Al'tshuler et al. approximation

This is an approximation of shock wave velocity - particle velocity dependences for shock Hugoniots of metals with normal density. In general it is given by:

D = a₀ + a₁U + a₂U², up to 3 parts,

where D - the shock wave velocity, U - particle velocity, a₀, a₁, a₂ - the coefficients. The approximations are constructed for more than 50 metals. The authors performed a very thorough statistical analysis of experimental data and found several types of shock Hugoniots:

1. a₂ = 0, a₁ > 0 (linear type);
2. a₀, a₁ > 0, a₂ < 0 (parabolic type);
3. a₀, a₁ > 0, a₂ > 0 (parabolic type);
4. The dependence consists of 2 parts: lower (linear type) and upper (linear or parabolic type);
5. The dependence consists of 3 parts: lower (linear type), middle (constant) and upper (linear or parabolic type).

Full reference: L. V. Al'tshuler, A. A. Bakanova, I. P. Dudoladov, E. A. Dynin, R. F. Trunin, B. S. Chekin, Shock adiabats for metals. New data, statistical analysis and general regularities, Zh. Prikl. Mekh. Tekhn. Fiz. 2, 3-34 (1981) [in Russian] (J. Appl. Mech. Techn. Phys. 22, 145 (1981))