Reduced Hugoniots

Abstract

Complex variable methods are used to make a further exploration of the consequences of a quadratic fit to shock wave data in the velocity plane on the form of the Hugoniot. When complex pressures and compressions are introduced, the Hugoniot has three branch points. One of them is a critical point of multiplicity two and defines the separation between two branches of the Hugoniot. The other two are complex conjugates and their positions depend on a parameter involving the three coefficients of the quadratic fit. Reduced Hugoniots are defined for each material introducing reduced coordinates referred to the pressure and relative compression at the critical point; the form of these curves depends only on the parameter that determines the positions of the conjugate branch points. It is suggested that this parameter might probably be interpreted as a new property of all materials in solid and liquid phases. Polyurethane, cesium, water, and corundum are used as examples to show the agreement with experimental data. Some experiments are needed to test the validity of results at pressures higher than those available in the literature.