Motivated by Rivlin's ideas on the thermomechanics of continuous media, we state the second law of thermodynamics in two parts and apply it to study the behavior of a mixture of an elastic solid and a viscous fluid.
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References
1.
[1] Green, A. E. and Naghdi, P. M.: A dynamical theory of interacting continua. Int. J. Eng. Sci., 3, 231-241 (1965).
2.
[2] Green, A. E. and Naghdi, P. M.: A theory of mixtures. Arch. Rat. Mech. Anal., 24, 243-263 (1967).
3.
[3] Green, A. E. and Naghdi, P. M.: On basic equations of mixtures. Quart. J. Mech. Appl. Math., 22, 427-438 (1969).
4.
[4] Muller, I.: A thermodynamic theory of mixtures of fluids. Arch. Rat. Mech. Anal., 28, 1-39 (1968).
5.
[5] Dunwoody, N. T.: A thermomechanical theory of diffusion in solid-fluid mixtures. Arch. Rat. Mech. Anal., 38, 348-371 (1970).
6.
[6] Atkin, R. J. and Craine, R. E.: Continuum theories of mixtures. Basic theory and historical development. Quart. J. Mech. Appl. Math., 29, 209-244 (1976).
7.
[7] Atkin, R. J. and Craine, R. E.: Continuum theories of mixtures: Applications. J. Inst. Math. Appl., 17, 153-207 (1976).
8.
[8] Bowen, R. M.: Theory of mixtures, in Continuum Physics, Vol. 3, pp. 1-127, ed., A. C. Eringen, Academic Press, New York, 1976.
9.
[9] Green, A. E. and Naghdi, P. M.: On thermodynamics and the nature of the second law for mixtures of interacting continua. Quart. J. Mech. Appl. Math., 31, 265-293 (1978).
10.
[10] Rivlin, R. S.: Comments on some recent researches in thermodynamics. Recent Advances in Engineering Science, 8, 1-23 (1973).
11.
[11] Rivlin, R. S.: The thermomechanics of materials with fading memory, in Theoretical Rheology, pp. 83-103, eds., J. F. Hutton, J.R.A. Pearson, and K. Walters, Academic Science Publishers, New York, 1975.
12.
[12] Rivlin, R. S.: Reflections on certain aspects of thermomechanics, Meeting on "Finite Thermoelasticity", Rome, May 30 - June 1, 1986, pp. 11-43.
13.
[13] Casey, J.: On elastic-thermo-plastic material at finite deformations. Int. J. Plasticity: forthcoming.
14.
[14] Casey, J. and Krishnaswamy, S.: On constrained thermoelastic materials, in Contemporary Research in the Mathematics and Mechanics of Solids, pp. 359-371, eds., R. C. Bartra and M. F. Beatty in Contributi del Centro Linceo Interdisciplinare di scienze Matematiche e loro applicazioni, No. 76-CIMNE, Barcelona, 1996.
15.
[15] Crochet, M. J. and Naghdi, P. M.: On constitutive equations for flow of fluid through an elastic solid. Int. J. Eng. Sci., 4, 383-401 (1966).
16.
[16] Rajagopal, K. R. and Tao, L.: Mechanics of Mixtures, World Scientific Publishing, Singapore, 1995.