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On the structure of the rate equations of materials with internal variables. (English) Zbl 0279.73002


MSC:

74A15 Thermodynamics in solid mechanics
74A99 Generalities, axiomatics, foundations of continuum mechanics of solids
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[1] Kestin, J., andJ. R. Rice: Paradoxes in the application of thermodynamics to strained solids, in: A Critical Review of Thermodynamics (Stuart, E. B. et al., eds.), pp. 275-298. Baltimore: Mono Book Corp. 1970.
[2] Coleman, B. D.: Thermodynamics of materials with memory. Arch. Rat. Mech. Anal.17, 1-46 (1964).
[3] Volterra, V.: Theory of Functionals. New York: Dover. 1959. · Zbl 0086.10402
[4] Ziegler, H.: An attempt to generalise Onsager’s principle, and its significance for rheological problems. Z. Angew. Math. Phys.9b, 748-763 (1958). · Zbl 0081.40002 · doi:10.1007/BF02424793
[5] Schapery, R. A.: Application of thermodynamics to thermomechanical fracture and birefringent phenomena in viscoelastic media. J. Appl. Phys.35, 1451-1465 (1964). · doi:10.1063/1.1713649
[6] Valanis, K. C.: Thermodynamics of large viscoelastic deformations. J. Math. Phys.45, 197-212 (1966). · Zbl 0146.21503
[7] Coleman, B. D., andM. E. Gurtin: Thermodynamics with internal state variables. J. Chemical Phys.47, 597-613 (1967). · doi:10.1063/1.1711937
[8] Valanis, K. C.: Entropy, fading memory and Onsager’s relations. J. Math. Phys.46, 164-174 (1967). · Zbl 0173.52704
[9] Lubliner, J.: On fading memory in materials of evolutionary type. Acta Mech.8, 75-81 (1969). · Zbl 0175.23701 · doi:10.1007/BF01178535
[10] Lubliner, J.: On the thermodynamic foundations of non-linear solid mechanics. Int. J. Non-Lin. Mech.7, 237-254 (1972). · Zbl 0265.73005 · doi:10.1016/0020-7462(72)90048-0
[11] Green, M. S., andA. V. Tobolsky: A new approach to the theory of relaxing polymeric media. J. Chemical Phys.14, 80-92 (1946). · doi:10.1063/1.1724109
[12] Schapery, R. A.: Further development of a thermodynamic constitutive theory: stress formulation. Report AA & ES 69-2, Purdue University, Lafayette, Ind., 1969.
[13] Truesdell, C., andW. Noll: The Non-Linear Field Theories of Mechanics, in: Handbuch der Physik (Flügge, S., ed.), Vol. III/3. Berlin-Heidelberg-New York: Springer. 1965. · Zbl 0779.73004
[14] Prigogine, I.: Introduction to Thermodynamics of Irreversible Processes, 3rd ed., p. 93. New York: Interscience. 1967. · Zbl 0115.23101
[15] Bogy, D. B., andP. M. Naghdi: On heat conduction and wave propagation in rigid solids. J. Mathematical Phys.11, 917-923 (1970). · Zbl 0189.10402 · doi:10.1063/1.1665228
[16] Perzyna, P.: The constitutive equations for rate-sensitive plastic materials. Q. Appl. Math.20, 321-332 (1963). · Zbl 0112.17204
[17] Perzyna, P.: On thermodynamic foundations of viscoplasticity, in: Mechanical Behavior of Materials under Dynamic Loads (Lindholm, U. S., ed.), pp. 61-76. New York: Springer 1968.
[18] Green, A. E., andP. M. Naghdi: A general theory of an elastic-plastic continuum. Arch. Rat. Mech. Anal.18, 251-281 (1965). · Zbl 0133.17701 · doi:10.1007/BF00251666
[19] Eisenberg, M. A., andA. Phillips: A theory of plasticity with non-coincident yield and loading surfaces. Acta Mech.11, 247-260 (1971). · Zbl 0225.73030 · doi:10.1007/BF01176559
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