This article focuses on the behavior of tires that appears to have little in common with expectations for nuclear weapons. However, they are similar enough that Sandia National Laboratories and Goodyear Tire and Rubber Co. are working together and sharing the same tools to understand their different products. Sandia uses computational mechanics to simulate phenomena such as non-linear mechanics, to predict how a component will perform when it is slammed into the ground. The biggest challenge in computational mechanics is to convince the engineer that we have captured all of the relevant physics that computational simulation is every bit as good as or better than the same experiment being performed.


At first glance, the behavior of tires appears to have little in common with expectations for nuclear weapons. But they are similar enough that Sandia National Laboratories and Goodyear Tire and Rubber Co. are working together and sharing the same tools to understand their different products.

The arrangement is an interesting example of how industry and national research labs work together. Goodyear has the opportunity to use powerful computer modeling tools developed by Sandia, while Sandia gets a partner that can validate its code.

Sandia National Laboratories in Albuquerque, N.M. , is one of three laboratories funded by the U.S. Department of Energy as custodians of the nation's nuclear weapons. (The other two are Lawrence Livermore and Los Alamos.)

Sandia has historically mounted a large-scale effort in computational mechanics, according to Thomas C. Bickel, the director of Sandia's engineering sciences. Computational mechanics captures engineering phenomena on a computer, which then can be simulated, he said.

Sandia uses computational mechanics to simulate phenomena such as nonlinear mechanics, to predict how a component will perform when it is slammed into the ground, for instance. "We do a lot of high-end, very high fidelity, nonlinear computational mechanics," Bickel said.

The work is done on advanced computer platforms. The laboratory's job is to capture engineering phenomena in the computers to help engineers design safety and performance into weapons systems, he said.


The lab faces some constraints in doing that. In the past, Sandia could confirm its calculations periodically by studying underground tests. Today, because of the Comprehensive Test Ban Treaty, that is no longer an option. This is what differentiates the lab from U.S. industry. Unlike Goodyear, which can test its tires, Sandia cannot conduct fullscale weapons tests, said Bickel.

According to Wing Kam Liu , a professor of mechanical engineering at Northwestern University in Evanston, Ill., and president of the United States Association of Computational Mechanics, well over 90 percent of weapons analysis is based on computational mechanics today. In the 1940s and 1950s, more than 90 percent of weapons design was based on experimental work, he said, referring to penetration experiments and computations. "Together with limited experiments and experiences, computational mechanics can be extremely useful in weapons analysis and design," Liu said. H e expects that advances in Computational mechanics, computer hardware and software, and declining costs of computers will continue to drive computer modeling and simulation applications.

Common Interests

Although it may be for different reasons, Goodyear and Sandia share the goal of radically reducing the design prototype-test loop and producing finished products faster and cheaper.

Both are test-based organizations, trying to use computational mechanics as a way of capturing the relevant physics to predict the design and its performance before manufacturing.

Sandia started discussions with Goodyear in 1992, and reached its first agreement with the company in 1993. Since then, Sandia and Goodyear have signed seven cooperative research and development agreements, or CRADAs. The first one covered finite element tools for predicting structural, thermal, and hydrodynamic responses of tires.

According to Sandia, as part of the CRADA, researchers used the lab's computational mechanics modeling capabilities to simulate the response of weapon systems and components, as well as to model the response of tires, including details of the tread and the complex layering of rubber, polyester cords, and steel belts.

Other CRADAs signed since then have covered vibration and noise analysis, as well as non-tire rubber products. Most recently, Goodyear signed an umbrella CRADA, which allows Goodyear and Sandia to embark on new research without having to sign a new agreement each time.

Bickel said that working with Goodyear gives Sandia more confidence in its simulations. Although Goodyear and Sandia each has its own separate job, in the engineering context they are similar. Both need to capture the relevant information, use it in the right computer models, and visualize and convey it to the design engineer. "The physics that we are using for our analyses are, in most cases, very similar and, in some cases, very dissimilar, but the fundamental engineering is identical," said Bickel.

Tests Change Role

Computational mechanics tools were never meant to replace live tests. "We are using a combination of an above-ground non-nuclear test and computational simulation married together," Bickel said.

Non-nuclear components are arming, fusing, and firing systems of nuclear weapons-for example, firing sets, use-control devices that determine appropriateness of signals that reach the weapon, radar, and acceleration sensors.

A variety of above-ground tests are run on the non-nuclear components. These tests include doing bomb drops with dummy warheads, placing components on shaker table to subject them to vibration, dropping weapons from towers, and burning weapons in fire test facilities.


Advances in computational mechanics have changed the way Sandia is conducting its tests. For one thing, computational ability is readily available, providing a more detailed representation of nature than traditional testing, which often had to be repeated several times, Bickel said.

Hal Morgan, Sandia's head of advanced mechanics tools for engineering process analysis, said that computational modeling is allowing the lab to become predictive enough to reduce the amount of testing. Morgan said that Sandia builds various components to test design concepts, and there could be several builds, depending on the number of iterations that a design has. Computer simulation has reduced the number of builds.

Morgan said that the nature of the mechanics of tires has resulted in particularly difficult equations to solve, including physical phenomena such as tire inflation, how tires deflect on the pavement and roll down the road, and how they respond to stresses and strains. The equations used to solve those problems are the same as those used to understand nuclear weapons, he said. "Consequently, by being able to solve a tire problem better, we are able to solve a nuclear weapon problem better," he said.

Sandia applied Goodyear's simulation of the response of tires to the rubber used to encapsulate nuclear weapons components, using the information to solve polymer equations more accurately than before. "With this computational ability, we were able to simulate and model the encapsulation process," said Morgan. The capability was applied to the curing step in the lab's manufacturing process to eliminate residual stresses that resulted in cracking, and also reduced in-mold curing time, speeding up the production process, he said.

Tire Development

Goodyear, for its part, is gaining tools to become more efficient in the design of its products and the simulation and prediction of tires' performance before they are ever tested in the traditional sense, according to John Lawrence, Goodyear's vice president of corporate research. He said that the company is using computational tools primarily to model the inflation of tires, deflection of the tire under load, and rolling of the tire to understand thermal and mechanical response.

Goodyear is using code developed by Sandia and altered to handle the types of structural mechanics problems that are encountered with tires, he said. Work is performed on Goodyear's computers.

"We put the material properties into the equations as new materials are developed, and build these into the models," he said. "Sandia has helped us modify the code to handle the type of conflicts on nonlinear problems that are concerned with mechanical response times," he said." It's a very powerful code that can be used for more than one type of problem."

Although Goodyear has used commercial software in the past and will continue to use it, the code developed by Sandia can handle far more complex types of problems, Lawrence said. "We can run these problems on massively parallel computers. The computational time for solving the problem is much shorter than the commercial code. The ability of the code to handle the complexity that we have with tires makes the problems solvable in a reasonable period of time," he said.

Goodyear is applying the knowledge to tire performance using computational tools to shorten tire development time. The company is gaining tools that allow it to become more efficient in the design of its products and the simulation of their performance before they are tested in the traditional sense, Lawrence said.

He said that Goodyear was highly dependent on the traditional design-build-test process before it started working with Sandia. Since then, the company has been able to eliminate some physical testing by using computer modeling instead, he said.

In October 2001, the company launched its Fortera tire for sport utility vehicles. It was designed using computational tools. The tire met the requirements of Goodyear's North American business unit the first time it was released to the customer, which is unusual, he said.

In Lawrence's view, the biggest advantage to using computational mechanics is being able to get to the final design faster. He declined to quantify the time saved, but said that the results of the modeling are reliable. The they operate are better understood, he said. Still, physical tests will continue to play a role in tire development, if only to verify computer models.


New Directions

Advances in high-performance computing have greatly increased the power of computational mechanics during the last decade, according to Bickel of Sandia. Computer models today may consist of 10 million finite elements, which would have been unthinkable 10 years ago. That level of detail brings the ability to look at three-dimensional geometries and the physics across joints, and to capture moving interfaces, he said.

The complexity of the problems that Sandia is trying to solve has increased dramatically, according to Bickel. Fifteen years ago, his customers were concerned primarily about why a component broke after a test. Ten years ago, they wanted help in designing a better test that stressed a component more severely. Over the past five years, they have wanted to predict computationally the margin of failure.

The biggest challenge in computational mechanics, Bickel said, is "to convince the engineer that we have captured all of the relevant physics, that computational simulation is every bit as good or better than the same experiment being performed."