An equation of state is a thermodynamic expression that relates the core variables of a substance: pressure ( ), volume ( ), and temperature (
Developed specifically for high-pressure, high-strain-rate regimes. The SG model assumes that the shear modulus and yield strength increase with pressure (due to lattice compression) and decrease with temperature (thermal softening), dropping to zero at the melting point.
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Understanding the EOS and strength of Earth-abundant minerals is vital for decoding seismic data and planetary evolution.
As computational power grows, tabular EOS libraries (LEOS, SESAME, PANDA) will increasingly be replaced by physics-informed neural network interfaces that return consistent ( P, T, \sigma_Y, G ) for any strain, strain-rate, temperature path. Until then, researchers must choose from the validated set of coupled models described here, ensuring that for each selected material, the coupling fidelity matches the application’s pressure and strain-rate regime.
$$P = P_H + \Gamma \rho (E - E_H)$$
Models material compression at a constant temperature. Common formulations include the Birch-Murnaghan equation (based on finite strain theory) and the Vinet equation (highly accurate for severe compression of solids).
). Under extreme conditions, two types of EOS are primarily used:
$$Y(P, E) = Y_0 f(\epsilon) (1 + \alpha P) (1 - \beta E)$$
Evaluating the materials bridges the gap between fundamental thermodynamic principles and practical engineering. Whether utilizing the static crushing power of diamond anvils, the violent energy of laser-driven shock waves, or the predictive accuracy of quantum simulations, mapping these properties provides the raw data needed to push the boundaries of human technology into the most extreme environments in the universe.
) phase at roughly 13 GPa. Knowing the high-pressure, high-temperature EOS of
Velocity Interferometer System for Any Reflector (VISAR) and Photonic Doppler Velocimetry (PDV) measure the free-surface velocity of a shocked sample with sub-nanosecond precision. Sudden changes in particle velocity reveal phase transitions and yielding behavior.