A consistent thermodynamical model of incompressible media as limit case of quasi-thermal-incompressible materials

In this paper we extend the conditions on quasi-thermal-incompressible materials presented in Gouin et al. (2011) [1] so that they satisfy all the principles of thermodynamics, including the stability condition associated with the concavity of the chemical potential. We analyze the approximations under which a quasi-thermal-incompressible medium can be considered as incompressible. We find that the pressure cannot exceed a very large critical value and that the compressibility factor must be greater than a lower limit that is very small. The analysis is first done for the case of fluids and then extended to the case of thermoelastic solids.