Morton E. Gurtin

Alumni Professor of Mathematical Science
Ph.D., Brown University

Office: Wean Hall 6130
Phone: (412) 268-2553
E-mail: mg0c@andrew.cmu.edu

Research

My research concerns nonlinear continuum mechanics and thermodynamics, with recent emphasis on applications to problems in materials science. I have discovered that, within a macroscopic framework, additional nonclassical force systems are useful in describing phenomena associated with the material structure of a body. 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. My recent research utilizes these nonclassical systems to develop general theories for phenomena such as phase transitions, fracture dynamics, atomic diffusion, and crystalline plasticity.

Selected Publications

Books and Encyclopedia Articles

Configurational Forces as Basic Concepts in Continuum Physics, SpringerVerlag (2000)

An Introduction to Continuum Mechanics, Academic Press (1982) ffl Thermomechanics of Evolving Phase Boundaries in the Plane, Oxford University Press (1993)

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)

Education

Bachelor of Mechanical Engineering, Rensselaer Polytechnic Institute

Ph.D., Applied Mathematics, Brown University

Major Awards

Agostinelli Prize (annual prize in pure and applied mathematics and mathematical physics), Accademia Nazionale dei Lincei, Italy

Dottore Honoris Causa, Civil Engineering, University of Rome

Distinguished Graduate School Alumnus Award, Brown University

Richard Moore Education Award, Carnegie Mellon University

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