On the thermodynamics of viscoelastic materials of single-integral type
Authors:
Morton E. Gurtin and William J. Hrusa
Journal:
Quart. Appl. Math. 49 (1991), 67-85
MSC:
Primary 73B30; Secondary 73F15, 73F99
DOI:
https://doi.org/10.1090/qam/1096233
MathSciNet review:
MR1096233
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Additional Information
- Deborah Brandon and William J. Hrusa, Construction of a class of integral models for heat flow in materials with memory, J. Integral Equations Appl. 1 (1988), no. 2, 175–201. MR 978740, DOI https://doi.org/10.1216/JIE-1988-1-2-175
- Bernard D. Coleman, Thermodynamics of materials with memory, Arch. Rational Mech. Anal. 17 (1964), 1–46. MR 171419, DOI https://doi.org/10.1007/BF00283864
- Bernard D. Coleman, On thermodynamics, strain impulses, and viscoelasticity, Arch. Rational Mech. Anal. 17 (1964), 230–254. MR 171420, DOI https://doi.org/10.1007/BF00282439
- William Alan Day, The thermodynamics of simple materials with fading memory, Springer-Verlag, New York-Heidelberg, 1972. Springer Tracts in Natural Philosophy, Vol. 22. MR 0366234
- Morton E. Gurtin, An introduction to continuum mechanics, Mathematics in Science and Engineering, vol. 158, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR 636255
- M. E. Gurtin and I. Herrera, On dissipation inequalities and linear viscoelasticity, Quart. Appl. Math. 23 (1965), 235–245. MR 189346, DOI https://doi.org/10.1090/S0033-569X-1965-0189346-9
- Morton E. Gurtin and William J. Hrusa, On energies for nonlinear viscoelastic materials of single-integral type, Quart. Appl. Math. 46 (1988), no. 2, 381–392. MR 950610, DOI https://doi.org/10.1090/S0033-569X-1988-0950610-9
- Carlos B. Navarro, Asymptotic stability in linear thermoviscoelasticity, J. Math. Anal. Appl. 65 (1978), no. 2, 399–431. MR 502613, DOI https://doi.org/10.1016/0022-247X%2878%2990191-9
- Michael Renardy, William J. Hrusa, and John A. Nohel, Mathematical problems in viscoelasticity, Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 35, Longman Scientific & Technical, Harlow; John Wiley & Sons, Inc., New York, 1987. MR 919738
L. S. Shu and E. T. Onat, On anisotropic linear viscoelastic solids, Proc. 4th Symp. Naval Structural Mech., Purdue University, April 1965. Reprinted in: Mechanics and Chemistry of Solid Propellants, Pergamon, New York-Oxford, 1966
- C. Truesdell and W. Noll, The non-linear field theories of mechanics, Handbuch der Physik, Band III/3, Springer-Verlag, Berlin, 1965, pp. 1–602. MR 0193816
D. Brandon and W. J. Hrusa, Construction of a class of integral models for heat flow in materials with memory, J. Integral Equations Appl. 1, 175–201 (1988)
B. D. Coleman, Thermodynamics of materials with memory, Arch. Rational Mech. Anal. 17, 1–46 (1964)
B. D. Coleman, On thermodynamics, strain impulses, and viscoelasticity, Arch. Rational Mech. Anal. 17, 230–254 (1964)
W. A. Day, The Thermodynamics of Simple Materials with Fading Memory, Springer, 1972
M. E. Gurtin, An Introduction to Continuum Mechanics, Academic Press, 1981
M. E. Gurtin and I. Herrera, On dissipation inequalities and linear viscoelasticity, Quart. Appl. Math. 23, 235–245 (1965)
M. E. Gurtin and W. J. Hrusa, On energies for nonlinear viscoelastic materials of single-integral type, Quart. Appl. Math. 46, 381–392 (1988)
C. B. Navarro, Asymptotic stability in linear thermoviscoelasticity, J. Math. Anal. Appl. 65, 399–431 (1978)
M. Renardy, W. J. Hrusa, and J. A. Nohel, Mathematical Problems in Viscoelasticity, Longman Scientific and Technical, Essex, England, and John Wiley, New York, 1987
L. S. Shu and E. T. Onat, On anisotropic linear viscoelastic solids, Proc. 4th Symp. Naval Structural Mech., Purdue University, April 1965. Reprinted in: Mechanics and Chemistry of Solid Propellants, Pergamon, New York-Oxford, 1966
C. Truesdell and W. Noll, The Non-linear Field Theories of Mechanics, Handbuch der Physik Vol. III/3 (S. Flugge, ed.), Springer, 1965
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Article copyright:
© Copyright 1991
American Mathematical Society