The constitutive equations (constitutive relations) differentiate between particular materials and complement the system of balance equations to determine the behavior of a body. On a general level the constitutive equations have been introduced in Sect. 4.1; this part is devoted to the constitutive equations of elastic materials with heat conduction and viscosity. Special cases are the Navier—Stokes—Fourier fluids, Kelvin—Voigt solids, thermoelastic materials, and ideal dissipationless “adiabatic materials” (in which the viscosity and heat conduction are absent). In the presence of heat conduction and viscosity, Carathéodory’s approach to thermodynamics is not applicable as the mechanical power and the rate of heating are not expressible as differential forms in the “external parameters”. Historically, it was this class of materials to which the “nonequilibrium” thermodynamics was first applied, and Sect. 12.2 is devoted to a brief discussion of this approach.
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