Shock and rarefaction waves in a hyperbolic model of incompressible materials

The aim of the present paper is to investigate shock and rarefaction waves in a hyperbolic model of incompressible materials. To this aim, we use the so-called extended quasi-thermal-incompressible (EQTI) model, recently proposed by Gouin & Ruggeri (H. Gouin, T. Ruggeri, Internat. J. Non-Linear Mech. 47 688–693 (2012)). In particular, we use as constitutive equation a variant of the well-known Bousinnesq approximation in which the specific volume depends not only on the temperature but also on the pressure. The limit case of ideal incompressibility, namely when the thermal expansion coefficient and the compressibility factor vanish, is also considered.