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Literature Cited
Goldberg and Lianis, “Behavior of a viscoelastic medium subjected to small sinusoidal vibrations superposed on a finite strain,” Trans. ASME, Appl. Mech. [Russian translation],35, No. 3, 1–9 (1968).
A. N. Guz', Stability of Elastic Solids under Finite Strains [in Russian], Naukova Dumka, Kiev (1973).
A. A. Il'yushin and B. E. Pobedrya, Principles of the Mathematical. Theory of Tehrmoviscoelasticity [in Russian], Nauka, Moscow (1970).
A. D. Kovalenko and V. G. Karnaukhov, “Linearized theory of thermoviscoelasticity,” Mekh. Polim., No. 2, 214–221 (1972).
R. Christensen, Theory of Viscoelasticity, Academic Press, New York (1970).
B. D. Coleman and W. Noll, “Foundations of linear viscoelasticity,” Rev. Mod. Phys.,33, No. 2, 239–249 (1961).
M. J. Crochet and P. M. Naghdi, “A class of simple solids with memory,” Int. J. Eng. Sci.,7, No. 12, 1173–1198 (1969).
M. J. Crochet and P. M. Naghdi, “On ‘thermo-rheologically simple’ solids,’ in: Thermo-inelasticity, Proc. IUTAM Symp., Springer Wien - New York (1970), pp. 59–86.
J. N. Flavin and A. E. Green, “Plane thermo-elastic waves in an initially stressed medium,” J. Mech. Phys. Solids9, 179–190 (1961).
J. N. Flavin and A. E. Green, “Thermo-elastic Rayleigh waves in a prestressed medium, Proc. Cambridge Philos. Soc., Math. Phys. Sci.,58, Pt. 3, 532–538 (1962).
M. E. Gurtin, “Variational principles for linear elastodynamics,” Arch. Rat. Mech. Anal.,16, No. 1, 34–50 (1964).
M. A. Hayes and R. S. Rivlin, “Propagation of sinusoidal small-amplitude waves in a deformed viscoelastic solid. I,” J. Acoust. Soc. Am.,46, No. 3 (Pt. 2), 610–616 (1969).
M. A. Hayes and R. S. Rivlin, “Propagation of sinusoidal small-amplitude waves in a deformed viscoelastic solid. II,” J. Acoust. Soc. Am.,51, No. 5 (Pt. 2), 1652–1663 (1972).
Hsiu-Lin Yuan and G. Lianis, “Experimental investigation of wave propagation in nonlinear viscoelastic materials,” Rheol. Acta,13, No. 1, 40–48 (1974).
A. F. Johnson, “Small-amplitude vibration in prestrained viscoelastic solids,” in: Mechanics Viscoelastic Media and bodies, Berlin (1975), pp. 58–73.
G. Lianis, “Small deformations superposed on an initial large deformation in viscoelastic bodies,” in: Proc. Fourth. Intern. Congress on Rheology, Pt. 2, Interscience, New York (1965), pp. 109–119.
F. J. Lockett, Nonlinear Viscoelastic Solids, Academic Press, London-New York (1972).
J. W. Nunziato E. K. Walsh, K. W. Schuler, and L. M. Barker, “Wave propagation in nonlinear viscoelastic solids,” in: Handbuch der Physik, Vol. III/4 (S. Flugge, ed.), Springer, Berlin-Heidelberg-New York (1974), pp. 1–108.
A. C. Pipkin and R. S. Rivlin, “Small deformation superposed on large deformations in materials with fading memory,” Arch. Rat. Mech. Anat.,8, 297–308 (1961).
A. C. Pipkin, “Small finite deformation of viscoelastic solids,” Rev. Mod. Phys.,36, No. 4, 1034–1041 (1964).
M. H. Sadd and B. Bernstein, “Small deformation on large deformations on BKZ viscoelastic liquids,” Int. J. Eng. Sci.,12, No. 3, 205–220 (1974).
Additional information
Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 13, No. 11, pp. 3–12, November, 1977.
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Karnaukhov, V.G. Fundamental relationships of the theory of small viscoelastic strains imposed on finite strains for thermorheological materials. Soviet Applied Mechanics 13, 1079–1085 (1977). https://doi.org/10.1007/BF00941528
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DOI: https://doi.org/10.1007/BF00941528