A note on Onsager’s relations. (English) Zbl 0809.73014

Šilhavý, M.

Q. Appl. Math. 52, No. 3, 469-479 (1994).

Summary: A nonlinear viscoelastic material with the heat flux obeying a generalization of Cattaneo’s law is considered. It is shown that for slow processes with small gradients of temperature the exact constitutive equations can be approximated by those of a linear viscous material with Fourier heat conduction. As a consequence of the thermodynamic restrictions on the original constitutive equations, the approximate constitutive equations are shown to satisfy the principle of local equilibrium for energy and entropy, and the kinetic coefficients giving the viscous stress and heat flux vector satisfy Onsager’s relations.

MSC:

74A15	Thermodynamics in solid mechanics
74A20	Theory of constitutive functions in solid mechanics
80A20	Heat and mass transfer, heat flow (MSC2010)

Keywords:

nonlinear viscoelastic material; generalization of Cattaneo’s law; Fourier heat conduction; thermodynamic restrictions; principle of local equilibrium for energy and entropy; kinetic coefficients