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# In memoriam: Ronald Rivlin

Ronald S. Rivlin, university professor emeritus of mathematics and mechanics and one of the 20th century’s leading experts in applied mechanics, died recently at his home in Palo Alto, Calif. He was 90 years old.

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.

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.

“Ronald Rivlin was one of the most brilliant people I ever met,” says 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.”

Herman Nied, chair of the mechanical engineering and mechanics department, said Rivlin was particularly innovative in applying 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, co-wrote a memorial resolution about Rivlin that describes him as “the father of the modern theory of finite elasticity,” whose research “had a major impact on theoretical and experimental analyses of non-linear elastic deformations.”

The practical applications of Rivlin’s work, says 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

“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

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

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 notes 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 recalls, 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 says. “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.”

Rivlin received an undergraduate degree in physics and mathematics from St. John’s College at Cambridge in 1937, and a doctorate from Cambridge in 1952.

He was a physicist for the British Rubber Producers Research Association before being named the association’s superintendent of research from 1950 to 1953.

He taught at Brown from 1953 to 1967, rising to the position of chair of the division of applied mathematics.

After retiring as director of Lehigh’s Center for the Application of Mathematics in 1980, Rivlin served 10 years as adjunct professor at Lehigh.

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.

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.

Memorial contributions may be made to the National Science Foundation or to a university sponsoring research.

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.

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.

“Ronald Rivlin was one of the most brilliant people I ever met,” says 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.”

**“The father of the modern theory of finite elasticity”**Herman Nied, chair of the mechanical engineering and mechanics department, said Rivlin was particularly innovative in applying 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, co-wrote a memorial resolution about Rivlin that describes him as “the father of the modern theory of finite elasticity,” whose research “had a major impact on theoretical and experimental analyses of non-linear elastic deformations.”

The practical applications of Rivlin’s work, says 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.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 notes 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 recalls, 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 says. “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.”

**An award-winning career**Rivlin received an undergraduate degree in physics and mathematics from St. John’s College at Cambridge in 1937, and a doctorate from Cambridge in 1952.

He was a physicist for the British Rubber Producers Research Association before being named the association’s superintendent of research from 1950 to 1953.

He taught at Brown from 1953 to 1967, rising to the position of chair of the division of applied mathematics.

After retiring as director of Lehigh’s Center for the Application of Mathematics in 1980, Rivlin served 10 years as adjunct professor at Lehigh.

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.

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.

Memorial contributions may be made to the National Science Foundation or to a university sponsoring research.

*--Kurt Pfitzer*Posted on Monday, December 12, 2005