Elastomers Stretch Modeling Abilities

With virtual prototypes now commonplace, particularly inthe automotive world, you might think engineers have mastered the intricacies of modeling components made from common materials. But the thermoplastic elastomers used in various sealing applications remain a glaring exception.

"An understanding of how to model these materials still escapes many experienced engineers," argues Mike Bednarik, who manages automotive weatherseal applications for a major thermoplastic elastomer (TPE) supplier, ExxonMobil's Santoprene Specialty Products Group. The reason boils down to a non-linear double whammy. "The materials themselves are non-linear," he says, meaning that TPE components usually perform under real-world conditions that correspond to the non-linear region of their stress-strain curve. "And they're often subjected to non-linear deformations," he says, meaning that TPE components often experience high-strains by design.

Failure to account for all this non-linear behavior during a structural analysis usually results in a dramatic over-prediction of a TPE component's stiffness, according to Ward Narhi, one of Santoprene's senior design engineers and elastomer modeling experts. "We've seen predictions that are 100 or 200 percent off measured results," he says.

Yet with the proper analysis methods and an understanding of elastomer behavior, FEA accuracy tightens up dramatically. Narhi reports that Santoprene's design engineers now routinely make stress predictions within ten percent of measured results. "Any engineer familiar with elastomers knows that's pretty darn good," he says.

Narhi credits improvements to commercial FEA codes that can handle viscoelastic, non-linear material models for some of the accuracy gains. "They've made huge strides over the past ten years," he says.

Elastomer modeling success, however, requires more than firing up the right FEA software. "It takes a lot of experience," he adds. Fortunately, Narhi is willing to share that experience. He and his fellow engineers, who model Santoprene's thermoplastic vulcanizate elastomers just about every day, offer the following three strategies for getting the best FEA results:

Don't Use a Linear Solver

It might seem obvious that a linear solver may not be the best analysis tool for TPEs. "But we still see it all the time," Narhi says. "And it's a grievous mistake." In fact, it's the mistake that bears most of the blame for the large stiffness prediction errors—results so far off the mark that Narhi describes them as "not from the wrong town, but the wrong planet."

How does the use of linear code affect stiffness? You may look at a TPE's stress strain curve, notice that it has a small linear region, and think that the linear code might work. And it can, in fact, provide a glimpse of initial stiffness. The problem is, though, that the linear region on TPEs typically ends at strains of two percent or less. "In the real-world, the materials are more often subject to strains that start at 10, 15, or even 20 percent, which is well into the non-linear portion of the curve," Narhi says.

On that non-linear portion of the curve, the elastomer's apparent modulus diverges from that initial stiffness prediction. For example, parts in tension are often significantly less stiff in use than in predictions based on the linear portion of the curve. "That's because elastomers soften as you pull them," Narhi explains. If carried through the design process, this stiffness over-prediction could result in under-designed parts that fail.

Parts in compression, Narhi continues, tend to be stiffer in use than a linear analysis would suggest. The design consequence here would be over-engineering. "We've seen parts that are three or four times thicker than they need to be," he says.

Initial stiffness prediction aside, there's really only one time that a linear solver has any value in elastomer analysis. Narhi says very hard elastomers, those with a Shore D durometer, have longer linear regions on their stress-strain curves, which could correspond to the real-world conditions seen by the component.

For most cases, though, Narhi steers clear of linear FEA codes when it comes to elastomers. He prefers to get rough initial stiffness estimates through quick back-of-the-envelope calculations using published stress-strain data. For anything more detailed, he and Santoprene's other design engineers go right to FEA software with strong non-linear capabilities. They overwhelmingly favor Abaqus for their work, though they also use MSC Marc. "Abaqus is the premier code for rubber and elastomers, but other non-linear codes work too," Narhi says.

Pick the Right Material Model

Even with the right software, engineers still have to pay extra attention to the FEA material models they use. "It's not like metals, where one material model fits all," says Narhi. With elastomers, a finite element analysis can succeed or fail based on the choice of material model.

The good news about material models is that commercial codes such as Abaqus make elastomer-friendly models readily available, including ones developed for the traditional rubber industry. By Narhi's count, Abaqus has about ten such models.

The bad news about material models is that even picking from the ten can require some in-depth knowledge of the models themselves, individual TPE grades, and the applications requirements. "Matching the material model to the application requirements is still something of a manual process that requires some experience," Narhi admits.

One important thing to realize is that you may need to apply several models to get meaningful FEA results—because each individual model addresses a limited slice of loading conditions. "You typically won't find one model that fits all the data sets that correspond to your application. One model may fit tension but not compression. Or vice versa," he says. Likewise, some models work best with high strains, others with low strains.

Narhi says most engineers he works with have a firm grasp on essential loading conditions—temperatures, deformation modes, cyclic loading, and strains. But he has noticed that engineers without a lot of elastomer experience tend to neglect the influence of the material itself. Modulus, in particular, has a strong relationship to the material model used in the simulation. "Harder materials act in more linear fashion. Softer ones tend to be more non-linear," he says.

Finally, it's also worth noting that more complex material models also require more computing power and add complexity to the FEA. "A lower order model may help speed the analysis or help when the analysis has trouble converging. So at times, an analyst may want to sacrifice the accuracy of a higher order model in order to complete the analysis quickly or help it converge," Narhi says.

Because so many applications-specific factors influence material model choices, Narhi is reluctant to be too prescriptive about which models to use. "It really does depend on the application," he says. But he does offer a few guidelines. He says that Mooney-Rivlin, a common model for rubber, works fairly well for strains less than 20 percent and serves as a good starting point for many applications. "But if the strains go above 50 or 60 percent, the results won't be very accurate at all," he says. In the case of higher strain rates, other models come into play. Narhi cites Arruda-Boyce, for example, as a suitable choice for applications whose strains hover around 50 percent.

A similar reasoning applies to deformation modes. For instance, Narhi says he sometimes applies the Ogden model, which he feels is most valid in tension but handles strains to 80 percent. "We use it primarily in very high stress applications," he says.

Get Good Data

The importance of applying the right material model also underscores the need for real-world test data, which forms the foundation for accurate simulations. On this score, Santoprene provides some valuable help.

The company has for years performed the physical testing needed to validate the various material models. The testing is an on-going and time-consuming effort. "We test each grade in tension, shear, and compression," says Narhi. "And that takes time." The result of all that testing, though, is that Santoprene has already done some of the hard work of matching experimental data to various material models (see sidebar for an example).

Over the past two years, the company has quietly made the fruits of its labor available to anyone who registers for its website. Within the site's "design your part" section are FEA data sheets that contain coefficients for suitable material models as well as a wealth of raw stress-strain data. Narhi notes that latter information can be useful even without FEA. "You can use it for engineering calculations that give you a quick take on stiffness," he says. Currently, Santoprene provides these data sheets for about 40 of its material grades, mainly those used in automotive and industrial applications. The list continues to grow.

And so does the company's FEA expertise. So far, the big accuracy gains have involved stress calculations. But the company has more ambitious plans to do more complex stress-relaxation and compression set predictions over extended time scales. "We want to predict what the materials will do after years on the job," says Narhi. The company has already put some of this capability into place and has developed a proprietary method for predicting compression set. "We don't have 100 percent confidence in it yet, but we're getting there," Narhi says.

Reach Ogando at jogando@reedbusiness.com.