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We present a model of metallic plastic flow suitable for numerical simulations of explosive loading and high velocity impacts. The dependence of the plastic strain rate on applied stress at low strain rates is of the Arrhenius form but with an activation energy that is singular at zero stress so that the deformation rate vanishes in that limit. Work hardening is modeled as a generalized Voce law. At strain rates exceeding 10 9 s Ϫ1 , work hardening is neglected, and the rate dependence of the flow stress is calculated using Wallace's theory of overdriven shocks in metals ͓D.C. Wallace, Phys. Rev. B 24, 5597 ͑1981͒; 24, 5607 ͑1981͔͒. The thermal-activation regime is continuously merged into the strong shock limit, yielding a model applicable over the 15 decades in strain rate from 10 Ϫ3 to 10 12 s Ϫ1. The model represents all aspects of constitutive behavior seen in Hopkinson bar and low-rate data, including a rapid increase in the constant-strain rate sensitivity, with 10% accuracy. High-pressure behavior is controlled by the shear modulus, G(,T), and the melting temperature, T m

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The phase-space region occupied by a dense fluid is characterized by significant multiparticle correlations, and by small density fluctuations. On the basis of this characterization, a statistical-mechanical formula is constructed, to represent the entropy of an equilibrium dense fluid. For the example of fluid sodium, the statistical entropy agrees well with the measured thermodynamic entropy.

The shock-induced ␣͑bcc͒→͑hcp͒ transition in iron begins at 13 GPa on the Hugoniot. In the two-phase region above 13 GPa, the Hugoniot lies well above the equilibrium surface defined by G ␣ ϭG , with G the Gibbs free energy. Also, the phase transition relaxation time is uncertain, with estimates ranging from Ͻ50 ns to Ϸ180 ns. Here we present an extensive study of these important aspects, metastability and dynamics, of the ␣transition in iron. Our primary theoretical tools are ͑a͒ accurate theoretically based free energies for ␣ and phases of iron and ͑b͒ accurate calculations of the wave evolution following planar impacts. We define metastable surfaces for forward and reverse transitions by the condition that the thermodynamic driving force G ␣ ϪG is just balanced by an opposing force resulting from elastic stresses, and we calibrate the forward surface from the Hugoniot and the reverse surface from the phase interface reflection feature of shock profiles. These metastable surfaces, corresponding to ␣↔ transitions proceeding at a rate of tens of nanoseconds, are in remarkable agreement with quasistatic diamond cell measurements. When the relaxation time is calibrated from the rise time of the P2 wave, our calculated wave profiles are in good agreement with VISAR data. The overall comparison of theory and experiment indicates that ͑a͒ depends on shock strength and is approximately 60→12 ns for shocks of 17→30 GPa, and ͑b͒ while expresses linear irreversible-thermodynamic relaxation, some nonlinear relaxation must also be present in the shock process in iron.