By Andrew Plemmons Pratt

Professor Cornelius O. Horgan, Wills Johnson Professor of Applied Mathematics and Mechanics in the University of Virginia Department of Civil Engineering, is in good company.

Each year, the Society for Engineering Science (SES) awards the A.C. Eringen Medal to a scientist or engineer "in recognition of sustained outstanding achievements in Engineering Science." Named for the founder of the Society, the first Eringen medal went to Lofti Zadeh of the University of California, Berkeley, in 1976 in honor of his work in the field of artificial intelligence. Edward Teller, one of the godfathers of the Manhattan Project, received the medal in 1980. Subrahmanyan Chandrasekhar, of the University of Chicago—famous for his predictions on the life cycles of stars—was posthumously granted the award in 1996; he is one of three Eringen medal recipients to also win a Nobel Prize.

Professor Horgan received the 2005 Eringen Medal in honor of his "seminal contributions to applied mathematics and the theory of elasticity." He received the medal at the joint SES/ASME/ASCE Meeting on Mechanics and Materials, where he delivered the plenary lecture to more than 600 attendees on "Continuum Mechanics-based Hyperelastic Strain-stiffening Constitutive Models for Rubberlike Materials."

Past winners have come from many of the most-respected universities throughout the world. Horgan is the first recipient from U.Va.

For many years, Horgan's research has focused on what he describes as the "synergy between applied mathematics, applied mechanics and the mechanical behavior of solid materials and structures." In this long-standing relationship, mathematical models simulate the complex behavior of various solid materials and structures. His recent work deals with the nonlinear behavior of elastic materials. Collaborators on the project include SEAS graduate students, as well as colleagues at the University of Lecce, in Italy, and at Dublin City University, in Ireland. Funding comes from the National Science Foundation. Their models predict what happens—at the molecular to the macro

level—to different rubbery materials under extreme stress. Taking the time to illustrate these principles one afternoon in his office, Professor Horgan explains:

"So if you take an ordinary piece of rubber material," he says, stretching a rubber band across the table, "and pull on it, it easily stretches; and when you release it, it is purely elastic and recovers its original shape. But what I'm particularly interested in is when you keep on stretching it and apply a large deformation like this"—and here the band looks dangerously close to snapping apart. "It undergoes what we call strain stiffening. That means it's getting much more difficult to do this"—the band now turning pale as he stretches it even further. "What is happening is that the molecular chains are actually being straightened until they cannot be stretched any further, and we have discovered new mathematical models that capture this behavior."

Applications for the rubberlike materials Professor Horgan's team has been modeling vary widely, ranging from vibration isolators for building structures to soft biological tissues such as arterial walls and human skin. Professor Horgan's teaching and research emphasize the fundamental nature of this sort of modeling. "Applied mathematics and applied mechanics are fundamental disciplines in engineering and applied science," he says. "A student trained in these fundamentals can direct those ideas to numerous application areas."