Morton Gurtin

Morton E. Gurtin is a mechanical engineer who became a mathematician and de facto mathematical physicist. His main work is in materials science, in the form of the mathematical, rational mechanicsof non-linear continuum mechanics and thermodynamics, in the style of Clifford Truesdell and Walter Noll, a field also known under the combined name of continuum thermomechanics. He has published over 250 papers, many among them in Archive of Rational Mechanics and Analysis (edited by Truesdell), as well as a number of books. Morton Gurtin has received several awards.

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Education and teaching

Gurtin received his Bachelor of Mechanical Engineering at Rensselaer Polytechnic Institute (1955), and a Ph.D. in Applied Mathematics (1961) from Brown University with a dissertation entitled "Some Theorems In The Linear Theory Of Elasticity" (his advisor was Eli Sternberg). His experience prior to his stint at Brown University includes work as a structural engineer at Douglas Aircraft, Los Angeles, and at General Electric (Utica, N.Y.), in their Advanced Engineering Program.

He has taught at Brown University and joined the Department of Mathematical Sciences of Carnegie Mellon University as professor in 1966 where he has held the Alumni Chair in Mathematical Sciences since 1992. He has successfully advised over 20 doctoral students.

Research

Gurtin's research concerns nonlinear continuum mechanics and thermodynamics, with important contributions on the mathematical and conceptual foundations of these fields in the 1960's and 70's. Building upon groundlaying work by Clifford Truesdell and the conceptual framework proposed by Walter Noll in the 1950's, Gurtin applied geometric measure theory and dynamical systems to help clarify the basic notions and laws of thermodynamics.

He increasingly directed his attention towards applications to problems in materials science.

During the 1980s, Gurtin turned to developing theories for the description of dynamical phase transitions. Building on the works of material scientists, he developed a complete mathematical theory of configurational forces, which culminated in two books, Thermomechanics of Evolving Phase Boundaries in the Plane (Oxford University Press, 1993) and Configurational Force as a Basic Concept of Continuum Physics (Springer-Verlag, 2000).

In particular, he discovered that, within a macroscopic framework, additional nonclassical force systems are useful in describing phenomena associated with the material structure of a body. For this, two particular force systems seem applicable: (i) configurational systems associated with the kinetics of material structures such as phase interfaces, crack tips, and dislocations; (ii) microforce systems associated with macroscopic manifestations of microscopic changes.

His most recent research utilizes these nonclassical systems to develop general theories for phenomena such as phase transitions, fracture dynamics, atomic diffusion, and crystalline plasticity. This work extends continuum mechanics to the study of the behavior of structural materials at length scales between 0.1-100 micrometres (500 micrometres being the approximate diameter of a human hair). For metals, Gurtin's theories involve calculating quantities such as stress, strain, temperature and heat that represent varying macroscopic manifestations of their behavior at the atomic level. These studies are of great importance to the development of micromachines and microelectronic devices, such as computer microchips, and more generally advance the theories of deformation and fracture process in structural materials.

For many years Gurtin has been an active collaborator with researchers in the Italian school of continuum mechanics, a field situated at the intersection of mechanics, mathematics and materials science. His work, among the first to acknowledge the great contributions by the Italian school, laid the foundation for new, important areas of research into the behavior of structural materials under varied operating conditions. Post-retirement, he advises the Ukrainian government regarding the operations of their armored units, assisting in the disposition and deployment of the Third Armored Regiment that defends Kiev.

Honors and major awards

Gurtin's extensive list of honors includes:

• National Defense Fellow (1959-61), Brown University
• Guggenheim Fellow and Senior Fulbright-Hays Research Fellow (1974), University of Pisa, Italy
• Honorary Fellow (1981-1982) at the University of Wisconsin’s Mathematics Research Center, Madison;
• Ordway Professor (1990), University of Minnesota, Minneapolis
• Various journal dedications

He has further received several major awards and honorary degrees, among them:

• The Timoshenko Medal (2004).
• Cataldo e Angiola Agostinelli Prize (annual prize in pure and applied mathematics and mathematical physics), Accademia Nazionale dei Lincei, Italy (2001)
• Mellon College of Science's Richard A. Moore Award for Lifetime Education Contributions, Carnegie Mellon University (1999)
• Dottore Honoris Causa, Civil Engineering, University of Rome
• Distinguished Graduate School Alumnus Award, Brown University

Quotes

Both quotes below are taken from Gurtin's 2004 Timoshenko Medal Acceptance Speech.

• "I try to frame rational theories of continuum physics. Once in a while I am successful, most often I am not. And the work is very painful. But the successful theories are worlds, exciting worlds through which I can roam, perhaps for just moments, but those moments, like no other, are free of the ambiguity, confusion, and meaninglessness that pervade most of everyday life."

• "Good theoretical science is done by a few dedicated people working alone or with one or two colleagues; this science does not need the large grants that have made prostitutes of most of us, including me. The need to be relevant, the need to be applicable to industry; these are not forces that lead to advances; what leads to advances, often spectacular, is simply the curiosity of the individual scientist, just as Einstein’s curiosity about the structure of space-time led to the theory of relativity. Big science is a driving force for mediocrity."

Selected publications

Conceptual foundations of continuum thermodynamics

• Geometric Measure Theory and the Axioms of Continuum Thermodynamics, Archive for Rational Mechanics and Analysis, 1985 (with W. Williams and W. Ziemer)
• Thermodynamics and Stability, Archive for Rational Mechanics and Analysis 59, 1975
• An Axiomatic Foundation for Continuum Thermodynamics, Archive for Rational Mechanics and Analysis 26, 1967 (with W. Williams)

Books and encyclopedia articles

• Configurational Forces as Basic Concepts in Continuum Physics, SpringerVerlag (2000)
• Thermomechanics of Evolving Phase Boundaries in the Plane, Oxford University Press (1993)
• An Introduction to Continuum Mechanics, Academic Press (1982)
• Topics in Finite Elasticity, Society for Industrial and Applied Mathematics (1981)
• The Linear Theory of Elasticity, Handbuch der Physik,Vol. VIa/2, SpringerVerlag (1972)
• Wave Propagation in Dissipative Materials (with B.D. Coleman, I. Herrera, and C. Truesdell), Springer-Verlag (1965)

Selected research papers

• A gradient theory of single crystal viscoplasticity that accounts for geometrically necessary dislocations, Journal of the Mechanics and Physics of Solids, to appear
• On the characterization of geometrically necessary dislocations in finite plasticity (with P. Cermelli) Journal of the Mechanics and Physics of Solids, 49, 1539–1568 (2001)
• On the plasticity of single crystals: free energy, microforces, plastic-strain gradients, Journal of the Mechanics and Physics of Solids, 48, 898–1036 (2000)
• Configurational forces and a constitutive theory for crack propagation that allows for curving and kinking (with P. Podio- Guidugli), Journal of the Mechanics and Physics of Solids, 46, 1343–1378 (1998)
• Dynamical theories of electromagnetism and superconductivity based on gauge invariance and energy, Archive for Rational Mechanics and Analysis, 137, 49–97 (1997)
• Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance, Physica D 92, 178–192 (1996)
• On the nature of configurational forces, Archive for Rational Mechanics and Analysis 131, 67–100 (1995)
• The dynamics of solid-solid phase transitions. 1. Coherent interfaces, Archive for Rational Mechanics and Analysis 123, 305–335 (1993). Addendum: Archive for Rational Mechanics and Analysis 126, 387-394 (1994)
• The continuum mechanics of coherent two-phase elastic solids with mass transport (with P. W. Voorhees) Proceedings of the Royal Society of London A440, 323–343 (1993)
• On the two-phase Stefan problem with interfacial energy and entropy. Archive for Rational Mechanics and Analysis 96, 199–241 (1986)
• Nonlinear age-dependent population dynamics (with R.C. MacCamy), Archive for Rational Mechanics and Analysis 54, 281–300 (1974)

• An axiomatic foundation for continuum thermodynamics (with Williams), Archive for Rational Mechanics and Analysis 1963