elastomer balloon used in the valve of several pneumatic circuits of a respiratory diagnostic device. These valves control which circuits the patient breathes through during the procedure, allowing or blocking flow in different parts of the machine. They must operate quickly without producing a mechanical reaction in the tubing that makes up the circuitry. Because pressures are not high and balloons have little mass and seal well constrained in a tube, we preferred them over plungers or other mechanisms. To complicate matters, the company simultaneously received news of discontinuation of the only approved balloon material. A search for a direct replacement for the traditional material was not successful. All candidate materials that we tested yielded either a much lower cycle life or slower response to pressure input than the current product. A consultant was retained, who proposed using FEA to configure a revised balloon geometry meeting the requirements for function: simply, it would fit into the current apparatus, have the rapid response capability to pressure input, as well as the ability to make a seal in the unmodified valve body in addition to longer life and construction from available silicone rubber medical formulations. The application required that the material must be a medical grade silicone rubber. Latex or other higher strength elastomers cannot be used. For practical reasons, the aggressive schedule also demanded that the part be moldable with tooling that can be produced quickly in a mold configuration amenable to modification should testing find the need to iterate upon the design.
Determining Material Properties
While simple linear stress analysis has become common in recent years thanks to the capabilities added to some popular CAD programs, analysis of elastomers requires some extra attention and capability beyond these introductory analysis tools.
Traditional linear static analysis is not generally applicable to elastomers, such as is the case with our example. In this case study these reasons are listed as follows:
- Large changes in geometry violating the underlying assumptions of “linear static stress analysis”
- The need to resolve changing conditions in the analysis such as parts coming into contact and time dependant pressure
- The need to understand the effect of any new geometry or material on response time
- The need to account for a non-linear stress strain phenomena inherent in hyperelastic materials such as rubber
Hyperelastic Material Properties Expressed Through FEA.
One common issue in the analysis of elastomers is the lack of information on their mechanical properties beyond durometer. Simple stiffness data, when it is available, is not adequate for accurate FEA of a balloon, even if non-linear analysis is performed. Physical testing throughout the entire range that the analysis will be performed at will usually be required and was done so in this case. This can become complex, but adequate accuracy may sometimes be achievable at reasonable expense with only the uniaxial strain results.
Next, we faced the issue is how to express these properties to the FEA software. Elastomers, including silicone rubber, do not have a constant stress to strain ratio throughout their elastic range. Recall that elastic deformation is reversible, and plastic deformation is permanent. One needs more than the simple Young’s modulus that served adequately in static linear analysis and even in non-linear analysis with lower strain materials. Researchers developed several “Hyper-Elastic” constitutive material models for this purpose and some FEA codes incorporate them. The generalized-Rivlin model, sometimes called the “Polynomial Hyperelastic Model”, is one of the earlier models, dating from the 1940’s; the Mooney Rivlin model is a special case
[i]. We used this model because it was easy to obtain the necessary empirical data. Mooney-Rivlin constants are rarely available from the material manufacturers or elsewhere at this time. Even uniaxial pull tensile data is often unavailable, so material testing will be part of the analysis if dealing with medical devices with elastomeric parts.
In this example, we found it convenient to use the “runners” from a similar part using the same mold base as shown above. We retained these scrap pieces, normally discarded, from a prototype run that subjected them to the same post-cure treatment as the actual parts, thus practicing green engineering, while saving time and expense for all. We engaged a testing laboratory that conducted a standard uniaxial pull test to generate uniaxial stress and strain results.
The software generates the needed “Mooney-Rivlin” constants after one enters or imports the test data. A screen shot, shown above, is an example of fitting Mooney Rivlin constants to experimental pull test data for a certain 50SHA silicone, one of several candidates for replacement material. Note that in this case, a “5 constant high-order” curve fit was used rather than the simpler “2-constant standard”. Several higher order models are available, 5 was the lowest order that fit the data very well. The reader (with very fine vision) can see the red points in the graph which are the actual stress and strain outputs entered, and that fit is reasonable.
At this point, the analyst now has the needed, but heretofore missing, material properties data. As a side benefit, one can now add the material properties to his or her “custom material library.”
[i] Mooney, M., 1940, A theory of large elastic deformation, Journal of Applied Physics, 11(9), pp. 582-592.