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Kumbakonam Rajagopal

By Gene Charleton

Luminary in continuum mechanics

When you drive to work in the morning, it's hard to see much similarity between the blood flowing through your veins and arteries and the asphalt paving on the street.

Unless you're Kumbakonam Rajagopal: Then it's still not easy, but you can explain how the two systems are not entirely different.

"Blood as it's flowing through your body is a fluid, but as it forms a clot it becomes less fluidlike and more solidlike with regard to the time, length and force scale of observation," he says. "Continuum mechanics allows you to describe its behavior all the way through."

Rajagopal is distinguished professor of mechanical engineering and Regents Professor in Texas A&M University's College of Engineering. He's also a professor of biomedical engineering, civil engineering, chemical engineering, and mathematics, and he holds the Forsyth Chair in Mechanical Engineering. And he is a senior scientist at the Texas Transportation Institute in The Texas A&M University System.

He's a pioneer of continuum mechanics, a mathematical discipline that allows engineers to build mathematical models of materials that are both solids and fluids, such as asphalt, glass and, yes, blood. Using these models, engineers can predict how much asphalt will yield when you drive on it or how much shear from the pumping action of an artificial heart will damage blood cells and increase the risk of life-threatening blood clots.

"As engineers, we usually think of materials as being either solid or fluid and model them separately," says Arun Srinivasa, an associate professor in Texas A&M's mechanical engineering department. "Rajagopal was one of the first to understand that you can treat some materials the same and that this would be very useful.

"Blood as it's flowing through your body is a fluid, but as it forms a clot it becomes less fluidlike and more solidlike. Continuum mechanics allows you to describe its behavior all the way through."

"If there is no clear distinction [between them], why are we building models that force you to choose one or the other?" Srinivasa says.

Srinivasa has worked with Rajagopal on continuum mechanics–related problems for more than 20 years. His own work draws heavily on techniques Rajagopal developed.

"He was a senior faculty member when I met him, and I was very junior," Srinivasa says. "I specialize in aspects of metal forming. Within a week of meeting him, he said to me, 'What's this stuff about metal forming?' He was not standoffish at all.

"I think I could have been as happy and productive as a professor of English literature or a philosopher."

"He is always willing to argue about technical points without worrying about whether he is talking to a young person or a senior person."

Rajagopal was born in New Delhi, India, and studied mechanical engineering at the Indian Institute of Technology. He received his master's degree at the Illinois Institute of Technology and his Ph.D. degree from the University of Minnesota. He joined the Texas A&M Engineering faculty in 1996.

Rajagopal's early engineering interests were not in continuum mechanics.

"As an undergraduate, I was very interested in control theory," he says. "But when I took a control theory course in graduate school, it didn't excite me." On the other hand, he found that courses in continuum mechanics fascinated him.

Rajagopal's work hasn't been confined to the academic side of engineering and mathematics. He holds patents for his continuum mechanics–related work in fields as divergent as biomechanics and granular material characterization to air brake control systems. He says that the strength of continuum mechanics as an analytical tool is that it can be used to describe materials as their forms change.

Continuum mechanics can't tell engineers everything about a material, he notes.

"It won't give you accuracy at the microscopic level, but it can at the macro level," he says. "As in other problems, you need the proper tool. You need the proper tool. You need to decide if you're going to use a knife or a screwdriver."

Rajagopal is an unusual engineer in other ways. He quotes English poetry and the great philosophers as readily as most engineers discuss Navier–Stokes equations or finite element analysis.

"I think I could have been as happy and productive as a professor of English literature or a philosopher," he says. He says that sometimes his students get frustrated with the way he weaves into his lectures allusions to philosophers and classical engineers and their contributions.

"It is important that students learn the foundations of engineering and science and to understand where the theories and techniques they will use in their work today originated. There is more to engineering than simply solving problems."

Rajagopal isn't only a creative researcher. The American Society of Engineering Education has presented him with the Archie Higdon Award in recognition of his effective teaching.

"It is important that students learn the foundations of engineering and science and to understand where the theories and techniques they will use in their work today originated," he says. "There is more to engineering than simply solving problems."

This approach is more than just a tip of the hat to the idea of being a well-rounded engineer. He puts it into practice in his own work.

"The best paper I've ever written was a consequence of a course I took in philosophy," he says. "I used the idea in thermodynamics."

He is among the top 1 percent of researchers cited in journals tracked by the Institute of Scientific Information.

Rajagopal has been recognized internationally for his significant contributions to the world of continuum mechanics, computational mechanics, biomechanics and technology. Among these honors was his election to the international Hall of Fame for Engineering, Science and Technology (HOFEST). HOFEST members are many of the heaviest hitters in engineering, science and technology, including such luminaries as George Eastman (Eastman Kodak), Thomas Alva Edison, Albert Einstein, Henry Ford, Bill Gates, Louis Pasteur and George Westinghouse (Westinghouse).

He also holds the Eringen Medal, the highest honor of the Society of Engineering Science. Several winners of the Nobel Prize also have received the Eringen Medal.

And he is president of the Society for Natural Philosophy.

His colleagues also have honored him by organizing international conferences on continuum mechanics–related topics in his honor. One, titled "Perambulations in Continuum Mechanics" to recognize the wide-ranging applications of Rajagopal's work, was held in November 2010 in College Station and featured presentations by researchers from the United States, Brazil, Canada, Chile, the Czech Republic, France, Hong Kong, Israel, Ireland, Italy, Japan, Portugal and South Africa. Two special sessions in his honor were held during the 2010 annual meeting of the Society of Engineering Science in Ames, Iowa. A similar conference held in Chennai, India, drew continuum mechanics researchers from across South Asia.

In 2010, the International Journal of Engineering Science published a special issue honoring him, and special issues of Mathematical Modeling and Methods in the Applied Sciences, Journal of Structural Changes in Solids, and Applications of Mathematics dedicated to him have been published in 2011. A special issue of Advances in Engineering Science and Applied Mathematics is forthcoming this year.

Srinivasa says Rajagopal's long list of accomplishments illustrates the researcher's approach to engineering and to life.

"His thirst for knowledge is mind-boggling," Srinivasa says.

Dr. Kumbakonam Rajagopal
Distinguished Professor
Regents Professor
Forsyth Chair in Mechanical Engineering
Professor of Mathematics
Professor of Biomedical Engineering
Professor of Civil Engineering
Professor of Chemic Engineering
Senior Research Scientist, Texas A&M Transportation Institute
Mechanical Engineering
979.862.4552