Abstract
We retrace the evolution in the construction of thermodynamic models of the mechanics of materials and choose the whole complex of thermodynamic ordered pairs as a basic parameter distinguishing various models. We state that the evolution of the models proceeded from the classical model of elastic bodies to the Pidstryhach model of diffusionally elastic bodies and later to the Bedford–Drumheller model of multiphase mixtures.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
A. A. Abduganiev, Development of a Microstructure Theory of Porous Media Saturated with Liquid and Analysis of Wave Propagation [in Russian], Author's Abstract of Candidate's Thesis (Physics and Mathematics), Kiev (1991).
A. I. Lur'e, Nonlinear Theory of Elasticity [in Russian], Nauka, Moscow (1980).
A. N. Guz' (ed.), Mechanics of Composites [in Russian], Naukova Dumka, Kiev (1993–1999).
Ya. S. Pidstryhach, ”Diffusion theory of inelasticity of metals, ” Zh. Prikl. Mekh. Tekh. Fiz., No. 5, 67–72 (1965).
Ya. S. Pidstryhach and Yu. Z. Povstenko, Introduction to the Mechanics of Surface Phenomena in Deformable Solids [in Russian], Naukova Dumka, Kiev (1985).
Ya. S. Pidstryhach and R. N. Shvets, ”A quasistatic problem of bound thermoelasticity, ” Prikl. Mekh., 5, No. 1, 43–51 (1969).
Ya. S. Pidstryhach and P. R. Shevchuk, “Variational form of the equations of the theory of thermodiffusion processes in a deformable solid, ” Prikl. Mat. Mekh., 33, No. 4, 774–777 (1969).
K. A. Putilov, Thermodynamics [in Russian], Nauka, Moscow (1971).
Ya. Ya. Rushchyts'kyi and A. A. Abduganiev, ”A new class of linearized problems depending on the parameters of the initial state, ” Prikl. Mekh., 30, No. 4, 9–16 (1994).
Ya. Ya. Rushchyts'kyi and S. I. Tsurpal, Waves in Materials with Microstructure [in Ukrainian], Timoshenko Institute of Mechanics, Kiev (1998).
A. Bedford and D. S. Drumheller, “Theories of immiscible and structured mixtures, ” Int. J. Eng. Sci., 21, No. 8, 863–960 (1983).
L. J. Broutman and R. H. Krock (editors), Composite Materials, Academic Press, New York (1974).
S. C. Cowin and M. A. Goodman, “A variational principle for granular materials, ” Z. Angew. Math. Mech., 56, 281–286 (1976).
M. A. Goodman and S. C. Cowin, “A continuum theory for granular materials, ” Arch. Ration. Mech. Anal., 44, 249–266 (1972).
G. A. Maugin, Continuum Mechanics of Electromagnetic Solids, North-Holland, Amsterdam (1988).
W. Nowacki, Elasticity Theory, PWN, Warsaw (1970).
J. J. Rushchitsky, “Interaction of elastic waves in an isotropic multiphase material, ” J. Theor. Appl. Mech. (Bulg. Acad. Sci.), No. 3–4, 82–93 (1994–1995).
J. J. Rushchitsky, “Interaction of waves in solid mixtures, ” Appl. Mech. Rev., 51, No. 12, 651–690 (1998).
C. Truesdell, A First Course in Rational Continuum Mechanics, John Hopkins Univ., Baltimore (1972).
C. Truesdell and W. Noll, “The nonlinear field theories of mechanics, ” in: S. Flügge (ed.), Encyclopedia of Physics, Vol. III/3, Springer, Berlin (1965), pp. 1–602.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rushchyts'kyi, Y.Y. Nontraditional Ordered Pairs of Thermodynamic Parameters: From the Pidstryhach Theory of Diffusion Elasticity to the Bedford–Drumheller Theory of Mixtures. Journal of Mathematical Sciences 104, 1538–1541 (2001). https://doi.org/10.1023/A:1011391821132
Issue Date:
DOI: https://doi.org/10.1023/A:1011391821132