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

Henri Gouin (1) , Tommaso Ruggeri (2)

1 IUSTI - Institut universitaire des systèmes thermiques industriels
2 CIRAM - Department of Mathematics and Research Center of Applied Mathematics

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.

Mots clés: Incompressible fluids and solids; Entropy principle; Chemical potential concavity

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]; Thermique [physics.class-ph]; Thermique [physics.class-ph]; Matériaux et structures en mécanique [physics.class-ph]; Matériaux et structures en mécanique [physics.class-ph]

Henri Gouin, Tommaso Ruggeri. A consistent thermodynamical model of incompressible media as limit case of quasi-thermal-incompressible materials. International Journal of Non-Linear Mechanics, 2012, 47, pp.688-693. ⟨10.1016/j.ijnonlinmec.2011.11.005⟩. ⟨hal-00700797⟩