Spotting Stress in Statues

David as seen with Scan and Solve.

The red and yellow regions are areas most likely to show stress.

The Spatial Automation Laboratory, University of Wisonsin-Madison

Monday, May 19th, 2008--

After years, decades, or centuries, statues can suffer stress injuries, according to the Getty Conservation Institute. They’re not the kinds of stress injuries we humans get from repeated motions, like typing on a keyboard, playing the piano, or tightening the same bolt on an auto assembly line. For statues, cracks and fractures can be caused by things like shaking from earthquakes, bumps from being moved, or even exposure to weather--and the amount of damage done depends on what they’re made of and the quality of the material. Predicting those points of stress can help experts take steps to stop the damage. Now, a team of scientists has developed a way to detect those hotspots. And they say it’s not just statues that could benefit from their so-called “Scan and Solve” technique; it could also be used to spot weaknesses in bones, engines, and even icebergs.

Right now, predicting stress points in statues is complicated process. The starting point is a digital representation of the object. Just like a CT scanner take lots of measurements to produce a three-dimensional image of a body part like the heart or brain, scans can also produce a virtual model of a statue.

Typically, computer-aided design (CAD) software puts that virtual model into a 3-D grid, or mesh. That means it breaks up the object into a number of best-fitting geometric shapes, triangular-shaped bricks for example, so they can be analyzed for stress points, among other things. That step, getting the statue ready for analysis by breaking the model down into many pieces--in engineering jargon, creating the mesh--is a big job. “It takes longer to prepare the data--days or weeks--than it does to run the analysis itself, which can be done in a day,” says Vadim Shapiro, professor of mechanical engineering and computer science at the University of Wisconsin-Madison.

The new technique, developed by Shapiro and his colleagues, is a streamlined way of doing that preparation. Instead of creating that mesh, or virtually breaking up the statue into pieces, Shapiro’s “Scan and Solve” method looks instead at the space around the edge of the statue. Think of it as putting the statue into a snug-fitting, virtual box, just big enough to enclose the object, but not so large that it’s got room to rattle around.

With the statue enclosed in that virtual “box”, Shapiro can skip over those complicated intermediate calculations and get right to the stress analysis. He computes the distance from a single point on the statue to its boundary, or that box. Taking those measurements for many points on the statue, Shapiro can get a good idea of where forces--like the push of gravity or the shaking of an earthquake--are concentrated, and he ends up with an estimate of those spots where cracks are likely to occur. Like a temperature scale, the resulting map shows areas of higher and lower stress. The areas that show up as “hot spots” are most likely to fracture.

To test out their new technique, the researchers picked perhaps the most famous statue of all time: Michaelangelo’s David. David has been the subject of much scientific study: for example, Stanford University and the University of Washington have produced 3-D scans of the statue as part of their Digital Michaelangelo Project, and a team of Italian engineers did a thorough analysis of cracks that were first discovered in the statue in the mid-1800s.

Shapiro ran the Scan and Solve technique on David. Using that data, along with information on the statue’s material and its properties, he and his colleagues were able to predict the cracks that have been found on the statue. For example, at one time the foundation upon which David stood wasn’t level, but inclined by about three degrees. That slight slant, factored into their analysis, predicted stresses at certain parts of the virtual statue, mirroring observed cracks in the real statue. Those cracks, in real life and in the Scan and Solve program, disappeared when the foundation was leveled.

Shapiro and his colleagues presented this research at the International Conference on Computational and Experimental Engineering earlier this spring. With the David study showing proof of principle, Shapiro’s team is ready to tackle other projects with their Scan and Solve method. And the technique, says Shapiro, will work for more than just statues. It could be used to analyze wear on engine blocks (Shapiro used to work for General Motors), predict whether bones weakened by disease may break, or predict whether icebergs softened by warming temperatures will calve off the larger ice shelf. If Shapiro’s onto something, David may be just the beginning.

--Karin Vergoth