A consistent thermodynamical model of incompressible media as limit case   of quasi-thermal-incompressible materials
  In this paper we consider the conditions on quasi-thermal-incompressible 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. 
Henri Gouin (M2P2), Tommaso Ruggeri (CIRAM)
physics.class-ph