Abstract
This paper addresses the construction of an equation of state considering three phases of tin for shock-induced phase transitions. First we present general results on such an equation of state which ensure the existence and uniqueness of the problem of maximization on the mixture entropy. Next, a multiphase equation of state under strict thermodynamic equilibrium is obtained using a combination of tabulation and Newton-Raphson iterations. Using this equation of state calibrated with standard static and dynamic experimental data, negative values of the fundamental derivative appear in the (β/γ) mixture zone. A major consequence is the occurrence of composite waves for shock-induced (β → γ) phase transition. We construct the five self-similar reference solutions, using Hugoniot relations and Riemann invariants. Finally, numerical simulations are provided, illustrating these self-similar regimes of the (β → γ) phase transition at thermodynamic equilibrium for increasing piston velocities.