Shock wave equation of state and finite strain theory

The linear shock‐velocity ( U s ), particle‐velocity ( u p ) relation, which is known to be exceptionally successful in describing a wide variety of Hugoniot equation of state measurements, is shown to be virtually indistinguishable from the Birch‐Murnaghan (third‐order Eulerian finite strain) equation of state. For typical values of zero‐pressure parameters, specifically for the pressure derivative of the adiabatic bulk modulus K ′ 0S ≃ 3 to 6, the Grüneisen parameter γ 0 ≃ 1.5 (±1.0), and the logarithmic volume derivative of the Grüneisen parameter q ≃ 1.0 (±1.0), the Eulerian finite strain formulation yields the appropriate compressional moduli at infinitesimal strains, and it closely reproduces the Hugoniot at large compressions when compared with the linear U s ‐ u p relation. Thus shock wave measurements provide strong empirical support for the success of the Eulerian finite strain equation of state in describing the compression of condensed matter to high pressures.