Chapter 10: Shock-Wave and Finite-Strain Equations of State at Large Expansion

The empirically observed linear relationship between shock-wave velocity and particle velocity is compatible with the Eulerian finite-strain equation of state under tension as well as compression, identifying an ideal value of dynamic strength −P_H = K_0S/(K_0S’ + 1) and dynamic cohesive energy E_H − E₀ = 8V₀K_0S/(K_0S’ + 1)² (V, K and K’ are volume, bulk modulus and its pressure derivative; subscripts 0, S and H refer to zero-pressure, isentrope and Hugoniot states). The corresponding finitestrain estimate of the isentropic cohesive energy is E_S − E₀ = 9V₀K_0S(2 + 2n − K_0S’)/(2n³), with strain parameter n = 2 for the Eulerian (spatial) frame of reference.