Abstract
This chapter contains an outline of the phenomenological theory of flow and deformation as a consequence of the conservation laws and the principles of non-equilibrium thermodynamics. We exploit the concept of internal thermodynamic variables that describe the deviation of a state of the system from equilibrium. This concept has a long history beginning with the pioneering work of Mandelstam and Leontovich (Zh. Exper. Theor. Fiziki 7:438–449, 1937) and has appeared to be useful in description of a deformable viscoelastic continuum (Coleman and Gurtin in J. Chem. Phys. 47:597–613, 1967; Pokrovskii in Polym. Mech. 6(5):693–702, 1970; Wood in The thermodynamics of fluid systems (Calendron, Oxford), 1975; Maugin in Thermomechanics of nonlinear irreversible processes (World Scientific, Singapore), 1999). The purpose of the chapter is to show how relaxation processes are included in the phenomenological theory of flow. The principles of the formulation of the phenomenological theory of viscoelasticity for any real materials are clear. In this sense, one can postulate a general phenomenological theory of viscoelasticity, which includes all known particular cases, among them those constitutive equations that are formulated on the basis of macromolecular dynamics in the previous and in the subsequent chapters. Principles of the theory, which allows classify the various phenomenological constitutive equations proposed for a viscoelastic medium, are discussed but no attempt is made to review available constitutive equations.
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References
Coleman BD, Gurtin ME (1967) Thermodynamics with internal state variables. J Chem Phys 47:597–613
Maugin GA (1999) Thermomechanics of nonlinear irreversible processes. World Scientific, Singapore
Mandelstam LI, Leontovich MA (1937) To the theory of the second sound. Zh Exper Theor Fiziki 7:438–449 (in Russian)
Pokrovskii VN (1970) Equations of motion of viscoelastic systems as derived from the conservation laws and the phenomenological theory of non-equilibrium processes. Polym Mech 6(5):693–702
Wood LC (1975) The thermodynamics of fluid systems. Clarendon, Oxford
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Pokrovskii, V.N. (2010). Relaxation Processes in the Phenomenological Theory. In: The Mesoscopic Theory of Polymer Dynamics. Springer Series in Chemical Physics, vol 95. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2231-8_8
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DOI: https://doi.org/10.1007/978-90-481-2231-8_8
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