CC/NUMFER 43 ~This— Week’s Citation— — Classic CCTOOER22. 1990 Coleman B 9 & Noll W. The of elastic materials with heat conduction and . Arch. Ration. Mech. ,4nal. 13:167-78. 1963. [Mellon Institute: and Department of Mathematics, Carnegie Institute ofTechnology. Pittsburgh. PA]: and Coleman B D. Thermodynamics of materials with memory. Arch. Ration. Mech. Anal. 17:1-46, 1964. [Mellon lostimume. Pittsburgh. PA] 2 In the first paper, the authors present a method for this column some years ago; another recently was determining the restrictions that the second law of suggested by ISI® editors for a commentary. A pri- thermodynamics places on constitutive relations. In mary goal of my own work on the theory of such the second paper, the method is applied to a general materials was the attainment ofan understanding of theory of materials with gradually fading memory. the restrictions that the second law places on their IThe Sd® indicates that these papers have been cited behavior. By 1961 I felt that I knew, on the basis of in over 295 and 330 publications, respective)y.I physical reasoning, what the restrictions were, but I had no framework in which to give a mathematical justification ofmy ideas. Thermodynamics and Constitutive Relations It was not until the fall of 1962 that Noll and I for Materials with Memory found, after several false starts, the methods pre- Bernard 0. Coleman sented in the paper of 1963 cited above for deriving Department of Mechanics and Materials Science conditions necessary and sufficient for a given class Rutgers University of constitutive assumptions to be compatible with Piscataway, Nj 08855-0909 the second law. In that paper we applied the April 13, 1990 method to a class of materials for which (in contrast In the early 1950s, for graduate courses in physi- to materials with gradually fading memory) the im- cal chemistry at Yale University, I read the then plications of the second law were already consid- standard texts on thermodynamics and selections ered self-evident. In an articl& published in the next from the works of Gibbs. I recall being awed by the issue of the same journal, Victor Mizel and I gave generality of the subject; it appeared to have deep the method an equivalent but more transparent implications in every branch of macroscopic phys- form and showed that the ~‘prindpIeof equipres- 4 5 ics; but I also recall being uneasy about the com- ence” that ’ had proposed as a pleteness or clarity (I was not sure which) of its guide for the formulation of constitutive assump- principles. About five years later, after discussions tions can be implemented when thermodynamical with Walter Noll, I recognized the source of my variables and principles are taken into account. uneasiness. If one truly understood the principles of Once the method was in hand, I believed I could thermodynamics, one should be able to give precise present a convincing justification of what I felt was mathematical procedures for finding not just condi- the complete set of thermodynamical restrictions tions for the stability of equilibrium, but also the on constitutive relations when gradually fading restrictions that the second law of thermodynamics memory is present, but I soon realized that I had to imposes on the equations (called “constitutive rela- learn more functional analysis before I could pre- tions”) that characterize the type of material under sent arguments that met the current standards of consideration, and such procedures were not avail- mathematical rigor. Another year had to pass before able. Of particular interest to me were constitutive the second paper cited above could be written. As relations that express the tensor as a function with the paper of 1963, shortly after the paper of of the history (i.e., of both the present and past 1964 went to press, a way was found to clarify its values) of the strain and temperature. principal concepts and extend its6 condusions, and I In the years 1958-1961, I worked with Noll on soon sent off a follow-up paper for the same vol- several problems in the theory ofviscoelastic mate- ume ofthe journal. The formalism ofthat follow-up rials, or, more generally, materials with gradually paper is that employed in nearly all subsequent t fading memory. One of our early joint papers on applications of the theory presented in the 1964 such materials was the subject of a commentary for paper.

I. Coleman B 0 & NoU W. An approximation theorem for functionals. with applications in . Arch. Ration. Mcch. Anul. 6:355-70, 1960. (Cited 350 times.) ISee also: Coleman B U. Citation Class,c. Current Contents/Engineering, Technology & Applied Sciences and CC/Physical,Chemical & Earth Sciences 13 January 1986. p. 16.) 2. - Foundations of linear . Rev. Mod. Phyt. 33:239-49, 1961. (Cited 310 times.) 3. Coleman B 0 & Mizel V J. Thermodynamics and departures from Fourier’s law of heat conduction. Arch. Ratton. Mech. Anal. 13:245-61, 1963. Cited 55 limes.) 4. Truesdefi C. A new definition of a . 11. The Maxwellian fluid. J, Math. Pure AppI. 30:111-55, 1951. 5. Truesdell C & Toupin It A. The classical field theories. (Fltgge S.ed.) Encyclopedia of physics. Berlin, FkG: Springer. 1960. Vol. Ill/I. p. 703-4. 6. Coleman B D, On thermodynamics, strain impulses, and viscoelasticity. Arch. Ration, Mech. Anal. 17:230.54, 1964. (Cited 150 times.)

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