When the I-35W Bridge in Minneapolis collapsed during the evening rush hour on August 1, 2007 killing 13 people, millions were stunned by the tragic scene. Images of cars, semi-trucks, and even a school bus, teetering some 115 feet over the mighty Mississippi River left many wondering, “Could that happen here, where I live?” In the days that followed, motorists around the country gave more careful consideration to the bridges and overpasses that they travel every day, which before had never garnered a second thought. While the specific cause of the collapse remains undetermined, most experts agree that some mechanical failure is to blame.

Crack Modeling
In collaboration with G. Francfort at Université Paris Nord, France and J.J. Marigo at Université Pierre et Marie Curie in Paris, Bourdin is using EnSight extreme visualization software by CEI, Inc., Apex, NC, to develop a system for creating 3D mathematical models that forecast the potential location and path of a crack in brittle materials like glass, concrete and steel. His is a novel approach to fracture mechanics that, through simulation and modeling, allows him to predict failure before it happens.

“Most methods in classical fracture mechanics assume that you know the solution before you can solve the problem,” Bourdin says. “You assume that you have a-priori knowledge of potential cracks and then solve for those cracks.”

Bourdin’s work does not follow this assumption. Beginning with mathematical data for the device in question, like a cylinder, beam, or other construction, Bourdin applies knowledge of the building material, how it behaves under stress and other factors, like temperature and load, to predict where potential cracks might form.

“We’re not writing the program based on observation of experiments,” Bourdin says. “Our results come from mathematical modeling based on the equations of motion. From this we derive the model that represents the fracture.”

In this numerical approach, cracks are approximated using a diffuse interface model. Each crack is represented by a smooth function defined at each node of a 2D or 3D domain, typically within an unstructured mesh. At each point in the domain, the crack is represented by a number between 0 and 1. Inside the crack is 0, increasing toward 1 further from the crack. Using these numerical models, Bourdin can simulate the temporal evolution of a crack, including branches and splits, over thousands of time steps.

Crack Computing
The models result in enormous amounts of data, sometimes up to 15 Gb for one simulation, and Bourdin relies on Teragrid, the nation-wide supercomputing network, to store and manipulate the data. This is critical to his ability to render the complicated models.

“EnSight allows me to visualize my data without removing it from the server – I can visualize at LSU data that are in Texas or Illinois or California,” Bourdin says. “I don’t have to wait until everything is transferred, and I don’t have to store it locally to view it.”

 

 
These still images from a mode-I traction simulation experiment on a pre-cracked perforated domain illustrate brutal propagation of a crack from one perforation hole to the next. The light blue to the right of the as yet in-tact perforation hole indicates the progression of stress as the crack propagates through the domain.

The visualizations he creates in EnSight allow Bourdin to both verify the geometry of his calculations and better understand and communicate the mathematical properties of the model. Bourdin uses Cubit, developed by Sandia National Laboratories, to generate the mesh. During this process, he will verify the geometry by outputting the data to EnSight for a quick checkup on how the model is coming together. Then, he uses EnSight to generate and analyze the results. Because EnSight reads most mesh file formats, Bourdin is able to quickly port data from the supercomputing network, generate an animation and share the results with colleagues.

“I have a very visual, geometric mind,” Bourdin says. “EnSight has helped me to understand my equations and understand some properties of the solutions, as opposed to just staring at the equations. For complicated 3D systems, EnSight allows us to extract some patterns of the solution – to walk in it, rotate it, interact with it and zoom in and out.”

In addition to shedding light on the mathematical data, EnSight’s robust features afford Bourdin the opportunity to expedite the research process. For example, the query function lets him track properties of the solution interactively, while the program is running, instead of recompiling and rerunning the simulation for each variable. Bourdin can test various scenarios, such as displacement load and material properties, and display the results – for material that doesn’t even really exist – all from his desktop. He has even written his own add-on software that performs batch processing, an incredible time saver.

“For one project, I had to conduct about 300 experiments and was able to visualize all of these results without having to interact with EnSight for each one,” Bourdin says. “It would have been impossible to do this manually; I simply wouldn’t have done it.”

In addition to the software’s full-featured capabilities for conducting experiments, Bourdin says EnSight, and the free companion EnLiten viewer, also by CEI, Inc., allow him to better communicate complicated solutions to colleagues. At a recent engineering conference, Bourdin found himself facing a room full of engineers, trying to describe some of the properties of his work involving two crack planes that intersect at a nonzero angle. With the 3D models generated in EnSight, he was able to demonstrate the evolution of the crack fronds as they grow toward each other, from multiple viewpoints.

Crack Prevention
Bourdin admits that while he won’t have a solution to the I-35 Bridge collapse in the very near future, his work, which is supported by the National Science Foundation, has vital implications in a wide variety of applications, including:

• Building construction – case in point: the collapse of a terminal at Paris’ Charles de Gaulle Airport in 2004 is believed to be the result of structural failure;
• Infrastructure safety – the Hoover Dam, for example; and
• Aerospace design – consider the force on the front landing gear of an aircraft each time it hits the runway, a prime candidate for stress fractures.

“As a mathematician, I am mostly interested in this fracture model because of the challenges posed by its numerical implementation,” Bourdin says. “Of course, it also happens that it is a good mechanical model, and can be used to analyze the potential soundness of materials and systems before they are put into place."