Operational Equations of State. 2. The Generalized Courant-Friedrichs Equation of State for Condensed Matter

Report No. ARL-TR-5745
Authors: M. A. Grinfeld
Date/Pages: September 2011; 18 pages
Abstract: The equation of state (EOS) with separable internal energy played a big role in the analysis of dynamics of condensed matter and development of the mathematical basis of the shock-wave physics (Courant, R.; Friedrichs, K. O. Supersonic Flow and Shock Waves; Interscience: New York, 1948). For such models, the internal energy density E , as a function of the specific volume V and entropy density S, can be presented as E(V,S)(V)+X(S), where functions Δ(V) and X(S) should be determined from experiment. We call this model the Courant-Friedrichs (CF) EOS. We suggest a generalized Courant-Friedrichs (gCF) EOS based on three functional degrees of freedom. It includes the CF EOS as a special case. The additional degree of freedom allows us to consider additional physical phenomena. We discuss the interrelations between the newly introduced gCF EOS and several classical EOS, including the incomplete Mie-Gr√ľneisen EOS and its complete extensions. We also discuss how the three functions can be recovered from experimental data.
Distribution: Approved for public release
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Last Update / Reviewed: September 1, 2011