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A mathematical foundation for thermodynamics. (English) Zbl 0306.73004

MSC:
74A15 Thermodynamics in solid mechanics
74A20 Theory of constitutive functions in solid mechanics
74A99 Generalities, axiomatics, foundations of continuum mechanics of solids
74D99 Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)
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[1] 1911 [1] Duhem, P., Traité d’Énergétique ou de Thermodynamique Générale. Paris: Gauthier-Villars.
[2] 1943 [1] Udeschini, P., Sull’energia di deformazione. Rend. Ist. Lombardo (3) 76, 25–34.
[3] 1952 [1] Truesdell, C., The mechanical foundations of elasticity and fluid dynamics. J. Rational Mech. Anal. 1, 125–300. · Zbl 0046.17306
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[6] 1960 [1] Coleman, B. D., & W. Noll, An approximation theorem for functional, with applications in continuum mechanics. Arch. Rational Mech. Anal. 6, 355–370. · Zbl 0097.16403
[7] 1960 [2] Truesdell, C., & R. Toupin, The Classical Field Theories. In: Encyclopedia of Physics, Vol. III/1, 226–793, edited by S. Flügge. Berlin-Göttingen-Heidelberg: Springer.
[8] 1961 [1] Coleman, B. D., & W. Noll, Foundations of linear viscoelasticity. Rev. Mod. Phys. 33, · Zbl 0103.40804
[9] 1961 [2] Truesdell, C., General and exact theory of waves in finite elastic strain. Arch. Rational Mech. Anal. 8, 263–296. · Zbl 0111.37703
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[11] 1962 [2] Coleman, B. D., & W. Noll, Simple fluids with fading memory. Proc. Intl. Sympos. Second-order Effects, Haifa, pp. 530–552.
[12] 1963 [1] Coleman, B. D., & V. J. Mizel, Thermodynamics and departures from Fourier’s law of heat conduction. Arch. Rational Mech. Anal. 13, 245–261. · Zbl 0114.44905
[13] 1963 [2] Coleman, B. D., & W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity. Arch. Rational Mech. Anal. 13, 167–178. · Zbl 0113.17802
[14] 1964 [1] Coleman, B. D., Thermodynamics of materials with memory. Arch. Rational Mech. Anal. 17, 1–46.
[15] 1964 [2] Coleman, B. D., On thermodynamics, strain impulses, and viscoelasticity. Arch. Rational Mech. Anal. 17, 230–254. · Zbl 0125.13603
[16] 1964 [3] Coleman, B. D., & V. J. Mizel, Existence of caloric equations of state in thermodynamics. J. Chem. Phys. 40, 1116–1125.
[17] 1965 [1] Coleman, B. D., & M. E. Gurtin, Waves in materials with memory. III. Thermodynamic influences on the growth and decay of acceleration waves. Arch. Rational Mech. Anal. 19, 266 · Zbl 0244.73018
[18] 1965 [2] Coleman, B. D., & M. E. Gurtin, Waves in materials with memory. IV. Thermodynamics and the velocity of general acceleration waves. Arch. Rational Mech. Anal. 19, 317–338. · Zbl 0244.73019
[19] 1966 [1] Coleman, B. D., & M. E. Gurtin, Thermodynamics and one-dimensional shock waves in materials with memory. Proc. Roy. Soc. (London) A 292, 562–574.
[20] 1966 [2] Coleman, B. D., & V. J. Mizel, Norms and semi-groups in the theory of fading memory. Arch. Rational Mech. Anal. 23, 87–123. · Zbl 0146.46104
[21] 1967 [1] Coleman, B. D., & M. E. Gurtin, Thermodynamics with internal state variables. J. Chem. Phys. 47, 597–613.
[22] 1967 [2] Coleman, B. D., & V. J. Mizel, A general theory of dissipation in materials with memory. Arch. Rational Mech. Anal. 27, 255–274.
[23] 1968 [1] Coleman, B. D., & E. H. Dill, On the stability of certain motions of incompressible materials with memory. Arch. Rational Mech. Anal. 30, 197–224. · Zbl 0167.54203
[24] 1968 [2] Coleman, B. D., & V. J. Mizel, On the general theory of fading memory. Arch. Rational Mech. Anal. 29, 18–31. · Zbl 0167.24704
[25] 1968 [3] Day, W. A., Thermodynamics based on a work axiom. Arch. Rational Mech. Anal. 31, 1–34. · Zbl 0188.58901
[26] 1968 [4] Owen, D. R., Thermodynamics of materials with elastic range. Arch. Rational Mech. Anal. 31, 91–112. · Zbl 0169.28003
[27] 1969 [1] Day, W. A., A theory of thermodynamics for materials with memory. Arch. Rational Mech. Anal. 34, 85–96. · Zbl 0214.52405
[28] 1970 [1] Coleman, B. D., On the stability of equilibrium states of general fluids. Arch. Rational Mech. Anal. 36, 1–32. · Zbl 0211.28802
[29] 1970 [2] Coleman, B. D., & D. R. Owen, On the thermodynamics of materials with memory. Arch. Rational Mech. Anal. 36, 245–269. · Zbl 0197.23402
[30] 1972 [1] Day, W. A., The Thermodynamics of Simple Materials with Fading Memory. Springer Tracts in Natural Philosophy, Vol. 22. Berlin-Heidelberg-New York: Springer. · Zbl 0295.73007
[31] 1972 [2] Noll, W., A new mathematical theory of simple materials. Arch. Rational Mech. Anal. 48, 1–50. · Zbl 0271.73006
[32] 1972 [3] Willems, J. C., Dissipative dynamical systems. Part I. General Theory. Arch. Rational Mech. Anal. 45, 321–351. · Zbl 0252.93002
[33] 1973 [1] Coleman, B. D., & E. H. Dill, On thermodynamics and the stability of motions of materials with memory. Arch. Rational Mech. Anal. 51, 1–53. · Zbl 0275.73003
[34] 1974 [1] Coleman, B. D., & D. R. Owen, The initial value problem for a class of functional-differential equations. Arch. Rational Mech. Anal., in press. · Zbl 0293.34094
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