A three-phase equation of state for shock-induced phase transitions in tin

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.