*1985 - Elected to National Academy of Engineering*

**Ronald S. Rivlin** was a Lehigh university professor of mathematics and mechanics and one of the 20th century's leading experts in applied mechanics. A native of London, England, Rivlin came to Lehigh in 1967 from Brown University to help establish the Center for the Application of Mathematics, which he directed until his retirement in 1980.

### Distinguished Honors

In 1985, Rivlin was elected to the National Academy of Engineering, one of the top honors bestowed on U.S. engineers. He was cited for his contributions to applied mathematics and mechanics, particularly his work in formulating theories to explain the elastic behaviors of rubber and rubber-like materials.

In 1992, the American Chemical Society awarded Rivlin the Charles Goodyear Medal in recognition of his theoretical and experimental work on the elasticity of vulcanized rubber.

In April, 2008, the International Rubber Science Hall of Fame selection committee chose Rivlin to be inducted into the Hall of Fame in early November, 2008 at the 50th anniversary celebration.

"Ronald Rivlin was one of the most brilliant people I ever met," said Chuck Smith, Lehigh professor and former chair of mechanical engineering and mechanics. "If he had done his life's work in physics instead of applied mathematics and mechanics, he would probably have won the Nobel Prize."

### Contributions to the field of nonlinear mechanics

Herman Nied, chair of that department as of fall, 2007, said Rivlin was particularly innovative in the application of concepts in nonlinear continuum mechanics to the solution of large deformation problems for rubber and rubber-like materials.

"Ronald Rivlin was pretty much universally recognized as one of the founding fathers of rubber elasticity," said Nied, a former student of Rivlin's. "Before World War II, it was widely considered to be virtually impossible to obtain rigorous solutions for elastic materials subjected to exceedingly large deformations. But Rivlin really surprised people with the rigor and simplicity of his solutions for this class of materials."

Philip Blythe, professor of mechanical engineering and mechanics, who co-wrote a memorial resolution about Rivlin, described Rivlin as "the father of the modern theory of finite elasticity," whose research "had a major impact on theoretical and experimental analysis of non-linear elastic deformations."

The practical applications of Rivlin's work, said the resolution, "range from the mechanics of fiber-reinforced materials to the design of rubber tires." The other co-writers of the resolution were Nied; Eric Varley, professor of mechanical engineering and mechanics; and Fazil Erdogan, the G. Whitney Snyder professor emeritus of mechanical engineering and mechanics.

An obituary in The New York Times concurred, noting that Rivlin's theoretical discoveries found wide application not only in the behavior of rubber and rubber-like materials but also in the larger area of materials engineering.

"Dr. Rivlin began his work in the 1940s," the obituary said, "using tools of theoretical physics to investigate the properties of vulcanized rubber. He and others experimented with the effects of various loads in deforming rubber and contributed to a field known as finite elasticity theory, which looks at how materials behave during elastic deformation. The work has had subsequent applications in materials engineering."

In addition to his work with rubber, Rivlin studied the behavior of fluids under different forces and developed equations to express the behavior of fluids and other complex materials, the Times said.

Working with other scientists, Rivlin developed the Reiner-Rivlin and Rivlin-Ericksen equations to explain the behavior of fluids, and the Mooney-Rivlin equation to explain the behavior of incompressible solids, which can be deformed but do not change in volume, the Times said.

### Fond memories of a brilliant professor

Rivlin was known as an avid storyteller, according to the Lehigh memorial resolution, and also as a keen listener who often appeared to be napping during a seminar only to awaken and interrupt the speaker with a devastating question.

The resolution noted that his former students still recall how Rivlin, a heavy smoker, used to write equations with chalk on a blackboard while clutching a cigarette with his other hand.

On one occasion, the resolution said, Rivlin was teaching a graduate course on continuum mechanics when he flicked a large piece of cigarette ash into the waste basket. Moments later, the basket caught fire. Rivlin tried to put out the fire by stamping on the paper.

"Unfortunately, his foot became caught in the basket," the resolution said. "After a heroic struggle, he extricated himself from the basket, the flames died down, and Ronald continued with the equation on the board as though nothing in the least unusual had happened."

### Career Highlights

Rivlin received an undergraduate degree in physics and mathematics from St. John's College at Cambridge in 1937, a master's degree from the same school in 1939, and a doctorate from Cambridge in 1952.

After receipt of his undergraduate degree, Rivlin spent time working as a research scientist at The General Electric Company in Wembley, England. In his five years with the company, Rivlin was involved with patenting seven inventions and writing a dozen papers. From 1942 to 1944, he worked at the Telecommunications Research Establishment of the Ministry of Aircraft Production developing radar.

Beginning in 1944, he was a physicist for the British Rubber Producers Research Association before being named the association's superintendent of research from 1950 to 1953.

Rivlin spent a year as a consultant to the Naval Research Laboratory in Washington D.C. in 1952. He decided to stay in the United States and taught at Brown from 1953 to 1967, rising to the position of chair of the division of applied mathematics. He was also an L. Herbert Ballow University Professor for four years.

After retiring as director of Lehigh's Center for the Application of Mathematics in 1980, Rivlin served 10 years as adjunct professor at Lehigh under the title of Centennial University Professor.

### Honors

Rivlin was also elected a fellow of the National Academy of Arts and Sciences and was accorded honorary membership of the Academia Nazionale dei Lincei and the Royal Irish Academy. In 1960, he spent a year at the University of Rome as a Guggenheim Fellow.

His awards crossed several disciplines and included the Timoshenko Medal from the American Society of Mechanical Engineers, the Von Karman Medal from the American Society of Civil Engineers, the Modesto Panetti Gold and Prize from the Accademia delle Scienze di Torino, and the Bingham Medal from the Society of Rheology, as well as ACS's Goodyear Medal.

Rivlin was awarded honorary doctorate degrees from the National University of Ireland, Nottingham University, Tulane University and the Aristotelian University of Thessaloniki. He died in 2005 at the age of 90 in his Palo Alto, California home.