Equation for the Shock Adiabat

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Abstract
The main difficulty in using a linear relationship to fit the experimental data on shock and particle velocities is the fact that the Hugoniot pressure tends to infinity as the relative compression tends to a maximum whose value depends on the material. It is shown in this paper that this difficulty is overcome by the use of a quadratic fit, since this leads to an expression free from infinity points for the Hugoniot as a function of volume. It is demonstrated, by the introduction of complex variable methods, that in the quadratic approximation the shock adiabat is a two branch function, with the branch point located precisely at the infinity point resulting from the linear approximation. Series expansions of the Hugoniot suggest the introduction of a quasilinear approximation as a limiting case. Numerical results obtained using the quadratic approximation for iron and cadmium are in very good agreement with the experimental data. The point of highest pressure reported for cadmium confirms the existence of the two branches for the Hugoniot.